## Monday, January 11, 2021

### Middle/H.S. Math

Middle School Math

A. Whole numbers

1 Place values in whole numbers

2 Writing numbers in words: convert words to digits

3 Writing numbers in words: convert digits to words

4 Spell word names for numbers up to one million

5 Roman numerals

6 Add and subtract whole numbers

7 Add and subtract whole numbers: word problems

B. Multiplication

1 Multiply whole numbers

2 Multiply whole numbers: word problems

3 Multiply whole numbers with four or more digits

4 Multiply numbers ending in zeroes

5 Multiply numbers ending in zeroes: word problems

6 Multiply three or more numbers

7 Multiply three or more numbers: word problems

8 Estimate products

C. Division

1 Divisibility rules

2 Division patterns with zeroes

3 Divide numbers ending in zeroes: word problems

4 Estimate quotients

5 Divide whole numbers - 2-digit divisors

6 Divide whole numbers - 3-digit divisors

D. Exponents

1 Write multiplication expressions using exponents

2 Evaluate exponents

3 Write powers of ten with exponents

4 Find the missing exponent or base

5 Exponents with decimal bases

6 Exponents with fractional bases

E. Number theory

1 Convert between standard and scientific notation

2 Compare numbers written in scientific notation

3 Prime or composite

4 Identify factors

5 Find all the factor pairs of a number

6 Prime factorization

7 Prime factorization with exponents

8 Greatest common factor

9 Greatest common factor of three or four numbers

10 Least common multiple

11 Least common multiple of three or four numbers

12 GCF and LCM: word problems

13 Sort factors of numerical expressions

14 Classify numbers

F. Decimals

1 What decimal number is illustrated?

2 Decimal place values

3 Word names for decimal numbers

4 Put decimal numbers in order

5 Inequalities with decimals

6 Round decimals

7 Round whole numbers and decimals: find the missing digit

8 Decimal number lines

9 Repeating decimals

1 Add and subtract decimal numbers

2 Add and subtract decimals: word problems

New! Complete the decimal addition or subtraction sentence

3 Estimate sums and differences of decimals

4 Maps with decimal distances

H. Multiply and divide decimals

1 Estimate products of decimal numbers

2 Multiply decimals

3 Inequalities with decimal multiplication

4 Divide decimals by whole numbers

5 Divide decimals by whole numbers: word problems

6 Multiply and divide decimals by powers of ten

7 Division with decimal quotients

8 Inequalities with decimal division

9 Multiply and divide decimals: word problems

I. Fractions and mixed numbers

1 Fractions on number lines

2 Understanding fractions: word problems

3 Equivalent fractions review

4 Write fractions in lowest terms

5 Least common denominator

6 Compare fractions with like and unlike denominators

7 Compare fractions: word problems

8 Convert between improper fractions and mixed numbers

9 Convert fractions to decimals

10 Convert decimals to fractions

11 Convert between decimals and fractions

12 Convert between decimals and mixed numbers

13 Put a mix of decimals and fractions in order

14 Put a mix of decimals, fractions, and mixed numbers in order

15 Understand fractions as division: word problems

1 Add and subtract fractions with like denominators

2 Add and subtract fractions with like denominators: word problems

3 Add and subtract fractions with unlike denominators

4 Add and subtract fractions with unlike denominators: word problems

5 Inequalities with addition and subtraction of like and unlike fractions

6 Add and subtract mixed numbers

7 Add and subtract mixed numbers: word problems

8 Estimate sums and differences of mixed numbers

9 Maps with fractional distances

K. Multiply fractions

1 Fractions of whole numbers I

2 Fractions of whole numbers II

3 Fractions of a number: word problems

4 Estimate products of fractions and whole numbers

5 Multiply two fractions using models

6 Multiply two fractions

7 Multiply fractions: word problems

9 Scaling by fractions and mixed numbers

10 Multiply three or more fractions and whole numbers

11 Estimate products of mixed numbers

12 Multiply mixed numbers and whole numbers

13 Multiply mixed numbers

14 Multiply mixed numbers: word problems

15 Multiply three or more mixed numbers, fractions, and/or whole numbers

L. Divide fractions

1 Divide whole numbers by unit fractions using models

2 Reciprocals

3 Divide whole numbers and unit fractions

4 Divide fractions by whole numbers in recipes

5 Divide fractions

6 Estimate quotients when dividing mixed numbers

7 Divide fractions and mixed numbers

8 Divide fractions and mixed numbers: word problems

M. Integers

1 Understanding integers

2 Integers on number lines

3 Graph integers on horizontal and vertical number lines

4 Understanding opposite integers

5 Understanding absolute value

6 Absolute value

7 Compare integers

8 Put integers in order

9 Integer inequalities with absolute values

10 Absolute value and integers: word problems

N. Operations with integers

2 Add integers using number lines

4 Subtract integers using counters

5 Subtract integers using number lines

6 Subtract integers

7 Add and subtract integers: find the sign

8 Add and subtract integers: word problems

9 Add and subtract integers: input/output tables

10 Add three or more integers

11 Multiply integers: find the sign

12 Multiply integers

13 Divide integers: find the sign

14 Divide integers

O. Mixed operations

1 Add, subtract, multiply, or divide two whole numbers

2 Add, subtract, multiply, or divide two whole numbers: word problems

3 Evaluate numerical expressions involving whole numbers

4 Identify mistakes involving the order of operations

5 Add, subtract, multiply, or divide two decimals

6 Add, subtract, multiply, or divide two decimals: word problems

7 Evaluate numerical expressions involving decimals

8 Add, subtract, multiply, or divide two fractions

9 Add, subtract, multiply, or divide two fractions: word problems

10 Evaluate numerical expressions involving fractions

11 Add, subtract, multiply, or divide two integers

12 Evaluate numerical expressions involving integers

P. Rational numbers

1 Rational numbers on number lines

2 Rational numbers: equal or not equal

3 Compare and order rational numbers using number lines

4 Compare rational numbers

5 Put rational numbers in order

6 Compare and order rational numbers: word problems

7 Opposites of rational numbers

8 Absolute value of rational numbers

9 Add and subtract rational numbers

10 Multiply and divide rational numbers

11 Rational numbers: find the sign

Q. Problem solving and estimation

1 Estimate to solve word problems

2 Multi-step word problems

3 Multi-step word problems: identify reasonable answers

4 Word problems with extra or missing information

5 Guess-and-check word problems

6 Distance/direction to starting point

7 Use logical reasoning to find the order

R. Ratios and rates

1 Write a ratio

2 Write a ratio using a fraction

3 Write a ratio: word problems

4 Which model represents the ratio?

5 Identify equivalent ratios

6 Write an equivalent ratio

7 Ratio tables

8 Equivalent ratios: word problems

9 Unit rates

10 Equivalent rates

11 Ratios and rates: complete a table and make a graph

12 Use tape diagrams to solve ratio word problems

13 Compare ratios: word problems

14 Compare rates: word problems

15 Ratios and rates: word problems

16 Do the ratios form a proportion?

17 Solve the proportion

18 Identify proportional relationships from graphs

19 Identify proportional relationships from tables

20 Identify proportional relationships by graphing

21 Interpret graphs of proportional relationships

22 Scale drawings: word problems

S. Percents

1 What percentage is illustrated?

2 Understanding percents: strip models

3 Convert fractions to percents using grid models

4 Convert between percents, fractions, and decimals

5 Convert between percents, fractions, and decimals: word problems

6 Compare percents to each other and to fractions

7 Compare percents and fractions: word problems

8 Solve percent problems using grid models

9 Solve percent problems using strip models

10 Percents of numbers and money amounts

11 Percents of numbers: word problems

12 Percents of numbers: fractional and decimal percents

13 Find what percent one number is of another

14 Find what percent one number is of another: word problems

15 Find the total given a part and a percent

16 Solve percent problems

17 Solve percent word problems

T. Units of measurement

1 Estimate customary measurements

2 Estimate metric measurements

3 Convert and compare customary units

4 Convert, compare, add, and subtract mixed customary units

5 Multiply and divide mixed customary units

6 Customary unit conversions involving fractions and mixed numbers

7 Convert and compare metric units

8 Convert between customary and metric systems

9 Compare temperatures above and below zero

10 Convert between Celsius and Fahrenheit

U. Money

1 Find the number of each type of coin

2 Add and subtract money amounts

3 Add and subtract money amounts: word problems

4 Multiply money by whole numbers and decimals

5 Multiply money: word problems

6 Divide money amounts

7 Divide money amounts: word problems

V. Consumer math

1 Which is the better coupon?

2 Unit prices

3 Unit prices with fractions and decimals

4 Unit prices with customary unit conversions

5 Sale prices

6 Sale prices: find the original price

7 Percents - calculate tax, tip, mark-up, and more

8 Simple interest

W. Time

1 Elapsed time

2 Time units

3 Find start and end times

X. Coordinate plane

1 Objects on a coordinate plane

2 Graph points on a coordinate plane

New! Reflect a point over an axis

4 Coordinate planes as maps

5 Distance between two points

6 Follow directions on a coordinate plane

7 Area and perimeter of squares and rectangles on the coordinate plane

Y. Expressions and properties

1 Write variable expressions: one operation

2 Write variable expressions: two operations

3 Write variable expressions: word problems

4 Evaluate variable expressions with whole numbers

5 Evaluate multi-variable expressions

6 Evaluate variable expressions with decimals, fractions, and mixed numbers

7 Evaluate variable expressions: word problems

8 Identify terms and coefficients

9 Sort factors of variable expressions

10 Identify equivalent expressions using strip models

12 Properties of multiplication

13 Multiply using the distributive property

14 Factor using the distributive property

15 Solve for a variable using properties of multiplication

16 Write equivalent expressions using properties

17 Add and subtract like terms

18 Identify equivalent expressions I

19 Identify equivalent expressions II

Z. One-variable equations

1 Does x satisfy an equation?

2 Which x satisfies an equation?

3 Write an equation from words

4 Identify expressions and equations

5 Model and solve equations using algebra tiles

6 Write and solve equations that represent diagrams

7 Solve one-step addition and subtraction equations with whole numbers

8 Solve one-step multiplication and division equations with whole numbers

9 Solve one-step equations with whole numbers

10 Solve one-step addition and subtraction equations with decimals, fractions, and mixed numbers

11 Solve one-step multiplication and division equations with decimals, fractions, and whole numbers

12 Solve one-step addition and subtraction equations: word problems

13 Solve one-step multiplication and division equations: word problems

14 Write a one-step equation: word problems

15 Solve one-step equations: word problems

16 Which word problem matches the one-step equation?

17 Solve one-step equations involving integers

18 Solve equations involving like terms

19 Solve two-step equations

AA. One-variable inequalities

1 Solutions to inequalities

2 Graph inequalities on number lines

3 Write inequalities from number lines

New! Write and graph inequalities: word problems

4 Solve one-step inequalities

5 Graph solutions to one-step inequalities

6 One-step inequalities: word problems

BB. Two-variable equations

1 Does (x, y) satisfy an equation?

2 Identify independent and dependent variables in tables and graphs

3 Write an equation from a graph using a table

4 Identify independent and dependent variables: word problems

5 Find a value using two-variable equations

6 Find a value using two-variable equations: word problems

