## Grade 10 Math

## CONTENTS

## Numbers

Factors

Prime factorization

Greatest common factor

Least common multiple

GCF and LCM: word problems

Square roots

Cube roots

Classify rational and irrational numbers

Classify numbers

Compare and order rational numbers

Absolute value and opposites

Number lines

Convert between decimals and fractions

## Exponents

Exponents with integer bases

Exponents with decimal and fractional bases

Negative exponents

Multiplication with exponents

Division with exponents

Multiplication and division with exponents

Power rule

Evaluate expressions using properties of exponents

Identify equivalent expressions involving exponents

## Scientific notation

Convert between standard and scientific notation

Compare numbers written in scientific notation

Multiply numbers written in scientific notation

Divide numbers written in scientific notation

## Radical expressions

Simplify radical expressions

Simplify radical expressions by rationalizing the denominator

Multiply radical expressions

Add and subtract radical expressions

Simplify radical expressions using the distributive property

Simplify radical expressions: mixed review

## Rational exponents

Evaluate rational exponents

Multiplication with rational exponents

Division with rational exponents

Power rule with rational exponents

Simplify expressions involving rational exponents I

Simplify expressions involving rational exponents II

## Coordinate plane

Coordinate plane review

Midpoints

Distance between two points

## Solve equations

Model and solve equations using algebra tiles

Write and solve equations that represent diagrams

Solve one-step linear equations

Solve two-step linear equations

Solve advanced linear equations

Solve equations with variables on both sides

Solve equations: complete the solution

Find the number of solutions

Create equations with no solutions or infinitely many solutions

Solve linear equations: word problems

Solve linear equations: mixed review

## Single-variable inequalities

Graph inequalities

Write inequalities from graphs

Identify solutions to inequalities

Solve one-step linear inequalities: addition and subtraction

Solve one-step linear inequalities: multiplication and division

Solve one-step linear inequalities

Graph solutions to one-step linear inequalities

Solve two-step linear inequalities

Graph solutions to two-step linear inequalities

Solve advanced linear inequalities

Graph solutions to advanced linear inequalities

Graph compound inequalities

Write compound inequalities from graphs

Solve compound inequalities

Graph solutions to compound inequalities

## Data and graphs

Interpret bar graphs, line graphs and histograms

Create bar graphs, line graphs and histograms

Interpret circle graphs

Interpret stem-and-leaf plots

Interpret box-and-whisker plots

Interpret a scatter plot

Scatter plots: line of best fit

## Relations and functions

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

Domain and range of relations

Identify independent and dependent variables

Identify functions

Identify functions: vertical line test

Find values using function graphs

Evaluate a function

Evaluate a function: plug in an expression

Complete a function table from a graph

Complete a function table from an equation

Interpret the graph of a function: word problems

## Direct and inverse variation

Identify proportional relationships

Find the constant of variation

Graph a proportional relationship

Write direct variation equations

Write and solve direct variation equations

Identify direct variation and inverse variation

Write inverse variation equations

Write and solve inverse variation equations

## Linear functions

Identify linear functions

Find the slope of a graph

Find the slope from two points

Find a missing coordinate using slope

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

Slope-intercept form: graph an equation

Slope-intercept form: write an equation from a graph

Slope-intercept form: write an equation

Slope-intercept form: write an equation from a table

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

Write linear functions to solve word problems

Complete a table and graph a linear function

Compare linear functions: graphs, tables and equations

Write equations in standard form

Standard form: find x- and y-intercepts

Standard form: graph an equation

Equations of horizontal and vertical lines

Graph a horizontal or vertical line

Point-slope form: graph an equation

Point-slope form: write an equation

Point-slope form: write an equation from a graph

Slopes of parallel and perpendicular lines

Write an equation for a parallel or perpendicular line

Find the distance between a point and a line

Find the distance between two parallel lines

Transformations of linear functions

## Systems of linear equations

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

Solve a system of equations by graphing

Solve a system of equations by graphing: word problems

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

Find the number of solutions to a system of equations

Classify a system of equations by graphing

Classify a system of equations

Solve a system of equations using substitution

Solve a system of equations using substitution: word problems

Solve a system of equations using elimination

Solve a system of equations using elimination: word problems

Solve a system of equations using any method

Solve a system of equations using any method: word problems

## Monomials

Identify monomials

Multiply monomials

Divide monomials

Multiply and divide monomials

Powers of monomials

## Polynomials

Polynomial vocabulary

Model polynomials with algebra tiles

Add and subtract polynomials using algebra tiles

Add and subtract polynomials

Add polynomials to find perimeter

Multiply a polynomial by a monomial

Multiply two polynomials using algebra tiles

Multiply two binomials

