###### January 31, 2014

### Maths: Year 10 topics

You can expect your child to learn the following topics in maths in Year 10:

**Numbers**

- Classify numbers
- Prime or composite
- Compare and order rational numbers
- Number lines
- Convert between decimals and fractions
- Square roots
- Cube roots

**Operations**

- Add, subtract, multiply and divide integers
- Order of operations with integers
- Evaluate variable expressions involving integers
- Add and subtract rational numbers
- Multiply and divide rational numbers
- Order of operations with rational numbers
- Evaluate variable expressions involving rational numbers

**Ratios and proportions**

- Identify equivalent ratios
- Equivalent ratios: fill in the missing number
- Unit rates
- Unit prices
- Solve proportions
- Solve proportions: word problems
- Scale drawings and scale factors

**Percents**

- Convert between percents, fractions and decimals
- Solve percent equations
- Percent word problems
- Percent of change
- Percent of change: word problems
- Percent of a number: VAT, discount and more
- Find the percent: discount and mark-up
- Multi-step problems with percents

**Measurement**

- Estimate metric measurements
- Convert rates and measurements
- Metric mixed units
- Imperial mixed units
- Convert between metric and imperial units
- Precision
- Greatest possible error
- Minimum and maximum area and volume
- Percent error
- Percent error: area and volume

**Geometry**

- Perimeter
- Area
- Symmetry
- Identify and classify polygons
- Interior angles of polygons
- Volume
- Surface area
- Congruent figures: side lengths and angle measures
- Similar figures: side lengths and angle measures
- Similar triangles and indirect measurement
- Area and perimeter of similar figures
- Area between two shapes
- Similar solids
- Volume and surface area of similar solids
- Perimeter, area and volume: changes in scale
- Identify reflections, rotations and translations
- Reflections, rotations and translations: find the coordinates
- Reflections, rotations and translations: graph the image
- Dilations and scale factors
- Pythagorean theorem
- Pythagorean theorem: word problems
- Converse of the Pythagorean theorem: is it a right triangle?

**Coordinate graphs**

- Points on coordinate graphs
- Quadrants and axes
- Distance between two points

**Properties**

- Properties of addition and multiplication
- Distributive property
- Simplify variable expressions using properties
- Properties of equality

**Logic**

- Identify hypotheses and conclusions
- Counterexamples

**Variable expressions and equations**

- Write variable expressions
- Simplify variable expressions involving like terms and the distributive property
- Write variable equations
- Does x satisfy the equation?
- Solve equations using order of operations

**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
- Identities and equations with no solutions
- Solve linear equations: word problems
- Solve linear equations: mixed review