7 Solve word problems by finding two-variable equations

8 Complete a table for a two-variable relationship

9 Write a two-variable equation from a table

10 Write a two-variable equation

11 Identify the graph of an equation

12 Complete a table and graph a two-variable equation

13 Graph a two-variable equation

14 Interpret a graph: word problems

CC. Two-dimensional figures

1 Identify and classify polygons

2 Measure and classify angles

3 Estimate angle measurements

4 Classify triangles

5 Triangle inequality

6 Identify trapezoids

9 Find missing angles in triangles

10 Find missing angles in special triangles

11 Find missing angles in quadrilaterals

12 Sums of angles in polygons

13 Lines, line segments, and rays

14 Name angles

15 Complementary and supplementary angles

16 Identify complementary, supplementary, vertical, adjacent, and congruent angles

17 Find measures of complementary, supplementary, vertical, and adjacent angles

DD. Symmetry and transformations

1 Line symmetry

2 Rotational symmetry

3 Rotational symmetry: amount of rotation

4 Reflection, rotation, and translation

5 Similar and congruent figures

6 Find side lengths of similar figures

EE. Three-dimensional figures

1 Identify polyhedra

2 Which figure is being described?

3 Nets of three-dimensional figures

4 Front, side, and top view

FF. Geometric measurement

1 Perimeter

2 Area of rectangles and squares

3 Understanding area of a parallelogram

4 Area of parallelograms

5 Understanding area of a triangle

6 Area of triangles

7 Understanding area of a trapezoid

8 Area of trapezoids

9 Area of rhombuses

11 Area of compound figures

12 Area of compound figures with triangles

13 Area between two rectangles

14 Area between two triangles

15 Rectangles: relationship between perimeter and area

16 Compare area and perimeter of two figures

17 Area of quadrilaterals and triangles: word problems

18 Volume of cubes and rectangular prisms

19 Volume of cubes and rectangular prisms with fractional side lengths

20 Volume of cubes and rectangular prisms: word problems

21 Surface area of cubes and rectangular prisms

22 Volume of triangular prisms

23 Surface area of triangular prisms

24 Surface area of pyramids

25 Relate volume and surface area

GG. Data and graphs

1 Interpret pictographs

2 Create pictographs

3 Interpret line plots

4 Create line plots

5 Create and interpret line plots with fractions

6 Create frequency charts

7 Interpret categorical data

8 Create relative frequency tables

9 Interpret bar graphs

10 Create bar graphs

11 Create percent bar graphs

12 Interpret double bar graphs

13 Create double bar graphs

14 Interpret histograms

15 Create histograms

16 Interpret circle graphs

17 Interpret line graphs

18 Create line graphs

19 Interpret double line graphs

20 Create double line graphs

21 Interpret stem-and-leaf plots

22 Create stem-and-leaf plots

23 Box plots

HH. Statistics

1 Identify statistical questions

2 Calculate mean, median, mode, and range

3 Interpret charts and graphs to find mean, median, mode, and range

4 Mean, median, mode, and range: find the missing number

5 Changes in mean, median, mode, and range

6 Calculate mean absolute deviation

7 Calculate quartiles and interquartile range

8 Identify an outlier

9 Identify an outlier and describe the effect of removing it

10 Describe distributions in line plots

11 Identify representative, random, and biased samples

II. Probability

1 Counting principle

2 Probability of one event

3 Make predictions

4 Probability of simple events and opposite events

JJ. Financial literacy

1 Compare checking accounts

2 Check registers

3 Debit cards and credit cards

4 Credit reports

5 Paying for college

6 Occupations, education, and income

A. Number theory

1 Prime or composite

2 Prime factorization

3 Multiplicative inverses

4 Divisibility rules

5 Greatest common factor

6 Least common multiple

7 GCF and LCM: word problems

8 Sort factors of numerical expressions

9 Scientific notation

10 Compare numbers written in scientific notation

11 Classify numbers

12 Factorials

B. Integers

1 Understanding integers

2 Integers on number lines

3 Graph integers on horizontal and vertical number lines

4 Absolute value and opposite integers

5 Quantities that combine to zero: word problems

6 Compare and order integers

7 Integer inequalities with absolute values

C. Operations with integers

3 Add integers using number lines

5 Add three or more integers

6 Integer subtraction rules

7 Subtract integers using counters

8 Subtract integers using number lines

9 Subtract integers

10 Integer addition and subtraction rules

11 Add and subtract integers using counters

13 Complete addition and subtraction equations with integers

14 Add and subtract integers: word problems

15 Integer multiplication rules

16 Multiply integers

17 Integer division rules

18 Equal quotients of integers

19 Divide integers

20 Integer multiplication and division rules

21 Multiply and divide integers

22 Complete multiplication and division equations with integers

23 Add, subtract, multiply, and divide integers

24 Evaluate numerical expressions involving integers

D. Decimals

1 Decimal numbers review

2 Compare and order decimals

3 Decimal number lines

4 Round decimals

E. Operations with decimals

2 Add and subtract decimals: word problems

3 Multiply decimals

4 Multiply decimals and whole numbers: word problems

5 Divide decimals

6 Divide decimals by whole numbers: word problems

7 Estimate sums, differences, and products of decimals

8 Add, subtract, multiply, and divide decimals: word problems

9 Multi-step inequalities with decimals

10 Maps with decimal distances

11 Evaluate numerical expressions involving decimals

F. Fractions and mixed numbers

1 Understanding fractions: word problems

2 Equivalent fractions

3 Write fractions in lowest terms

4 Fractions: word problems with graphs and tables

5 Least common denominator

6 Compare and order fractions

7 Compare fractions: word problems

8 Convert between mixed numbers and improper fractions

9 Compare mixed numbers and improper fractions

10 Round mixed numbers

G. Operations with fractions

2 Add and subtract fractions: word problems

3 Add and subtract mixed numbers

4 Add and subtract mixed numbers: word problems

5 Inequalities with addition and subtraction of fractions and mixed numbers

6 Estimate sums and differences of mixed numbers

7 Multiply fractions and whole numbers

8 Multiply two fractions using models

9 Multiply fractions

10 Multiply mixed numbers

11 Multiply fractions and mixed numbers: word problems

12 Divide fractions

13 Divide mixed numbers

14 Divide fractions and mixed numbers: word problems

15 Estimate products and quotients of fractions and mixed numbers

16 Add, subtract, multiply, and divide fractions and mixed numbers: word problems

17 Maps with fractional distances

18 Evaluate numerical expressions involving fractions

H. Rational numbers

1 Convert fractions or mixed numbers to decimals

2 Convert decimals to fractions or mixed numbers

3 Convert between decimals and fractions or mixed numbers

4 Identify rational numbers

5 Classify rational numbers using a diagram

6 Absolute value of rational numbers

7 Compare rational numbers

8 Put rational numbers in order

9 Add and subtract positive and negative decimals

10 Add and subtract positive and negative fractions

11 Add and subtract rational numbers

12 Rational numbers: find the sign

13 Apply addition and subtraction rules

14 Identify quotients of rational numbers: word problems

15 Multiply and divide positive and negative decimals

16 Multiply and divide positive and negative fractions

17 Multiply and divide rational numbers

18 Apply multiplication and division rules

I. Exponents and square roots

1 Understanding exponents

2 Evaluate exponents

3 Solve equations with variable exponents

4 Exponents with negative bases

5 Exponents with decimal and fractional bases

6 Powers of ten

7 Evaluate numerical expressions involving exponents

8 Square roots of perfect squares

9 Estimate square roots

J. Ratios, rates, and proportions

1 Understanding ratios

2 Identify equivalent ratios

3 Write an equivalent ratio

4 Equivalent ratios: word problems

5 Unit rates

6 Calculate unit rates with fractions

7 Word problems involving ratios

8 Compare rates: word problems

9 Scale drawings: word problems

10 Scale drawings: scale factor word problems

11 Do the ratios form a proportion?

12 Do the ratios form a proportion: word problems

13 Solve proportions

14 Solve proportions: word problems

15 Estimate population size using proportions

16 Rate of change: tables

17 Rate of change: graphs

18 Constant rate of change

K. Proportional relationships

1 Find the constant of proportionality from a table

2 Write equations for proportional relationships from tables

3 Identify proportional relationships by graphing

4 Find the constant of proportionality from a graph

5 Write equations for proportional relationships from graphs

6 Identify proportional relationships from graphs and equations

7 Identify proportional relationships from tables

8 Complete a table and graph a proportional relationship

9 Graph a proportional relationship using slope

10 Interpret graphs of proportional relationships

11 Write and solve equations for proportional relationships

L. Percent

1 What percentage is illustrated?

2 Convert between percents, fractions, and decimals

3 Compare percents to fractions and decimals

4 Estimate percents of numbers

New! Solve percent problems using strip models

5 Percent of numbers and money amounts

6 Percent of numbers: word problems

7 Solve percent equations

8 Solve percent equations: word problems

9 Percent of change

10 Percent of change: word problems

11 Percent of change: find the original amount word problems

M. Consumer math

1 Add, subtract, multiply, and divide money amounts: word problems

2 Price lists

3 Unit prices

4 Unit prices with unit conversions

5 Unit prices: find the total price

6 Percent of a number: tax, discount, and more

7 Which is the better coupon?

8 Find the percent: tax, discount, and more

9 Sale prices: find the original price

10 Multi-step problems with percents

11 Estimate tips

12 Simple interest

13 Compound interest

N. Problem solving and estimation

1 Estimate to solve word problems

2 Multi-step word problems

3 Multi-step word problems: identify reasonable answers

4 Guess-and-check word problems

5 Use Venn diagrams to solve problems

6 Find the number of each type of coin

7 Elapsed time word problems

O. Units of measurement

1 Estimate customary measurements

2 Estimate metric measurements

3 Compare and convert customary units

4 Mixed customary units

5 Compare and convert metric units

6 Convert between customary and metric systems

7 Precision

8 Celsius and Fahrenheit temperatures

P. Coordinate plane

1 Coordinate plane review

3 Follow directions on a coordinate plane

4 Distance between two points

Q. Number sequences

1 Identify arithmetic and geometric sequences

2 Arithmetic sequences

3 Geometric sequences

4 Number sequences: mixed review

5 Number sequences: word problems

6 Evaluate variable expressions for number sequences

7 Write variable expressions for arithmetic sequences

R. Expressions and properties

1 Write variable expressions: one operation

2 Write variable expressions: two or three operations

3 Write variable expressions: word problems

4 Evaluate linear expressions

5 Evaluate multi-variable expressions

6 Evaluate absolute value expressions

7 Evaluate nonlinear expressions

8 Identify terms and coefficients

9 Sort factors of variable expressions

10 Properties of addition and multiplication

11 Multiply using the distributive property

12 Solve equations using properties

13 Write equivalent expressions using properties

14 Add and subtract linear expressions

15 Add and subtract like terms: with exponents

16 Factors of linear expressions

17 Identify equivalent linear expressions using algebra tiles

18 Identify equivalent linear expressions I

19 Identify equivalent linear expressions II

20 Identify equivalent linear expressions: word problems

S. One-variable equations

1 Which x satisfies an equation?

2 Write an equation from words

3 Model and solve equations using algebra tiles

4 Write and solve equations that represent diagrams

5 Solve one-step equations

6 Solve two-step equations