Multiply two binomials: special cases

Multiply polynomials

## Factoring

GCF of monomials

Factor out a monomial

Factor quadratics with leading coefficient 1

Factor quadratics with other leading coefficients

Factor quadratics using algebra tiles

Factor quadratics: special cases

Factor by grouping

Factor polynomials

## Quadratic equations

Characteristics of quadratic functions

Complete a function table: quadratic functions

Solve a quadratic equation using square roots

Solve a quadratic equation using the zero product property

Solve a quadratic equation by factoring

Complete the square

Solve a quadratic equation by completing the square

Solve a quadratic equation using the quadratic formula

Using the discriminant

## Parabolas

Identify the direction a parabola opens

Find the vertex of a parabola

Find the axis of symmetry of a parabola

Write equations of parabolas in vertex form from graphs

Write equations of parabolas in vertex form using properties

Graph parabolas

## Functions: linear, quadratic, exponential

Identify linear, quadratic and exponential functions from graphs

Identify linear, quadratic and exponential functions from tables

Write linear, quadratic and exponential functions

Linear functions over unit intervals

Exponential functions over unit intervals

Describe linear and exponential growth and decay

## Rational functions and expressions

Rational functions: asymptotes and excluded values

Simplify complex fractions

Simplify rational expressions

Multiply and divide rational expressions

Divide polynomials

Add and subtract rational expressions

Solve rational equations

## Circles in the coordinate plane

Find the centre of a circle

Find the radius or diameter of a circle

Write equations of circles in standard form from graphs

Write equations of circles in standard form using properties

Graph circles

## Logic

Identify hypotheses and conclusions

Counterexamples

Truth tables

Truth values

Conditionals

Negations

Converses, inverses and contrapositives

Biconditionals

## Measurement

Estimate metric measurements

Convert rates and measurements: metric units

Estimate imperial measurements of length

Convert rates and measurements: imperial units of length

Unit rates

Unit prices with imperial length conversions

Imperial mixed units of length

Convert between metric and imperial units of length

Scale drawings: word problems

## Constructions

Construct an angle bisector

Construct a congruent angle

## Two-dimensional figures

Polygon vocabulary

Interior angles of polygons

Perimeter

Area of triangles and quadrilaterals

Area and perimeter in the coordinate plane I

Area and perimeter in the coordinate plane II

Area and circumference of circles

Area of compound figures

Area between two shapes

Area and perimeter of similar figures

Identify trapezoids

Classify quadrilaterals

Graph quadrilaterals

Properties of parallelograms

Properties of rhombuses

## Three-dimensional figures

Three-dimensional figure vocabulary

Parts of three-dimensional figures

Nets and drawings of three-dimensional figures

Introduction to surface area and volume

Surface area of prisms and cylinders

Surface area of pyramids and cones

Volume of prisms and cylinders

Volume of pyramids and cones

Surface area and volume of spheres

Introduction to similar solids

Surface area and volume of similar solids

Surface area and volume review

Cross-sections of three-dimensional figures

Solids of revolution

## Congruent figures

Congruent line segments

Congruence statements and corresponding parts

Solve problems involving corresponding parts

Identify congruent figures

SSS and SAS Theorems

ASA and AAS Theorems

SSS, SAS, ASA and AAS Theorems

SSS Theorem in the coordinate plane

Congruency in isosceles and equilateral triangles

Hypotenuse-Leg Theorem

## Triangles

**Triangle is a polygon with 3 sides. **

Classify triangles

Triangle Angle-Sum Theorem

Midsegments of triangles

Triangles and bisectors

Identify medians, altitudes, angle bisectors and perpendicular bisectors

Angle-side relationships in triangles

Triangle Inequality Theorem

## Similarity

Identify similar figures

Similarity ratios

Similarity statements

Side lengths and angle measures in similar figures

Similar triangles and indirect measurement

Perimeters of similar figures

Similarity rules for triangles

Similar triangles and similarity transformations

Similarity of circles

Triangle Proportionality Theorem

Areas of similar figures

## Right triangles

Pythagorean Theorem

Converse of the Pythagorean theorem

Pythagorean Inequality Theorems

Special right triangles

## Trigonometry

Trigonometric ratios: sin, cos and tan

Trigonometric ratios: csc, sec and cot

Find trigonometric functions of special angles

Find trigonometric functions using a calculator

Inverses of trigonometric functions

Trigonometric ratios: find a side length

Trigonometric ratios: find an angle measure

Solve a right triangle

## Transformations

Translations: graph the image

Translations: find the coordinates

Translations: write the rule

Reflections: graph the image

Reflections: find the coordinates

Rotate polygons about a point

Rotations: graph the image

Rotations: find the coordinates

Classify congruence transformations

Compositions of congruence transformations: graph the image

Transformations that carry a polygon onto itself

Congruence transformations: mixed review

Dilations: graph the image

Dilations: find the coordinates

Dilations: scale factor and classification

Dilations and parallel lines

## Probability

Theoretical and experimental probability

Compound events: find the number of outcomes

Independent and dependent events

Factorials

Permutations

Counting principle

Permutation and combination notation

Geometric probability

## Statistics

Mean, median, mode and range

Quartiles

Identify biased samples

Mean absolute deviation

Variance and standard deviation