# Year 10 maths

Here is a list of all of the maths skills students learn in year 10! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. To start practising, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Numbers

## Consumer maths

## Coordinate plane

## Solve equations

- D.1 Model and solve equations using algebra tiles
- D.2 Write and solve equations that represent diagrams
- D.3 Solve one-step linear equations
- D.4 Solve two-step linear equations
- D.5 Solve advanced linear equations
- D.6 Solve equations with variables on both sides
- D.7 Solve equations: complete the solution
- D.8 Find the number of solutions
- D.9 Create equations with no solutions or infinitely many solutions
- D.10 Solve linear equations: word problems
- D.11 Solve linear equations: mixed review

## Single-variable inequalities

- E.1 Graph inequalities
- E.2 Write inequalities from graphs
- E.3 Identify solutions to inequalities
- E.4 Solve one-step linear inequalities: addition and subtraction
- E.5 Solve one-step linear inequalities: multiplication and division
- E.6 Solve one-step linear inequalities
- E.7 Graph solutions to one-step linear inequalities
- E.8 Solve two-step linear inequalities
- E.9 Graph solutions to two-step linear inequalities
- E.10 Solve advanced linear inequalities
- E.11 Graph solutions to advanced linear inequalities

## Relations and functions

- F.1 Relations: convert between tables, graphs, mappings and lists of points
- F.2 Domain and range of relations
- F.3 Identify independent and dependent variables
- F.4 Identify functions
- F.5 Find values using function graphs
- F.6 Evaluate a function
- F.7 Complete a function table from a graph
- F.8 Complete a function table from an equation
- F.9 Interpret the graph of a function: word problems

## Linear functions

- G.1 Identify linear functions
- G.2 Find the gradient of a graph
- G.3 Find the gradient from two points
- G.4 Find a missing coordinate using gradient
- G.5 Find the gradient and y-intercept of a linear equation
- G.6 Graph an equation in y=mx+c form
- G.7 Write an equation in y=mx+c form from a graph
- G.8 Write an equation in y=mx+c form
- G.9 Write an equation in y=mx+c form from a table
- G.10 Write an equation in y=mx+c form from a word problem
- G.11 Write linear functions to solve word problems
- G.12 Complete a table and graph a linear function
- G.13 Compare linear functions: graphs, tables and equations
- G.14 Write equations in standard form
- G.15 Standard form: find x- and y-intercepts
- G.16 Standard form: graph an equation
- G.17 Equations of horizontal and vertical lines
- G.18 Graph a horizontal or vertical line
- G.19 Point-gradient form: graph an equation
- G.20 Point-gradient form: write an equation
- G.21 Point-gradient form: write an equation from a graph
- G.22 Gradients of parallel and perpendicular lines
- G.23 Write an equation for a parallel or perpendicular line
- G.24 Find the distance between a point and a line
- G.25 Find the distance between two parallel lines
- G.26 Transformations of linear functions

## Simultaneous equations

- H.1 Is (x, y) a solution to the simultaneous equations?
- H.2 Solve simultaneous equations by graphing
- H.3 Solve simultaneous equations by graphing: word problems
- H.4 Find the number of solutions to simultaneous equations by graphing
- H.5 Find the number of solutions to simultaneous equations
- H.6 Solve simultaneous equations using substitution
- H.7 Solve simultaneous equations using substitution: word problems
- H.8 Solve simultaneous equations using elimination
- H.9 Solve simultaneous equations using elimination: word problems
- H.10 Solve a system of equations using any method
- H.11 Solve a system of equations using any method: word problems

## Inequalities and linear programming

- I.1 Does (x, y) satisfy the inequality?
- I.2 Linear inequalities: solve for y
- I.3 Graph a linear inequality in the coordinate plane
- I.4 Linear inequalities: word problems
- I.5 Is (x, y) a solution to the system of inequalities?
- I.6 Solve systems of inequalities by graphing
- I.7 Find the vertices of a solution set
- I.8 Linear programming