7 Solve equations: word problems

8 Solve equations involving like terms

9 Solve equations: complete the solution

T. One-variable inequalities

1 Solutions to inequalities

2 Graph inequalities on number lines

3 Write inequalities from number lines

4 Solve one-step inequalities

5 Graph solutions to one-step inequalities

6 One-step inequalities: word problems

7 Solve two-step inequalities

8 Graph solutions to two-step inequalities

U. Two-variable equations

1 Does (x, y) satisfy the equation?

2 Identify independent and dependent variables

3 Find a value using two-variable equations

4 Solve word problems involving two-variable equations

5 Complete a table for a two-variable relationship

6 Write a two-variable equation

7 Identify the graph of an equation

8 Graph a two-variable equation

9 Interpret a graph: word problems

10 Write an equation from a graph using a table

V. Linear functions

1 Find the slope from a graph

2 Find the slope from two points

3 Find a missing coordinate using slope

4 Find the slope from an equation

5 Graph a line using slope

6 Write a linear function

7 Identify linear and nonlinear functions

W. Two-dimensional figures

1 Identify and classify polygons

2 Name, measure, and classify angles

3 Classify triangles

4 Triangle inequality

5 Identify trapezoids

9 Find missing angles in triangles

10 Find missing angles in triangles using ratios

11 Find missing angles in quadrilaterals I

12 Find missing angles in quadrilaterals II

13 Interior angles of polygons

14 Lines, line segments, and rays

15 Parallel, perpendicular, and intersecting lines

16 Identify complementary, supplementary, vertical, and adjacent angles

17 Find measures of complementary, supplementary, vertical, and adjacent angles

18 Identify alternate interior and alternate exterior angles

19 Transversals of parallel lines: name angle pairs

20 Transversals of parallel lines: find angle measures

21 Find lengths and measures of bisected line segments and angles

22 Parts of a circle

23 Central angles of circles

X. Transformations and congruence

1 Line symmetry

2 Rotational symmetry

3 Rotational symmetry: amount of rotation

4 Identify reflections, rotations, and translations

5 Combinations of reflections, rotations, and translations

6 Translations: graph the image

7 Translations: find the coordinates

8 Reflections over the x- and y-axes: graph the image

9 Reflections over the x- and y-axes: find the coordinates

10 Reflections: graph the image

11 Reflections: find the coordinates

12 Rotations: graph the image

13 Rotations: find the coordinates

14 Similar and congruent figures

15 Congruence statements and corresponding parts

16 Side lengths and angle measures of congruent figures

17 Side lengths and angle measures of similar figures

18 Similar figures and indirect measurement

Y. Pythagorean theorem

1 Pythagorean theorem: find the length of the hypotenuse

2 Pythagorean theorem: find the missing leg length

3 Pythagorean theorem: word problems

4 Converse of the Pythagorean theorem: is it a right triangle?

Z. Three-dimensional figures

1 Bases of three-dimensional figures

2 Nets of three-dimensional figures

3 Front, side, and top view

4 Cross sections of three-dimensional figures

AA. Geometric measurement

1 Perimeter

2 Area of rectangles and parallelograms

3 Area of triangles and trapezoids

4 Area and perimeter: word problems

5 Area of circles

6 Circumference of circles

7 Circles: word problems

8 Volume of cubes and prisms

9 Volume of cubes and rectangular prisms: word problems

10 Volume of pyramids

11 Volume of cylinders

12 Surface area of cubes and prisms

13 Surface area of pyramids

14 Surface area of cylinders

15 Perimeter and area: changes in scale

16 Semicircles: calculate area, perimeter, radius, and diameter

17 Quarter circles: calculate area, perimeter, and radius

18 Area of compound figures with triangles

19 Area of compound figures with triangles, semicircles, and quarter circles

20 Area between two shapes

BB. Data and graphs

1 Interpret tables

2 Interpret line plots

3 Create line plots

4 Create and interpret line plots with fractions

5 Interpret stem-and-leaf plots

6 Create stem-and-leaf plots

7 Interpret bar graphs

8 Create bar graphs

9 Interpret histograms

10 Create histograms

11 Create frequency charts

12 Interpret circle graphs

13 Circle graphs and central angles

14 Interpret line graphs

15 Create line graphs

16 Box plots

17 Identify trends with scatter plots

18 Make predictions with scatter plots

CC. Statistics

1 Calculate mean, median, mode, and range

2 Interpret charts and graphs to find mean, median, mode, and range

3 Mean, median, mode, and range: find the missing number

4 Changes in mean, median, mode, and range

5 Calculate mean absolute deviation

6 Calculate quartiles and interquartile range

7 Identify an outlier

8 Identify representative, random, and biased samples

DD. Probability

1 Probability of simple events

2 Probability of simple events and opposite events

3 Probability of mutually exclusive events and overlapping events

4 Experimental probability

5 Make predictions using experimental probability

6 Make predictions using theoretical probability

7 Compound events: find the number of outcomes

8 Compound events: find the number of sums

9 Probability of compound events

10 Identify independent and dependent events

11 Probability of independent and dependent events

12 Find the number of outcomes: word problems

A. Number theory

1 Factors

2 Divisibility rules

3 Prime or composite

4 Prime factorization

5 Greatest common factor

6 Least common multiple

7 GCF and LCM: word problems

8 Sort factors of numerical expressions

9 Classify numbers

B. Integers

1 Integers on number lines

2 Graph integers on horizontal and vertical number lines

3 Absolute value and opposite integers

4 Compare and order integers

5 Integer inequalities with absolute values

C. Operations with integers

1 Integer addition and subtraction rules

2 Add and subtract integers using counters

4 Add and subtract three or more integers

5 Add and subtract integers: word problems

6 Integer multiplication and division rules

7 Multiply and divide integers

8 Evaluate numerical expressions involving integers

D. Rational numbers

1 Write fractions in lowest terms

2 Least common denominator

3 Round decimals and mixed numbers

New! Write a repeating decimal as a fraction

4 Convert between decimals and fractions or mixed numbers

New! Identify rational and irrational square roots

5 Identify rational and irrational numbers

6 Absolute value of rational numbers

7 Compare rational numbers

8 Put rational numbers in order

E. Operations with rational numbers

1 Reciprocals and multiplicative inverses

2 Add and subtract rational numbers

3 Add and subtract rational numbers: word problems

4 Apply addition and subtraction rules

5 Multiply and divide rational numbers

6 Multiply and divide rational numbers: word problems

7 Apply multiplication and division rules

8 Apply addition, subtraction, multiplication, and division rules

9 Evaluate numerical expressions involving rational numbers

F. Exponents and roots

1 Understanding exponents

2 Evaluate exponents

3 Solve equations with variable exponents

4 Exponents with negative bases

5 Exponents with decimal and fractional bases

6 Understanding negative exponents

7 Evaluate negative exponents

8 Multiplication with exponents

9 Division with exponents

10 Multiplication and division with exponents

11 Power rule

12 Evaluate expressions using properties of exponents

13 Identify equivalent expressions involving exponents I

14 Identify equivalent expressions involving exponents II

15 Square roots of perfect squares

16 Estimate positive square roots

17 Positive and negative square roots

18 Estimate positive and negative square roots

19 Relationship between squares and square roots

20 Solve equations using square roots

21 Cube roots of positive perfect cubes

22 Cube roots of positive and negative perfect cubes

23 Solve equations using cube roots

24 Estimate cube roots

G. Scientific notation

1 Convert between standard and scientific notation

2 Compare numbers written in scientific notation

3 Add and subtract numbers written in scientific notation

4 Multiply numbers written in scientific notation

5 Divide numbers written in scientific notation

H. Ratios, rates, and proportions

1 Understanding ratios

2 Identify equivalent ratios

3 Write an equivalent ratio

4 Equivalent ratios: word problems

5 Unit rates

6 Word problems involving ratios

7 Solve proportions: word problems

8 Do the ratios form a proportion?

9 Do the ratios form a proportion: word problems

10 Solve proportions

11 Estimate population size using proportions

12 Scale drawings: word problems

13 Scale drawings: scale factor word problems

I. Proportional relationships

1 Find the constant of proportionality from a table

2 Write equations for proportional relationships from tables

3 Identify proportional relationships by graphing

4 Find the constant of proportionality from a graph

5 Write equations for proportional relationships from graphs

6 Identify proportional relationships from graphs and equations

7 Identify proportional relationships from tables

8 Graph proportional relationships and find the slope

9 Interpret graphs of proportional relationships

10 Write and solve equations for proportional relationships

J. Percents

1 Convert between percents, fractions, and decimals

2 Compare percents to fractions and decimals

3 Find what percent one number is of another

4 Find what percent one number is of another: word problems

5 Estimate percents of numbers

6 Percents of numbers and money amounts

7 Percents of numbers: word problems

8 Compare percents of numbers

9 Solve percent equations

10 Percent of change

11 Percent of change: word problems

12 Percent of change: find the original amount word problems

K. Consumer math

1 Price lists

2 Unit prices

3 Unit prices with unit conversions

4 Unit prices: find the total price

5 Percent of a number: tax, discount, and more

6 Find the percent: tax, discount, and more

7 Sale prices: find the original price

8 Multi-step problems with percents

9 Estimate tips

10 Simple interest

11 Compound interest

L. Units of measurement

1 Convert rates and measurements: customary units

2 Convert rates and measurements: metric units

3 Mixed customary units

4 Convert between customary and metric systems

5 Precision

6 Convert between Celsius and Fahrenheit

M. Problem solving

1 Multi-step word problems

2 Guess-and-check word problems

3 Use Venn diagrams to solve problems

4 Elapsed time word problems

N. Coordinate plane

1 Coordinate plane review

3 Follow directions on a coordinate plane

4 Find the distance between two points

O. Two-dimensional figures

1 Identify and classify polygons

2 Classify triangles

3 Identify trapezoids

7 Find missing angles in triangles

8 Find missing angles in triangles using ratios

9 Triangle Angle-Sum Theorem

10 Find missing angles in quadrilaterals I

11 Find missing angles in quadrilaterals II

12 Exterior Angle Theorem

13 Interior angles of polygons

14 Identify complementary, supplementary, vertical, adjacent, and congruent angles

15 Find measures of complementary, supplementary, vertical, and adjacent angles

16 Identify alternate interior and alternate exterior angles

17 Transversals of parallel lines: name angle pairs

18 Transversals of parallel lines: find angle measures

19 Find lengths and measures of bisected line segments and angles

20 Parts of a circle

P. Transformations and congruence

1 Line symmetry

2 Rotational symmetry

3 Rotational symmetry: amount of rotation

4 Identify reflections, rotations, and translations

5 Describe a sequence of transformations

6 Translations: graph the image

7 Translations: find the coordinates

8 Translations: write the rule

9 Reflections over the x- and y-axes: graph the image

10 Reflections over the x- and y-axes: find the coordinates

11 Reflections: graph the image

12 Reflections: find the coordinates

13 Rotations: graph the image

14 Rotations: find the coordinates

15 Sequences of congruence transformations: graph the image

16 Congruence statements and corresponding parts

17 Side lengths and angle measures of congruent figures

18 Congruent triangles: SSS, SAS, and ASA

Q. Transformations and similarity