**Single-variable inequalities**

L.1 Graph inequalities

L.2 Write inequalities from graphs

L.3 Identify solutions to inequalities

L.4 Solve one-step linear inequalities: addition and subtraction

L.5 Solve one-step linear inequalities: multiplication and division

L.6 Solve one-step linear inequalities

L.7 Graph solutions to one-step linear inequalities

L.8 Solve two-step linear inequalities

L.9 Graph solutions to two-step linear inequalities

L.10 Solve advanced linear inequalities

L.11 Graph solutions to advanced linear inequalities

L.12 Graph compound inequalities

L.13 Write compound inequalities from graphs

L.14 Solve compound inequalities

L.15 Graph solutions to compound inequalities

L.2 Write inequalities from graphs

L.3 Identify solutions to inequalities

L.4 Solve one-step linear inequalities: addition and subtraction

L.5 Solve one-step linear inequalities: multiplication and division

L.6 Solve one-step linear inequalities

L.7 Graph solutions to one-step linear inequalities

L.8 Solve two-step linear inequalities

L.9 Graph solutions to two-step linear inequalities

L.10 Solve advanced linear inequalities

L.11 Graph solutions to advanced linear inequalities

L.12 Graph compound inequalities

L.13 Write compound inequalities from graphs

L.14 Solve compound inequalities

L.15 Graph solutions to compound inequalities

**Data and graphs**

M.1 Interpret bar graphs, line graphs and histograms

M.2 Create bar graphs, line graphs and histograms

M.3 Circle graphs

M.4 Interpret stem-and-leaf plots

M.5 Interpret box-and-whisker plots

M.6 Interpret a scatter plot

M.7 Scatter plots: line of best fit

Relations and functions

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

N.2 Identify independent and dependent variables

N.3 Identify functions

N.4 Identify functions: vertical line test

N.5 Identify types of functions from graphs

N.6 Complete a function table

N.7 Evaluate function rules I

N.8 Evaluate function rules II

N.9 Graph a function

N.10 Write a function rule: word problems

N.11 Find points on a function graph

N.12 Write a rule for a function table

Direct and inverse variation

O.1 Identify proportional relationships

O.2 Find the constant of variation

O.3 Graph a proportional relationship

O.4 Write direct variation equations

O.5 Write and solve direct variation equations

O.6 Identify direct variation and inverse variation

O.7 Write inverse variation equations

O.8 Write and solve inverse variation equations

**Linear functions**

P.1 Identify linear functions

P.2 Find the slope of a graph

P.3 Find slope from two points

P.4 Slope-intercept form: find slope and y-intercept

P.5 Slope-intercept form: graph an equation

P.6 Slope-intercept form: write an equation from a graph

P.7 Slope-intercept form: write an equation

P.8 Linear equations: solve for y

P.9 Linear function word problems

P.10 Write equations in standard form

P.11 Standard form: find x- and y-intercepts

P.12 Standard form: graph an equation

P.13 Equations of horizontal and vertical lines

P.14 Graph a horizontal or vertical line

P.15 Point-slope form: graph an equation

P.16 Point-slope form: write an equation from a graph

P.17 Point-slope form: write an equation

P.18 Slopes of parallel and perpendicular lines

P.19 Write an equation for a parallel or perpendicular line

**Linear inequalities**

Q.1 Does (x, y) satisfy the inequality?

Q.2 Linear inequalities: solve for y

Q.3 Graph a linear inequality in two variables

Q.4 Linear inequalities: word problems

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

**Simultaneous equations**

R.1 Is (x, y) a solution to the simultaneous equations?

R.2 Solve simultaneous equations by graphing

R.3 Solve simultaneous equations by graphing: word problems

R.4 Find the number of solutions to simultaneous equations by graphing

R.5 Find the number of solutions to simultaneous equations

R.6 Solve simultaneous equations using substitution

R.7 Solve simultaneous equations using substitution: word problems

R.8 Solve simultaneous equations using elimination

R.9 Solve simultaneous equations using elimination: word problems

**Exponents**

S.1 Exponents with integer bases

S.2 Exponents with decimal and fractional bases

S.3 Negative exponents

S.4 Multiplication with exponents

S.5 Division with exponents

S.6 Multiplication and division with exponents

S.7 Power rule

S.8 Simplify expressions involving exponents

**Number sequences**

T.1 Identify arithmetic and geometric sequences

T.2 Arithmetic sequences

T.3 Geometric sequences

T.4 Evaluate variable expressions for number sequences

T.5 Write variable expressions for arithmetic sequences

T.6 Write variable expressions for geometric sequences

T.7 Number sequences: mixed review

**Scientific notation**

U.1 Convert between standard and scientific notation

U.2 Compare numbers written in scientific notation

U.3 Multiply numbers written in scientific notation

U.4 Divide numbers written in scientific notation

**Exponential functions**

V.1 Evaluate an exponential function

V.2 Match exponential functions and graphs

V.3 Exponential growth and decay: word problems

**Monomials**

W.1 Identify monomials

W.2 Multiply monomials

W.3 Divide monomials

W.4 Multiply and divide monomials

W.5 Powers of monomials

**Polynomials**

X.1 Polynomial vocabulary

X.2 Model polynomials with algebra tiles

X.3 Add and subtract polynomials using algebra tiles

X.4 Add and subtract polynomials

X.5 Add polynomials to find perimeter

X.6 Multiply a polynomial by a monomial

X.7 Multiply two polynomials using algebra tiles

X.8 Multiply two binomials

X.9 Multiply two binomials: special cases

X.10 Multiply polynomials

**Factorising**

Y.1 GCF of monomials

Y.2 Factorise out a monomial

Y.3 Factorise quadratics with leading coefficient 1

Y.4 Factorise quadratics with other leading coefficients

Y.5 Factorise quadratics: special cases

Y.6 Factorise by grouping

Y.7 Factorise polynomials

**Quadratic equations**

Z.1 Characteristics of quadratic functions

Z.2 Complete a function table: quadratic functions

Z.3 Solve a quadratic equation using square roots

Z.4 Solve an equation using the zero product property

Z.5 Solve a quadratic equation by factorising

Z.6 Complete the square

Z.7 Solve a quadratic equation by completing the square

Z.8 Solve a quadratic equation using the quadratic formula

**Radical expressions**

AA.1 Simplify radical expressions

AA.2 Simplify radical expressions by rationalising the denominator

AA.3 Multiply radical expressions

AA.4 Add and subtract radical expressions

AA.5 Simplify radical expressions using the distributive property

AA.6 Simplify radical expressions: mixed review

**Rational functions and expressions**

BB.1 Rational functions: asymptotes and excluded values

BB.2 Simplify complex fractions

BB.3 Simplify rational expressions

BB.4 Multiply and divide rational expressions

BB.5 Divide polynomials

BB.6 Add and subtract rational expressions

BB.7 Solve rational equations

**Problem solving**

CC.1 Word problems: mixed review

CC.2 Word problems with money

CC.3 Consecutive integer problems

CC.4 Rate of travel: word problems

CC.5 Weighted averages: word problems

**Probability**

DD.1 Theoretical probability

DD.2 Experimental probability

DD.3 Compound events: find the number of outcomes

DD.4 Identify independent and dependent events

DD.5 Probability of independent and dependent events

**Statistics**

EE.1 Calculate mean, median, mode and range

EE.2 Interpret charts to find mean, median, mode and range

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

EE.4 Quartiles

EE.5 Identifying biased samples