## Matrices

- J.1 Matrix vocabulary
- J.2 Matrix operation rules
- J.3 Add and subtract matrices
- J.4 Multiply a matrix by a scalar
- J.5 Linear combinations of matrices
- J.6 Multiply two matrices
- J.7 Simplify matrix expressions
- J.8 Properties of matrices
- J.9 Solve matrix equations
- J.10 Determinant of a matrix
- J.11 Is a matrix invertible?
- J.12 Inverse of a matrix
- J.13 Identify inverse matrices
- J.14 Solve matrix equations using inverses

## Exponents

- K.1 Exponents with integer bases
- K.2 Exponents with decimal and fractional bases
- K.3 Negative exponents
- K.4 Multiplication with exponents
- K.5 Division with exponents
- K.6 Multiplication and division with exponents
- K.7 Power rule
- K.8 Evaluate expressions using properties of exponents
- K.9 Identify equivalent expressions involving exponents

## Logarithms

- L.1 Convert between exponential and logarithmic form: rational bases
- L.2 Evaluate logarithms
- L.3 Change of base formula
- L.4 Identify properties of logarithms
- L.5 Product property of logarithms
- L.6 Quotient property of logarithms
- L.7 Power property of logarithms
- L.8 Properties of logarithms: mixed review
- L.9 Evaluate logarithms: mixed review

## Exponential and logarithmic functions

- M.1 Domain and range of exponential and logarithmic functions
- M.2 Evaluate an exponential function
- M.3 Match exponential functions and graphs
- M.4 Solve exponential equations by factorising
- M.5 Solve exponential equations using common logarithms
- M.6 Solve logarithmic equations I
- M.7 Solve logarithmic equations II
- M.8 Exponential growth and decay: word problems

## Monomials

## Polynomials

- O.1 Polynomial vocabulary
- O.2 Model polynomials with algebra tiles
- O.3 Add and subtract polynomials using algebra tiles
- O.4 Add and subtract polynomials
- O.5 Add polynomials to find perimeter
- O.6 Multiply a polynomial by a monomial
- O.7 Multiply two polynomials using algebra tiles
- O.8 Multiply two binomials
- O.9 Multiply two binomials: special cases
- O.10 Multiply polynomials
- O.11 Write a polynomial from its roots
- O.12 Find the roots of factorised polynomials
- O.13 Conjugate roots
- O.14 Match polynomials and graphs

## Factorising

## Quadratic equations

- Q.1 Characteristics of quadratic functions
- Q.2 Complete a function table: quadratic functions
- Q.3 Transformations of quadratic functions
- Q.4 Find a quadratic function
- Q.5 Graph a quadratic function
- Q.6 Match quadratic functions and graphs
- Q.7 Solve a quadratic equation using square roots
- Q.8 Solve a quadratic equation using the zero product property
- Q.9 Solve a quadratic equation by factorising
- Q.10 Complete the square
- Q.11 Solve a quadratic equation by completing the square
- Q.12 Solve a quadratic equation using the quadratic formula
- Q.13 Using the discriminant

## Functions: linear, quadratic, exponential

- R.1 Identify linear, quadratic and exponential functions from graphs
- R.2 Identify linear, quadratic and exponential functions from tables
- R.3 Write linear, quadratic and exponential functions
- R.4 Linear functions over unit intervals
- R.5 Exponential functions over unit intervals
- R.6 Describe linear and exponential growth and decay

## Parabolas

- S.1 Identify the direction a parabola opens
- S.2 Find the vertex of a parabola
- S.3 Find the focus or directrix of a parabola
- S.4 Find the axis of symmetry of a parabola
- S.5 Write equations of parabolas in vertex form from graphs
- S.6 Write equations of parabolas in vertex form using properties
- S.7 Convert equations of parabolas from general to vertex form
- S.8 Find properties of a parabola from equations in general form
- S.9 Graph parabolas

## Hyperbolas

- T.1 Find the centre of a hyperbola
- T.2 Find the vertices of a hyperbola
- T.3 Find the length of the transverse or conjugate axes of a hyperbola
- T.4 Find the equations for the asymptotes of a hyperbola
- T.5 Find the foci of a hyperbola
- T.6 Write equations of hyperbolas in standard form from graphs
- T.7 Write equations of hyperbolas in standard form using properties
- T.8 Convert equations of hyperbolas from general to standard form
- T.9 Find properties of hyperbolas from equations in general form