1 Similar and congruent figures

2 Dilations: graph the image

3 Dilations: find the coordinates

4 Dilations: scale factor and classification

5 Identify similar triangles

6 Side lengths and angle measures of similar triangles

7 Side lengths and angle measures of similar figures

8 Find missing side lengths in proportional triangles

R. Pythagorean theorem

1 Pythagorean theorem: find the length of the hypotenuse

2 Pythagorean theorem: find the missing leg length

3 Pythagorean theorem: find the missing leg or hypotenuse length

4 Pythagorean theorem: find the perimeter

5 Pythagorean theorem: word problems

6 Converse of the Pythagorean theorem: is it a right triangle?

S. Three-dimensional figures

1 Parts of three-dimensional figures

2 Nets of three-dimensional figures

3 Front, side, and top view

4 Base plans

5 Similar solids

T. Geometric measurement

1 Perimeter

2 Area

3 Area and perimeter: word problems

4 Area between two shapes

5 Area and circumference of circles

6 Circles: word problems

7 Area and perimeter of semicircles and quarter circles

8 Volume of cubes, prisms, and pyramids

9 Surface area of cubes, prisms, and pyramids

10 Volume of cylinders

11 Volume of cones

12 Surface area of cylinders

13 Surface area of cones

14 Volume of spheres

15 Surface area of spheres

16 Volume and surface area of similar solids

17 Perimeter and area: changes in scale

U. Number sequences

1 Identify arithmetic and geometric sequences

2 Arithmetic sequences

3 Geometric sequences

4 Number sequences: mixed review

5 Number sequences: word problems

6 Evaluate variable expressions for number sequences

7 Write variable expressions for arithmetic sequences

V. Expressions and properties

1 Write variable expressions: one operation

2 Write variable expressions: two or three operations

3 Write variable expressions from diagrams

4 Write variable expressions: word problems

5 Evaluate one-variable expressions

6 Evaluate multi-variable expressions

7 Evaluate absolute value expressions

9 Evaluate rational expressions

10 Identify terms and coefficients

11 Sort factors of variable expressions

12 Properties of addition and multiplication

13 Multiply using the distributive property

14 Write equivalent expressions using properties

15 Add and subtract like terms

16 Add and subtract linear expressions

17 Factors of linear expressions

18 Identify equivalent linear expressions I

19 Identify equivalent linear expressions II

20 Identify equivalent linear expressions: word problems

W. One-variable equations

1 Which x satisfies an equation?

2 Write an equation from words

3 Model and solve equations using algebra tiles

4 Write and solve equations that represent diagrams

5 Properties of equality

6 Identify equivalent equations

7 Solve one-step equations

8 Solve two-step equations

New! Solve equations with the distributive property

9 Solve multi-step equations

10 Solve equations involving like terms

11 Solve equations with variables on both sides

12 Solve equations: mixed review

13 Solve equations: complete the solution

14 Solve one-step and two-step equations: word problems

15 Find the number of solutions

16 Create equations with no solutions or infinitely many solutions

X. One-variable inequalities

1 Solutions to inequalities

2 Graph inequalities on number lines

3 Write inequalities from number lines

4 Solve one-step inequalities

5 Graph solutions to one-step inequalities

6 Solve two-step inequalities

7 Graph solutions to two-step inequalities

8 Solve multi-step inequalities

9 Graph solutions to multi-step inequalities

Y. Linear equations

1 Find the slope of a graph

2 Find the slope from two points

3 Find a missing coordinate using slope

4 Slope-intercept form: find the slope and y-intercept

5 Graph a line using slope

6 Graph a line from an equation in slope-intercept form

7 Graph a line from an equation in point-slope form

8 Write a linear equation from a slope and y-intercept

9 Write a linear equation from a graph

10 Write a linear equation from a slope and a point

11 Write a linear equation from two points

12 Convert a linear equation in standard form to slope-intercept form

13 Graph a line from an equation in standard form

14 Slopes of parallel and perpendicular lines

Z. Functions

1 Identify functions

2 Identify functions: graphs

3 Does (x, y) satisfy the linear function?

4 Identify independent and dependent variables

5 Rate of change: tables

6 Rate of change: graphs

7 Constant rate of change

8 Evaluate a linear function

9 Complete a table for a linear function

10 Complete a table and graph a linear function

11 Interpret points on the graph of a linear function

12 Write a linear function from a table

13 Compare linear functions: graphs and equations

14 Compare linear functions: tables, graphs, and equations

15 Write linear functions: word problems

16 Evaluate a linear function: word problems

17 Identify linear and nonlinear functions: graphs and equations

18 Identify linear and nonlinear functions: tables

19 Does (x, y) satisfy the nonlinear function?

20 Evaluate a nonlinear function

21 Find values using function graphs

22 Complete a table for a function graph

23 Domain and range of functions

AA. Systems of linear equations

1 Is (x, y) a solution to the system of equations?

2 Solve a system of equations by graphing

3 Solve a system of equations by graphing: word problems

4 Find the number of solutions to a system of equations by graphing

5 Find the number of solutions to a system of equations

6 Classify a system of equations by graphing

7 Classify a system of equations

8 Solve a system of equations using substitution

9 Solve a system of equations using substitution: word problems

10 Solve a system of equations using elimination

11 Solve a system of equations using elimination: word problems

12 Solve a system of equations using any method

13 Solve a system of equations using any method: word problems

BB. Monomials and polynomials

1 Identify monomials

2 Model polynomials with algebra tiles

3 Add and subtract polynomials using algebra tiles

5 Add polynomials to find perimeter

6 Multiply monomials

7 Divide monomials

8 Multiply and divide monomials

9 Powers of monomials

10 Square and cube roots of monomials

11 Multiply polynomials using algebra tiles

12 Multiply polynomials

13 Multiply polynomials to find area

CC. Data and graphs

1 Interpret tables

2 Interpret bar graphs

3 Create bar graphs

4 Interpret line graphs

5 Create line graphs

6 Interpret line plots

7 Create line plots

8 Create and interpret line plots with fractions

9 Interpret stem-and-leaf plots

10 Create stem-and-leaf plots

11 Interpret histograms

12 Create histograms

13 Create frequency charts

14 Box plots

15 Create scatter plots

16 Identify trends with scatter plots

17 Make predictions with scatter plots

18 Interpret circle graphs

19 Circle graphs and central angles

DD. Statistics

1 Calculate mean, median, mode, and range

2 Interpret charts and graphs to find mean, median, mode, and range

3 Mean, median, mode, and range: find the missing number

4 Changes in mean, median, mode, and range

New! Calculate mean absolute deviation

5 Calculate quartiles and interquartile range

6 Identify an outlier

7 Identify an outlier and describe the effect of removing it

8 Outliers in scatter plots

9 Scatter plots: line of best fit

10 Identify representative, random, and biased samples

EE. Probability

1 Probability of simple events

2 Probability of opposite, mutually exclusive, and overlapping events

3 Experimental probability

4 Find probabilities using two-way frequency tables

5 Make predictions

6 Compound events: find the number of outcomes

7 Compound events: find the number of sums

8 Identify independent and dependent events

9 Probability of independent and dependent events

10 Factorials

11 Permutations

12 Counting principle

13 Combination and permutation notation

High School

Algebra 1

A. Numbers

1 Compare and order rational numbers

2 Absolute value and opposites

3 Number lines

4 Convert between decimals and fractions

5 Convert between repeating decimals and fractions

6 Square roots

7 Cube roots

8 Sort rational and irrational numbers

9 Classify rational and irrational numbers

10 Properties of operations on rational and irrational numbers

11 Classify numbers

B. Operations

1 Add, subtract, multiply, and divide integers

2 Evaluate numerical expressions involving integers

3 Evaluate variable expressions involving integers

4 Add and subtract rational numbers

5 Multiply and divide rational numbers

6 Evaluate numerical expressions involving rational numbers

7 Evaluate variable expressions involving rational numbers

C. Ratios, rates, and proportions

1 Identify equivalent ratios

2 Write an equivalent ratio

3 Unit rates

4 Unit prices

5 Solve proportions

6 Solve proportions: word problems

7 Scale drawings: word problems

D. Percents

1 Convert between percents, fractions, and decimals

2 Solve percent equations

3 Percent word problems

4 Percent of change

5 Percent of change: word problems

6 Percent of change: find the original amount word problems

7 Percent of a number: tax, discount, and more

8 Find the percent: tax, discount, and more

9 Multi-step problems with percents

E. Measurement

1 Convert rates and measurements: customary units

2 Convert rates and measurements: metric units

3 Unit prices with unit conversions

4 Multi-step problems with unit conversions

5 Precision

6 Greatest possible error

7 Minimum and maximum area and volume

8 Percent error

9 Percent error: area and volume

F. Geometry

1 Perimeter

2 Area

3 Area and perimeter: word problems

4 Volume

5 Surface area

6 Similar figures: side lengths and angle measures

7 Similar triangles and indirect measurement

8 Dilations and scale factors

9 Area and perimeter of similar figures

10 Area between two shapes

11 Similar solids

12 Volume and surface area of similar solids

13 Perimeter and area: changes in scale

14 Surface area and volume: changes in scale

15 Perimeter, area, and volume: changes in scale

16 Pythagorean theorem

17 Pythagorean theorem: word problems

18 Converse of the Pythagorean theorem: is it a right triangle?

19 Special right triangles

G. Coordinate plane

1 Coordinate plane review

2 Midpoint formula: find the midpoint

3 Midpoint formula: find the endpoint

4 Distance between two points

H. Properties

1 Properties of addition and multiplication

2 Distributive property

3 Simplify variable expressions using properties

4 Properties of equality

5 Identify equivalent equations

I. Variable expressions and equations

1 Write variable expressions

2 Sort factors of variable expressions

3 Simplify variable expressions involving like terms and the distributive property

4 Identify equivalent linear expressions

5 Write variable equations

6 Does x satisfy the equation?

7 Which x satisfies an equation?

8 Solve equations using order of operations

9 Rearrange multi-variable equations

J. Solve equations

1 Model and solve equations using algebra tiles

2 Write and solve equations that represent diagrams

3 Solve one-step linear equations

4 Solve two-step linear equations

6 Solve equations with variables on both sides

7 Solve equations: complete the solution

8 Find the number of solutions

9 Create equations with no solutions or infinitely many solutions

10 Solve linear equations: word problems

11 Solve linear equations: mixed review

K. Single-variable inequalities

1 Graph inequalities

2 Write inequalities from graphs

3 Identify solutions to inequalities

4 Solve one-step linear inequalities: addition and subtraction

5 Solve one-step linear inequalities: multiplication and division

6 Solve one-step linear inequalities

7 Graph solutions to one-step linear inequalities

8 Solve two-step linear inequalities

9 Graph solutions to two-step linear inequalities

11 Graph solutions to advanced linear inequalities

12 Graph compound inequalities

13 Write compound inequalities from graphs

14 Solve compound inequalities

15 Graph solutions to compound inequalities

L. Absolute value equations and inequalities

1 Solve absolute value equations

2 Graph solutions to absolute value equations

3 Solve absolute value inequalities

4 Graph solutions to absolute value inequalities

M. Matrices

1 Matrix vocabulary

2 Matrix operation rules

4 Multiply a matrix by a scalar

5 Add and subtract scalar multiples of matrices

6 Multiply two matrices

7 Properties of matrices

N. Data and graphs

New! Interpret line plots

New! Create line plots

New! Interpret histograms

New! Create histograms

1 Interpret bar graphs, line graphs, and histograms

2 Create bar graphs, line graphs, and histograms

3 Interpret circle graphs

4 Interpret stem-and-leaf plots

5 Box plots

O. Problem solving

1 Word problems: mixed review

2 Word problems with money

3 Consecutive integer problems

4 Rate of travel: word problems

5 Weighted averages: word problems

P. Number sequences

1 Identify arithmetic and geometric sequences

2 Arithmetic sequences

3 Geometric sequences

4 Evaluate variable expressions for number sequences

5 Evaluate recursive formulas for sequences

6 Identify a sequence as explicit or recursive

7 Write variable expressions for arithmetic sequences

8 Write variable expressions for geometric sequences

9 Write a formula for a recursive sequence

10 Convert a recursive formula to an explicit formula

11 Convert an explicit formula to a recursive formula

12 Number sequences: mixed review

Q. Relations and functions

1 Relations: convert between tables, graphs, mappings, and lists of points

2 Domain and range of relations

3 Identify independent and dependent variables

4 Identify functions

5 Identify functions: vertical line test

6 Find values using function graphs

7 Evaluate a function

8 Evaluate a function: plug in an expression

10 Multiply functions

11 Find the inverse of a function

12 Complete a function table from a graph

13 Complete a function table from an equation

New! Find solutions using a table

14 Interpret the graph of a function: word problems

15 Interpret functions using everyday language

16 Rate of change: tables

17 Rate of change: graphs

R. Direct and inverse variation

1 Identify proportional relationships

2 Find the constant of variation

3 Graph a proportional relationship

4 Write direct variation equations

5 Write and solve direct variation equations

6 Identify direct variation and inverse variation

7 Write inverse variation equations

8 Write and solve inverse variation equations

S. Linear functions

1 Identify linear functions from graphs and equations

2 Identify linear functions from tables

3 Find the slope of a graph

4 Find the slope from two points

5 Find a missing coordinate using slope

6 Slope-intercept form: find the slope and y-intercept

7 Slope-intercept form: graph an equation

8 Slope-intercept form: write an equation from a graph

9 Slope-intercept form: write an equation

10 Slope-intercept form: write an equation from a table

11 Slope-intercept form: write an equation from a word problem

12 Linear equations: solve for y

13 Write linear functions: word problems

14 Complete a table and graph a linear function

15 Compare linear functions: graphs and equations

16 Compare linear functions: tables, graphs, and equations

17 Write equations in standard form

18 Standard form: find x- and y-intercepts

19 Standard form: graph an equation

20 Equations of horizontal and vertical lines

21 Graph a horizontal or vertical line

22 Point-slope form: graph an equation

23 Point-slope form: write an equation

24 Point-slope form: write an equation from a graph

25 Slopes of parallel and perpendicular lines

26 Write an equation for a parallel or perpendicular line

27 Transformations of linear functions

T. Linear inequalities

1 Does (x, y) satisfy the inequality?

2 Linear inequalities: solve for y

3 Graph a two-variable linear inequality

4 Linear inequalities: word problems

5 Is (x, y) a solution to the system of inequalities?

6 Solve systems of linear inequalities by graphing

U. Systems of linear equations

1 Is (x, y) a solution to the system of equations?

2 Solve a system of equations by graphing

3 Solve a system of equations by graphing: word problems

4 Find the number of solutions to a system of equations by graphing

5 Find the number of solutions to a system of equations

6 Classify a system of equations by graphing

7 Classify a system of equations

8 Solve a system of equations using substitution

9 Solve a system of equations using substitution: word problems

10 Solve a system of equations using elimination

11 Solve a system of equations using elimination: word problems

12 Solve a system of equations using augmented matrices

13 Solve a system of equations using augmented matrices: word problems

14 Solve a system of equations using any method

15 Solve a system of equations using any method: word problems

V. Exponents

1 Exponents with integer bases

2 Exponents with decimal and fractional bases

3 Negative exponents

4 Multiplication with exponents

5 Division with exponents

6 Multiplication and division with exponents

7 Power rule

8 Evaluate expressions using properties of exponents

9 Identify equivalent expressions involving exponents I

10 Identify equivalent expressions involving exponents II

11 Evaluate integers raised to positive rational exponents

12 Evaluate integers raised to rational exponents

13 Multiplication with rational exponents

14 Division with rational exponents

15 Power rule with rational exponents

16 Simplify expressions involving rational exponents

W. Scientific notation

1 Convert between standard and scientific notation

2 Compare numbers written in scientific notation

3 Add and subtract numbers written in scientific notation

4 Multiply numbers written in scientific notation

5 Divide numbers written in scientific notation

X. Exponential functions

1 Evaluate an exponential function

2 Match exponential functions and graphs

3 Domain and range of exponential functions: graphs

4 Domain and range of exponential functions: equations

5 Exponential growth and decay: word problems

6 Compound interest: word problems

Y. Monomials

1 Identify monomials

2 Multiply monomials

3 Divide monomials

4 Multiply and divide monomials

5 Powers of monomials

Z. Polynomials

1 Polynomial vocabulary

2 Model polynomials with algebra tiles

3 Add and subtract polynomials using algebra tiles

5 Add polynomials to find perimeter

6 Multiply a polynomial by a monomial

7 Multiply two polynomials using algebra tiles

8 Multiply two binomials

9 Multiply two binomials: special cases

10 Multiply polynomials

AA. Factoring

1 GCF of monomials

2 Factor out a monomial

3 Factor quadratics using algebra tiles

7 Factor by grouping

8 Factor polynomials

1 Characteristics of quadratic functions: graphs

2 Characteristics of quadratic functions: equations

3 Complete a function table: quadratic functions

5 Graph quadratic functions in vertex form

6 Solve a quadratic equation using square roots

7 Solve a quadratic equation using the zero product property

8 Solve a quadratic equation by factoring

9 Complete the square

10 Solve a quadratic equation by completing the square

12 Using the discriminant

New! Write a quadratic function in vertex form

13 Graph quadratic functions in standard form

14 Match quadratic functions and graphs

15 Write a quadratic function from its vertex and another point

16 Systems of linear and quadratic equations

1 Identify linear and exponential functions from graphs

2 Identify linear, quadratic, and exponential functions from graphs

3 Identify linear and exponential functions from tables

4 Identify linear, quadratic, and exponential functions from tables

New! Write linear and exponential functions

5 Write linear, quadratic, and exponential functions

6 Linear functions over unit intervals

7 Exponential functions over unit intervals

8 Describe linear and exponential growth and decay

DD. Absolute value and function families

1 Complete a function table: absolute value functions

2 Graph an absolute value function

3 Domain and range of absolute value functions: graphs

4 Domain and range of absolute value functions: equations

5 Transformations of absolute value functions

New! Function transformation rules

New! Translations of functions

New! Reflections of functions

New! Dilations of functions

New! Transformations of functions

New! Describe function transformations

2 Simplify radical expressions with variables

3 Simplify radical expressions involving fractions

6 Simplify radical expressions using the distributive property

8 Simplify radical expressions: mixed review

2 Domain and range of radical functions: graphs

3 Domain and range of radical functions: equations

GG. Rational functions and expressions

1 Rational functions: asymptotes and excluded values

2 Simplify complex fractions

3 Simplify rational expressions

4 Multiply and divide rational expressions

5 Divide polynomials by monomials

6 Divide polynomials using long division

7 Add and subtract rational expressions

New! Simplify mixed rational expressions

8 Solve rational equations

9 Evaluate rational expressions

HH. Trigonometry

1 Trigonometric ratios: sin, cos, and tan

2 Find trigonometric ratios using a calculator

3 Inverses of trigonometric functions

4 Trigonometric ratios: find a side length

5 Trigonometric ratios: find an angle measure

6 Solve a right triangle

II. Logic

1 Identify hypotheses and conclusions

2 Counterexamples

JJ. Probability

1 Theoretical probability

2 Experimental probability

3 Find probabilities using two-way frequency tables

4 Find conditional probabilities using two-way frequency tables

5 Outcomes of compound events

6 Identify independent and dependent events

7 Probability of independent and dependent events

8 Counting principle

9 Permutations

10 Permutation and combination notation

KK. Statistics

1 Identify biased samples

2 Mean, median, mode, and range

3 Calculate quartiles and interquartile range

4 Identify an outlier

5 Identify an outlier and describe the effect of removing it

6 Mean absolute deviation

7 Variance and standard deviation

8 Interpret a scatter plot

9 Outliers in scatter plots

10 Match correlation coefficients to scatter plots

11 Calculate correlation coefficients

12 Scatter plots: line of best fit

13 Find the equation of a regression line

14 Interpret regression lines

15 Analyze a regression line of a data set

Geometry

A. Algebra review

1 Ratios and proportions

2 Scale drawings: word problems

3 Properties of exponents

5 Write variable expressions

6 Solve linear equations

7 Solve linear inequalities

8 Solve systems of linear equations

9 Solve a quadratic equation by factoring

B. Points, lines, line segments, and planes

1 Lines, line segments, and rays

2 Properties of planes, lines, and points

3 Describe intersections in a plane

4 Lengths of segments on number lines

6 Midpoints

7 Congruent line segments

8 Perpendicular Bisector Theorem

9 Midpoint formula: find the midpoint

10 Midpoint formula: find the endpoint

11 Distance formula

12 Distance to the origin in three dimensions

13 Construct the midpoint or perpendicular bisector of a segment

C. Angles

1 Angle vocabulary

2 Angle measures

3 Identify complementary, supplementary, vertical, adjacent, and congruent angles

4 Find measures of complementary, supplementary, vertical, and adjacent angles

5 Angle bisectors

6 Construct an angle bisector

7 Construct a congruent angle

8 Proofs involving angles

D. Parallel and perpendicular lines

1 Identify parallel, intersecting, and skew lines and planes

2 Construct a perpendicular line

3 Transversals: name angle pairs

4 Transversals of parallel lines: find angle measures

5 Construct parallel lines

6 Proofs involving parallel lines I

7 Proofs involving parallel lines II

E. Lines in the coordinate plane

1 Coordinate plane review

2 Slopes of lines

3 Graph a linear equation

4 Equations of lines

5 Slopes of parallel and perpendicular lines

6 Equations of parallel and perpendicular lines

7 Find the distance between a point and a line

8 Find the distance between two parallel lines

F. Introduction to triangles

1 Classify triangles

2 Triangle Angle-Sum Theorem

3 Exterior Angle Theorem

4 Exterior Angle Inequality

G. Two-dimensional figures

1 Polygon vocabulary

2 Interior angles of polygons

3 Exterior angles of polygons

4 Review: interior and exterior angles of polygons

5 Construct an equilateral triangle or regular hexagon

6 Construct a square

H. Three-dimensional figures

1 Parts of three-dimensional figures

2 Three-dimensional figure vocabulary

3 Nets and drawings of three-dimensional figures

4 Cross sections of three-dimensional figures

5 Solids of revolution

I. Logic

1 Identify hypotheses and conclusions

2 Counterexamples

3 Conditionals

4 Negations

5 Converses, inverses, and contrapositives

6 Biconditionals

7 Truth tables

8 Truth values

J. Introduction to congruent figures

1 Congruence statements and corresponding parts

2 Solve problems involving corresponding parts

3 Identify congruent figures

K. Congruent triangles

1 SSS and SAS Theorems

2 Proving triangles congruent by SSS and SAS

3 ASA and AAS Theorems

4 Proving triangles congruent by ASA and AAS

5 SSS, SAS, ASA, and AAS Theorems

6 SSS Theorem in the coordinate plane

7 Proving triangles congruent by SSS, SAS, ASA, and AAS

8 Proofs involving corresponding parts of congruent triangles

9 Congruency in isosceles and equilateral triangles

10 Proofs involving isosceles triangles

11 Hypotenuse-Leg Theorem

L. Transformations

1 Classify congruence transformations

2 Translations: graph the image

3 Translations: find the coordinates

4 Translations: write the rule

5 Reflections: graph the image

6 Reflections: find the coordinates

7 Rotate polygons about a point

8 Rotations: graph the image

9 Rotations: find the coordinates

10 Sequences of congruence transformations: graph the image

11 Transformations that carry a polygon onto itself

12 Congruence transformations: mixed review

13 Dilations: graph the image

14 Dilations: find the coordinates

New! Dilations: find length, perimeter, and area

15 Dilations: scale factor and classification

New! Dilations: find the scale factor and center of the dilation

16 Dilations and parallel lines

M. Triangles

1 Midsegments of triangles

2 Triangles and bisectors

3 Identify medians, altitudes, angle bisectors, and perpendicular bisectors

4 Angle-side relationships in triangles

5 Triangle Inequality Theorem

6 Construct the circumcenter or incenter of a triangle

7 Construct the centroid or orthocenter of a triangle

8 Proofs involving triangles I

9 Proofs involving triangles II

1 Identify trapezoids

4 Find missing angles in quadrilaterals

6 Properties of parallelograms

7 Proving a quadrilateral is a parallelogram

8 Properties of rhombuses

9 Properties of squares and rectangles

10 Properties of trapezoids

11 Properties of kites

13 Proofs involving triangles and quadrilaterals

O. Symmetry

1 Line symmetry

2 Rotational symmetry

3 Draw lines of symmetry

4 Count lines of symmetry

P. Similarity

1 Similarity ratios

2 Similarity statements

3 Identify similar figures

4 Side lengths and angle measures in similar figures

5 Similar triangles and indirect measurement

6 Perimeters of similar figures

7 Similarity rules for triangles

8 Similar triangles and similarity transformations

9 Similarity of circles

10 Triangle Proportionality Theorem

11 Similarity and altitudes in right triangles

12 Areas of similar figures

13 Prove similarity statements

14 Prove proportions or angle congruences using similarity

15 Proofs involving similarity in right triangles

16 Prove the Pythagorean theorem

Q. Right triangles

1 Pythagorean theorem

2 Converse of the Pythagorean theorem

3 Pythagorean Inequality Theorems

4 Special right triangles

R. Trigonometry

1 Trigonometric ratios: sin, cos, and tan

2 Trigonometric ratios: csc, sec, and cot

3 Trigonometric ratios in similar right triangles

4 Trigonometric functions of complementary angles

5 Find trigonometric functions of special angles

6 Find trigonometric functions using a calculator

7 Inverses of trigonometric functions

8 Trigonometric ratios: find a side length

9 Trigonometric ratios: find an angle measure

10 Solve a right triangle

11 Law of Sines

12 Law of Cosines

13 Solve a triangle

14 Area of a triangle: sine formula

15 Area of a triangle: Law of Sines

S. Area and perimeter

1 Perimeter

2 Area of rectangles and squares

3 Area of parallelograms and triangles

4 Area of trapezoids

5 Area and perimeter in the coordinate plane I

6 Area and perimeter in the coordinate plane II

7 Area and circumference of circles

8 Area of compound figures

9 Area between two shapes

10 Area and perimeter of similar figures

11 Perimeter and area: changes in scale

12 Heron's formula

13 Area and perimeter mixed review

T. Surface area and volume

1 Surface area and volume of rectangular prisms

2 Surface area of prisms and cylinders

3 Surface area of pyramids and cones

4 Surface area of spheres

5 Volume of prisms and cylinders

6 Volume of pyramids and cones

7 Volume of spheres

New! Volume of compound figures

8 Similar solids: find the missing length

9 Surface area and volume of similar solids

10 Surface area and volume: changes in scale

11 Perimeter, area, and volume: changes in scale

12 Surface area and volume review

U. Circles

1 Parts of a circle

2 Central angles and arc measures

3 Arc length

4 Convert between radians and degrees

6 Area of sectors

7 Circle measurements: mixed review

8 Arcs and chords

9 Tangent lines

10 Perimeter of polygons with an inscribed circle

11 Inscribed angles

12 Angles in inscribed right triangles

13 Angles in inscribed quadrilaterals I

14 Angles in inscribed quadrilaterals II

15 Construct a tangent line to a circle

16 Construct an equilateral triangle inscribed in a circle

17 Construct a square inscribed in a circle

18 Construct a regular hexagon inscribed in a circle

19 Construct the inscribed or circumscribed circle of a triangle

V. Circles and parabolas in the coordinate plane

1 Find the center of a circle

2 Find the radius or diameter of a circle

3 Write equations of circles in standard form from graphs

4 Write equations of circles in standard form using properties

5 Convert equations of circles from general to standard form

6 Find properties of circles from equations in general form

7 Graph circles from equations in standard form

8 Graph circles from equations in general form

9 Find the vertex of a parabola

10 Find the focus or directrix of a parabola

11 Find the axis of symmetry of a parabola

12 Write equations of parabolas in vertex form from graphs

13 Write equations of parabolas in vertex form using properties

14 Convert equations of parabolas from general to vertex form

15 Find properties of a parabola from equations in general form

16 Graph parabolas

W. Measurement

1 Convert rates and measurements: customary units

2 Convert rates and measurements: metric units

3 Convert square and cubic units of length

4 Precision

5 Greatest possible error

6 Minimum and maximum area and volume

7 Percent error

8 Percent error: area and volume

9 Calculate density, mass, and volume

X. Probability

1 Theoretical and experimental probability

2 Outcomes of compound events

3 Identify independent and dependent events

4 Probability of independent and dependent events

5 Counting principle

6 Permutations

7 Permutation and combination notation

8 Find probabilities using combinations and permutations

9 Find probabilities using two-way frequency tables

10 Identify independent events

11 Find conditional probabilities

12 Independence and conditional probability

13 Find conditional probabilities using two-way frequency tables

14 Geometric probability

15 Find probabilities using the addition rule

Y. Vectors

1 Compass directions and vectors

2 Find the magnitude of a vector

3 Find the component form of a vector

4 Find the component form of a vector given its magnitude and direction angle

5 Graph a resultant vector using the triangle method

6 Graph a resultant vector using the parallelogram method

8 Subtract vectors

Algebra 2

A. Variable expressions

1 Evaluate variable expressions involving integers

2 Evaluate variable expressions involving rational numbers

3 Simplify variable expressions using properties

4 Sort factors of single-variable expressions

5 Sort factors of multi-variable expressions

B. Equations

1 Solve linear equations

2 Solve linear equations: word problems

3 Solve equations: complete the solution

4 Solve absolute value equations

5 Graph solutions to absolute value equations

6 Solve multi-variable equations

C. Inequalities

1 Graph a linear inequality in one variable

2 Write inequalities from graphs

3 Write a linear inequality: word problems

4 Solve linear inequalities

5 Graph solutions to linear inequalities

6 Solve absolute value inequalities

7 Graph solutions to absolute value inequalities

8 Graph a two-variable linear inequality

9 Graph solutions to two-variable absolute value inequalities

10 Graph solutions to quadratic inequalities

D. Functions

1 Domain and range

2 Identify functions

3 Evaluate functions

4 Find values using function graphs

5 Complete a table for a function graph

6 Find the slope of a linear function

7 Graph a linear function

8 Write the equation of a linear function

9 Linear functions over unit intervals

10 Average rate of change

11 Graph an absolute value function

12 Domain and range of absolute value functions: graphs

13 Domain and range of absolute value functions: equations

14 Transformations of absolute value functions

E. Systems of equations

1 Is (x, y) a solution to the system of equations?

2 Solve a system of equations by graphing

3 Solve a system of equations by graphing: word problems

4 Find the number of solutions to a system of equations

5 Classify a system of equations

6 Solve a system of equations using substitution

7 Solve a system of equations using substitution: word problems

8 Solve a system of equations using elimination

9 Solve a system of equations using elimination: word problems

10 Solve a system of equations using any method

11 Solve a system of equations using any method: word problems

12 Solve a system of equations in three variables using substitution

13 Solve a system of equations in three variables using elimination

14 Determine the number of solutions to a system of equations in three variables

15 Solve a system of linear and quadratic equations

16 Solve a nonlinear system of equations

F. Systems of inequalities

1 Is (x, y) a solution to the system of inequalities?

2 Solve systems of linear inequalities by graphing

3 Solve systems of linear and absolute value inequalities by graphing

4 Find the vertices of a solution set

5 Linear programming

G. Matrices

1 Matrix vocabulary

2 Matrix operation rules

4 Multiply a matrix by a scalar

5 Add and subtract scalar multiples of matrices

6 Multiply two matrices

7 Simplify matrix expressions

8 Properties of matrices

9 Solve matrix equations

10 Determinant of a matrix

11 Is a matrix invertible?

12 Inverse of a matrix

13 Identify inverse matrices

14 Solve matrix equations using inverses

15 Identify transformation matrices

16 Transformation matrices: write the vertex matrix

17 Transformation matrices: graph the image

18 Solve a system of equations using augmented matrices

19 Solve a system of equations using augmented matrices: word problems

H. Real numbers

1 Sort rational and irrational numbers

2 Classify rational and irrational numbers

3 Properties of operations on rational and irrational numbers

I. Complex numbers

1 Introduction to complex numbers

2 Add and subtract complex numbers

3 Complex conjugates

4 Multiply complex numbers

5 Divide complex numbers

6 Add, subtract, multiply, and divide complex numbers

7 Absolute values of complex numbers

8 Powers of i

J. Factoring

1 Factor out a monomial

2 Factor quadratics using algebra tiles

4 Factor using a quadratic pattern

5 Factor by grouping

6 Factor sums and differences of cubes

7 Factor polynomials

1 Characteristics of quadratic functions: graphs

2 Characteristics of quadratic functions: equations

3 Complete a function table: quadratic functions

6 Solve a quadratic equation using square roots

7 Solve a quadratic equation using the zero product property

8 Solve a quadratic equation by factoring

9 Complete the square

10 Solve a quadratic equation by completing the square

12 Using the discriminant

13 Match quadratic functions and graphs

14 Write a quadratic function from its zeroes

15 Write a quadratic function from its vertex and another point

L. Polynomials

1 Polynomial vocabulary

3 Multiply polynomials

4 Divide polynomials using long division

5 Divide polynomials using synthetic division

6 Evaluate polynomials using synthetic division

7 Solve polynomial equations

8 Find the roots of factored polynomials

9 Write a polynomial from its roots

10 Rational root theorem

11 Complex conjugate theorem

12 Conjugate root theorems

13 Descartes' Rule of Signs

14 Match polynomials and graphs

15 Domain and range of polynomials

16 Fundamental Theorem of Algebra

17 Pascal's triangle

18 Pascal's triangle and the Binomial Theorem

19 Binomial Theorem I

20 Binomial Theorem II

1 Roots of integers

2 Roots of rational numbers

3 Find roots using a calculator

4 Simplify radical expressions with variables I

5 Simplify radical expressions with variables II

6 Nth roots

10 Simplify radical expressions using the distributive property

11 Simplify radical expressions using conjugates

12 Domain and range of radical functions

N. Rational exponents

1 Evaluate rational exponents

2 Multiplication with rational exponents

3 Division with rational exponents

4 Power rule

5 Simplify expressions involving rational exponents I

6 Simplify expressions involving rational exponents II

O. Rational functions and expressions

1 Rational functions: asymptotes and excluded values

2 Evaluate rational expressions I

3 Evaluate rational expressions II

4 Simplify rational expressions

5 Multiply and divide rational expressions

6 Add and subtract rational expressions

7 Solve rational equations

P. Function operations

2 Multiply functions

3 Divide functions

4 Composition of linear functions: find a value

5 Composition of linear functions: find an equation

6 Composition of linear and quadratic functions: find a value

7 Composition of linear and quadratic functions: find an equation

8 Identify inverse functions

9 Find values of inverse functions from tables

10 Find values of inverse functions from graphs

11 Find inverse functions and relations

Q. Families of functions

1 Function transformation rules

2 Translations of functions

3 Reflections of functions

4 Dilations of functions

5 Transformations of functions

6 Describe function transformations

R. Variation

1 Write and solve direct variation equations

2 Write and solve inverse variation equations

3 Classify variation

4 Write joint and combined variation equations I

5 Find the constant of variation

6 Write joint and combined variation equations II

7 Solve variation equations

S. Logarithms

1 Convert between exponential and logarithmic form: rational bases

2 Convert between natural exponential and logarithmic form

3 Convert between exponential and logarithmic form: all bases

4 Evaluate logarithms

5 Evaluate natural logarithms

6 Change of base formula

7 Evaluate logarithms using a calculator

8 Identify properties of logarithms

9 Product property of logarithms

10 Quotient property of logarithms

11 Power property of logarithms

12 Properties of logarithms: mixed review

13 Evaluate logarithms using properties

T. Exponential and logarithmic functions

1 Domain and range of exponential and logarithmic functions

2 Evaluate exponential functions

3 Match exponential functions and graphs

4 Solve exponential equations using factoring

5 Solve exponential equations using common logarithms

6 Solve exponential equations using natural logarithms

7 Solve logarithmic equations I

8 Solve logarithmic equations II

9 Exponential functions over unit intervals

10 Identify linear and exponential functions

11 Describe linear and exponential growth and decay

12 Exponential growth and decay: word problems

13 Compound interest: word problems

14 Continuously compounded interest: word problems

U. Parabolas

1 Identify the direction a parabola opens

2 Find the vertex of a parabola

3 Find the focus or directrix of a parabola

4 Find the axis of symmetry of a parabola

5 Write equations of parabolas in vertex form from graphs

6 Write equations of parabolas in vertex form using properties

7 Convert equations of parabolas from general to vertex form

8 Find properties of a parabola from equations in general form

9 Graph parabolas

V. Circles

1 Find the center of a circle

2 Find the radius or diameter of a circle

3 Write equations of circles in standard form from graphs

4 Write equations of circles in standard form using properties

5 Convert equations of circles from general to standard form

6 Find properties of circles from equations in general form

7 Graph circles

W. Ellipses

1 Find the center, vertices, or co-vertices of an ellipse

2 Find the length of the major or minor axes of an ellipse

3 Find the foci of an ellipse

4 Write equations of ellipses in standard form from graphs

5 Write equations of ellipses in standard form using properties

6 Convert equations of ellipses from general to standard form

7 Find properties of ellipses from equations in general form

X. Hyperbolas

1 Find the center of a hyperbola

2 Find the vertices of a hyperbola

3 Find the length of the transverse or conjugate axes of a hyperbola

4 Find the equations for the asymptotes of a hyperbola

5 Find the foci of a hyperbola

6 Write equations of hyperbolas in standard form from graphs

7 Write equations of hyperbolas in standard form using properties

8 Convert equations of hyperbolas from general to standard form

9 Find properties of hyperbolas from equations in general form

Y. Angle measures

1 Convert between radians and degrees

3 Graphs of angles

5 Coterminal angles

6 Reference angles

Z. Trigonometry

1 Pythagorean Theorem and its converse

2 Special right triangles

3 Trigonometric ratios: sin, cos, and tan

4 Trigonometric ratios: csc, sec, and cot

5 Trigonometric ratios in similar right triangles

6 Find trigonometric ratios using the unit circle

7 Sin, cos, and tan of special angles

8 Csc, sec, and cot of special angles

9 Find trigonometric functions using a calculator

10 Inverses of sin, cos, and tan

11 Inverses of csc, sec, and cot

12 Solve trigonometric equations I

13 Solve trigonometric equations II

14 Trigonometric ratios: find a side length

15 Trigonometric ratios: find an angle measure

16 Solve a right triangle

17 Law of Sines

18 Law of Cosines

19 Solve a triangle

20 Area of a triangle: sine formula

21 Area of a triangle: Law of Sines

AA. Trigonometric functions

1 Find properties of sine functions

2 Write equations of sine functions from graphs

3 Write equations of sine functions using properties

4 Graph sine functions

5 Graph translations of sine functions

6 Find properties of cosine functions

7 Write equations of cosine functions from graphs

8 Write equations of cosine functions using properties

9 Graph cosine functions

10 Graph translations of cosine functions

11 Graph sine and cosine functions

12 Graph translations of sine and cosine functions

BB. Trigonometric identities

1 Complementary angle identities

2 Symmetry and periodicity of trigonometric functions

3 Trigonometric identities I

4 Trigonometric identities II

CC. Sequences and series

1 Find terms of an arithmetic sequence

2 Find terms of a geometric sequence

3 Evaluate explicit formulas for sequences

4 Evaluate recursive formulas for sequences

5 Classify formulas and sequences

6 Write a formula for an arithmetic sequence

7 Write a formula for a geometric sequence

8 Write a formula for a recursive sequence

9 Sequences: mixed review

10 Identify arithmetic and geometric series

11 Introduction to sigma notation

12 Find the sum of an arithmetic series

13 Find the sum of a finite geometric series

14 Introduction to partial sums

15 Partial sums of arithmetic series

16 Partial sums of geometric series

17 Partial sums: mixed review

18 Convergent and divergent geometric series

19 Find the value of an infinite geometric series

20 Write a repeating decimal as a fraction

DD. Probability

1 Introduction to probability

2 Calculate probabilities of events

3 Counting principle

4 Combinations and permutations

5 Find probabilities using combinations and permutations

6 Find probabilities using two-way frequency tables

7 Identify independent events

8 Probability of independent and dependent events

9 Find conditional probabilities

10 Independence and conditional probability

11 Find conditional probabilities using two-way frequency tables

12 Find probabilities using the addition rule

EE. Probability distributions

1 Identify discrete and continuous random variables

2 Write a discrete probability distribution

3 Graph a discrete probability distribution

4 Expected values of random variables

5 Variance of random variables

6 Standard deviation of random variables

7 Write the probability distribution for a game of chance

8 Expected values for a game of chance

9 Choose the better bet

10 Find probabilities using the binomial distribution

11 Find probabilities using the normal distribution I

12 Find probabilities using the normal distribution II

13 Find z-values

14 Find values of normal variables

15 Distributions of sample means

FF. Statistics

1 Identify biased samples

2 Variance and standard deviation

3 Identify an outlier

4 Identify an outlier and describe the effect of removing it

5 Outliers in scatter plots

6 Find the equation of a regression line

7 Interpret regression lines

8 Analyze a regression line of a data set

9 Find confidence intervals for population means

10 Find confidence intervals for population proportions

11 Interpret confidence intervals for population means

12 Experiment design

13 Analyze the results of an experiment using simulations

Precalculus

A. Functions

1 Domain and range

2 Identify functions

3 Evaluate functions

4 Find values using function graphs

5 Complete a table for a function graph

6 Find the slope of a linear function

7 Graph a linear function

8 Write the equation of a linear function

9 Linear functions over unit intervals

10 Average rate of change

11 Add, subtract, multiply, and divide functions

12 Composition of functions

13 Identify inverse functions

14 Find values of inverse functions from tables

15 Find values of inverse functions from graphs

16 Find inverse functions and relations

B. Families of functions

1 Function transformation rules

2 Translations of functions

3 Reflections of functions

4 Dilations of functions

5 Transformations of functions

6 Describe function transformations

1 Find the maximum or minimum value of a quadratic function

4 Match quadratic functions and graphs

5 Solve a quadratic equation using square roots

6 Solve a quadratic equation by factoring

7 Solve a quadratic equation by completing the square

9 Using the discriminant

D. Polynomials

1 Divide polynomials using long division

2 Divide polynomials using synthetic division

3 Evaluate polynomials using synthetic division

4 Find the roots of factored polynomials

5 Write a polynomial from its roots

6 Rational root theorem

7 Complex conjugate theorem

8 Conjugate root theorems

9 Descartes' Rule of Signs

10 Fundamental Theorem of Algebra

11 Match polynomials and graphs

12 Domain and range of polynomials

13 Factor sums and differences of cubes

14 Solve equations with sums and differences of cubes

15 Factor using a quadratic pattern

16 Solve equations using a quadratic pattern

17 Pascal's triangle

18 Pascal's triangle and the Binomial Theorem

19 Binomial Theorem I

20 Binomial Theorem II

E. Rational functions

1 Rational functions: asymptotes and excluded values

2 Solve rational equations

3 Check whether two rational functions are inverses

F. Exponential and logarithmic functions

1 Domain and range of exponential and logarithmic functions

2 Convert between exponential and logarithmic form

3 Solve exponential equations using factoring

4 Evaluate logarithms

5 Change of base formula

6 Product property of logarithms

7 Quotient property of logarithms

8 Power property of logarithms

9 Evaluate logarithms using properties

10 Solve exponential equations using logarithms

11 Solve logarithmic equations with one logarithm

12 Solve logarithmic equations with multiple logarithms

13 Exponential functions over unit intervals

14 Identify linear and exponential functions

15 Describe linear and exponential growth and decay

16 Exponential growth and decay: word problems

17 Compound interest: word problems

1 Domain and range of radical functions

H. Roots and rational exponents

1 Roots of integers

2 Roots of rational numbers

3 Find roots using a calculator

4 Evaluate rational exponents

5 Operations with rational exponents

6 Simplify radical expressions with variables

7 Nth roots

8 Simplify expressions involving rational exponents

I. Systems of equations

1 Solve a system of equations by graphing

2 Solve a system of equations by graphing: word problems

3 Classify a system of equations

4 Solve a system of equations using substitution

5 Solve a system of equations using substitution: word problems

6 Solve a system of equations using elimination

7 Solve a system of equations using elimination: word problems

8 Solve a system of equations using augmented matrices

9 Solve a system of equations using augmented matrices: word problems

10 Solve a system of equations in three variables using substitution

11 Solve a system of equations in three variables using elimination

12 Determine the number of solutions to a system of equations in three variables

J. Systems of inequalities

1 Solve systems of linear inequalities by graphing

2 Solve systems of linear and absolute value inequalities by graphing

3 Find the vertices of a solution set

4 Linear programming

K. Nonlinear inequalities

1 Graph solutions to quadratic inequalities

3 Graph solutions to higher-degree inequalities

4 Solve higher-degree inequalities

L. Matrices

1 Matrix vocabulary

2 Matrix operation rules

4 Multiply a matrix by a scalar

5 Add and subtract scalar multiples of matrices

6 Multiply two matrices

7 Simplify matrix expressions

8 Properties of matrices

9 Solve matrix equations

10 Determinant of a matrix

11 Is a matrix invertible?

12 Inverse of a 2 x 2 matrix

13 Inverse of a 3 x 3 matrix

14 Identify inverse matrices

15 Solve matrix equations using inverses

16 Identify transformation matrices

17 Transformation matrices: write the vertex matrix

18 Transformation matrices: graph the image

M. Trigonometry

1 Convert between radians and degrees

4 Coterminal and reference angles

5 Find trigonometric ratios using right triangles

6 Find trigonometric ratios using the unit circle

7 Find trigonometric ratios of special angles

8 Find trigonometric ratios using reference angles

9 Inverses of trigonometric functions

10 Solve trigonometric equations

11 Trigonometric ratios: find a side length

12 Trigonometric ratios: find an angle measure

13 Solve a right triangle

14 Law of Sines

15 Law of Cosines

16 Solve a triangle

17 Area of a triangle: sine formula

18 Area of a triangle: Heron's formula

N. Trigonometric functions

1 Find properties of sine functions

2 Write equations of sine functions from graphs

3 Write equations of sine functions using properties

4 Graph sine functions

5 Graph translations of sine functions

6 Find properties of cosine functions

7 Write equations of cosine functions from graphs

8 Write equations of cosine functions using properties

9 Graph cosine functions

10 Graph translations of cosine functions

11 Graph sine and cosine functions

12 Graph translations of sine and cosine functions

O. Trigonometric identities

1 Complementary angle identities

2 Symmetry and periodicity of trigonometric functions

3 Trigonometric identities I

4 Trigonometric identities II

P. Conic sections

1 Find properties of parabolas

2 Write equations of parabolas in vertex form

3 Graph parabolas

4 Find properties of circles

5 Write equations of circles in standard form

6 Graph circles

7 Find properties of ellipses

8 Find the eccentricity of an ellipse

9 Write equations of ellipses in standard form

10 Find properties of hyperbolas

11 Find the eccentricity of a hyperbola

12 Write equations of hyperbolas in standard form

13 Convert equations of conic sections from general to standard form

Q. Real numbers

1 Sort rational and irrational numbers

2 Classify rational and irrational numbers

3 Properties of operations on rational and irrational numbers

R. Complex numbers

1 Add and subtract complex numbers

2 Complex conjugates

3 Multiply and divide complex numbers

4 Add, subtract, multiply, and divide complex numbers

5 Absolute values of complex numbers

6 Powers of i

S. Complex plane

1 Introduction to the complex plane

2 Graph complex numbers

3 Addition in the complex plane

4 Subtraction in the complex plane

5 Graph complex conjugates

6 Absolute value in the complex plane

7 Midpoints in the complex plane

8 Distance in the complex plane

T. Polar form

1 Find the modulus and argument of a complex number

2 Convert complex numbers from rectangular to polar form

3 Convert complex numbers from polar to rectangular form

4 Convert complex numbers between rectangular and polar form

5 Match polar equations and graphs

U. Two-dimensional vectors

1 Find the magnitude of a vector

2 Find the component form of a vector

3 Find the direction angle of a vector

4 Find the component form of a vector from its magnitude and direction angle

5 Graph a resultant vector using the triangle method

6 Graph a resultant vector using the parallelogram method

8 Subtract vectors

9 Find the magnitude and direction of a vector sum

10 Multiply a vector by a scalar

11 Find the magnitude of a vector scalar multiple

12 Determine the direction of a vector scalar multiple

13 Find a unit vector

14 Linear combinations of vectors

V. Three-dimensional vectors

1 Find the magnitude of a three-dimensional vector

2 Find the component form of a three-dimensional vector

3 Add and subtract three-dimensional vectors

4 Scalar multiples of three-dimensional vectors

5 Find a three-dimensional unit vector

6 Linear combinations of three-dimensional vectors

W. Sequences and series

1 Find terms of a sequence

2 Find terms of a recursive sequence

3 Identify a sequence as explicit or recursive

4 Find a recursive formula

5 Find recursive and explicit formulas

6 Convert a recursive formula to an explicit formula

7 Convert an explicit formula to a recursive formula

8 Convert between explicit and recursive formulas

9 Identify arithmetic and geometric series

10 Introduction to sigma notation

11 Find the sum of an arithmetic series

12 Find the sum of a finite geometric series

13 Introduction to partial sums

14 Partial sums of arithmetic series

15 Partial sums of geometric series

16 Partial sums: mixed review

17 Convergent and divergent geometric series

18 Find the value of an infinite geometric series

19 Write a repeating decimal as a fraction

X. Probability

1 Introduction to probability

2 Calculate probabilities of events

3 Combinations and permutations

4 Find probabilities using combinations and permutations

5 Find probabilities using two-way frequency tables

6 Identify independent events

7 Find conditional probabilities

8 Independence and conditional probability

9 Find conditional probabilities using two-way frequency tables

10 Find probabilities using the addition rule

Y. Probability distributions

1 Identify discrete and continuous random variables

2 Write a discrete probability distribution

3 Graph a discrete probability distribution

4 Expected values of random variables

5 Variance of random variables

6 Standard deviation of random variables

7 Write the probability distribution for a game of chance

8 Expected values for a game of chance

9 Choose the better bet

10 Find probabilities using the binomial distribution

11 Mean, variance, and standard deviation of binomial distributions

12 Find probabilities using the normal distribution I

13 Find probabilities using the normal distribution II

14 Find z-values

15 Find values of normal variables

16 Distributions of sample means

17 The Central Limit Theorem

18 Use normal distributions to approximate binomial distributions

Z. Statistics

1 Identify biased samples

2 Variance and standard deviation

3 Identify an outlier

4 Identify an outlier and describe the effect of removing it

5 Outliers in scatter plots

6 Match correlation coefficients to scatter plots

7 Calculate correlation coefficients

8 Find the equation of a regression line

9 Interpret regression lines

10 Analyze a regression line of a data set

11 Analyze a regression line using statistics of a data set

12 Find confidence intervals for population means

13 Find confidence intervals for population proportions

14 Interpret confidence intervals for population means

15 Experiment design

16 Analyze the results of an experiment using simulations

Calculus

A. Functions

1 Find values of functions from graphs

2 Add, subtract, multiply, and divide functions

3 Composition of functions

4 Identify inverse functions

5 Find values of inverse functions from tables

6 Find values of inverse functions from graphs

7 Find inverse functions and relations

B. Families of functions

1 Function transformation rules

2 Translations of functions

3 Reflections of functions

4 Dilations of functions

5 Transformations of functions

6 Describe function transformations

C. Trigonometric functions

1 Convert between radians and degrees

3 Coterminal and reference angles

4 Find trigonometric ratios using right triangles

5 Find trigonometric ratios using the unit circle

6 Find trigonometric ratios using reference angles

7 Inverses of trigonometric functions

8 Find properties of sine functions

9 Write equations of sine functions from graphs

10 Write equations of sine functions using properties

11 Graph sine functions

12 Find properties of cosine functions

13 Write equations of cosine functions from graphs

14 Write equations of cosine functions using properties

15 Graph cosine functions

16 Graph sine and cosine functions

D. Exponential and logarithmic functions

1 Domain and range of exponential and logarithmic functions

2 Convert between exponential and logarithmic form

3 Evaluate logarithms

4 Change of base formula

5 Product property of logarithms

6 Quotient property of logarithms

7 Power property of logarithms

8 Evaluate logarithms using properties

9 Describe linear and exponential growth and decay

E. Introduction to limits

1 Find limits using graphs

2 Find one-sided limits using graphs

3 Determine if a limit exists

F. Calculate limits

1 Find limits using addition, subtraction, and multiplication laws

2 Find limits using the division law

3 Find limits using power and root laws

4 Find limits using limit laws

5 Find limits of polynomials and rational functions

6 Find limits involving factorization and rationalization

7 Find limits involving absolute value functions

8 Find limits involving trigonometric functions

G. Limits involving infinity

1 Find limits at vertical asymptotes using graphs

2 Determine end behavior using graphs

3 Determine end behavior of polynomial and rational functions

H. Rational functions

1 Find the limit at a vertical asymptote of a rational function I

2 Find the limit at a vertical asymptote of a rational function II

I. Continuity

1 Identify graphs of continuous functions

2 Determine continuity using graphs

3 Determine one-sided continuity using graphs

4 Find and analyze points of discontinuity using graphs

5 Determine continuity on an interval using graphs

6 Determine the continuity of a piecewise function at a point

7 Make a piecewise function continuous

8 Intermediate Value Theorem

J. Introduction to derivatives

1 Average rate of change I

2 Average rate of change II

3 Find instantaneous rates of change

4 Velocity as a rate of change

5 Find values of derivatives using limits

6 Find the slope of a tangent line using limits

7 Find equations of tangent lines using limits

K. Derivative rules

1 Sum and difference rules

2 Product rule

3 Quotient rule

4 Power rule I

5 Power rule II

6 Chain rule

7 Inverse function rule

L. Calculate derivatives

1 Find derivatives of polynomials

2 Find derivatives of rational functions

3 Find derivatives of trigonometric functions I

4 Find derivatives of trigonometric functions II

5 Find derivatives of exponential functions

6 Find derivatives of logarithmic functions

7 Find derivatives of inverse trigonometric functions

8 Find derivatives of radical functions

9 Find derivatives using the product rule I

10 Find derivatives using the product rule II

11 Find derivatives using the quotient rule I

12 Find derivatives using the quotient rule II

13 Find derivatives using the chain rule I

14 Find derivatives using the chain rule II

M. Derivative strategies

1 Find derivatives using implicit differentiation

2 Find tangent lines using implicit differentiation

3 Find derivatives using logarithmic differentiation

N. Calculate higher derivatives

1 Find higher derivatives of polynomials

2 Find higher derivatives of rational and radical functions

3 Find second derivatives of trigonometric, exponential, and logarithmic functions

4 Find higher derivatives of exponential and trigonometric functions

5 Find higher derivatives of logarithmic and power functions