## Rational exponents

## Radical functions and expressions

- V.1 Roots of integers
- V.2 Roots of rational numbers
- V.3 Find roots using a calculator
- V.4 Nth roots
- V.5 Simplify radical expressions
- V.6 Simplify radical expressions involving fractions
- V.7 Multiply radical expressions
- V.8 Add and subtract radical expressions
- V.9 Simplify radical expressions using the distributive property
- V.10 Simplify radical expressions: mixed review
- V.11 Domain and range of radical functions
- V.12 Solve radical equations

## Rational functions and expressions

- W.1 Rational functions: asymptotes and excluded values
- W.2 Simplify complex fractions
- W.3 Simplify rational expressions
- W.4 Multiply and divide rational expressions
- W.5 Divide polynomials
- W.6 Divide polynomials using synthetic division
- W.7 Add and subtract rational expressions
- W.8 Solve rational equations

## Two-dimensional figures

- X.1 Classify triangles
- X.2 Polygon vocabulary
- X.3 Triangle Angle-Sum Theorem
- X.4 Perimeter
- X.5 Area of triangles and quadrilaterals
- X.6 Area and perimeter in the coordinate plane I
- X.7 Area and perimeter in the coordinate plane II
- X.8 Area and circumference of circles
- X.9 Area of compound figures
- X.10 Area between two shapes
- X.11 Area and perimeter of similar figures

## Logic

## Introduction to congruent figures

## Congruent triangles

- AA.1 SSS and SAS Theorems
- AA.2 ASA and AAS Theorems
- AA.3 SSS, SAS, ASA and AAS Theorems
- AA.4 SSS Theorem in the coordinate plane
- AA.5 Congruency in isosceles and equilateral triangles
- AA.6 Hypotenuse-Leg Theorem
- AA.7 Proving triangles congruent by SSS and SAS
- AA.8 Proving triangles congruent by ASA and AAS
- AA.9 Proving triangles congruent by SSS, SAS, ASA and AAS
- AA.10 Proofs involving corresponding parts of congruent triangles
- AA.11 Proofs involving isosceles triangles

## Similarity

- BB.1 Identify similar figures
- BB.2 Similarity ratios
- BB.3 Similarity statements
- BB.4 Side lengths and angle measures in similar figures
- BB.5 Similar triangles and indirect measurement
- BB.6 Perimeters of similar figures
- BB.7 Similarity rules for triangles
- BB.8 Similar triangles and similarity transformations
- BB.9 Similarity of circles
- BB.10 Areas of similar figures
- BB.11 Proofs involving triangles I
- BB.12 Proofs involving triangles II

## Right triangles

## Trigonometry

- EE.1 Trigonometric ratios: sin, cos and tan
- EE.2 Trigonometric ratios: csc, sec and cot
- EE.3 Trigonometric ratios in similar right triangles
- EE.4 Find trigonometric ratios using the unit circle
- EE.5 Trigonometric functions of complementary angles
- EE.6 Sin, cos and tan of special angles
- EE.7 Csc, sec and cot of special angles
- EE.8 Find trigonometric functions using a calculator
- EE.9 Symmetry and periodicity of trigonometric functions
- EE.10 Inverses of sin, cos and tan
- EE.11 Inverses of csc, sec and cot
- EE.12 Solve trigonometric equations I
- EE.13 Solve trigonometric equations II
- EE.14 Trigonometric ratios: find a side length
- EE.15 Trigonometric ratios: find an angle measure
- EE.16 Solve a right triangle
- EE.17 Law of Sines
- EE.18 Law of Cosines
- EE.19 Solve a triangle
- EE.20 Area of a triangle: sine formula
- EE.21 Area of a triangle: Law of Sines

## Surface area and volume

- FF.1 Introduction to surface area and volume
- FF.2 Surface area of prisms and cylinders
- FF.3 Surface area of pyramids and cones
- FF.4 Volume of prisms and cylinders
- FF.5 Volume of pyramids and cones
- FF.6 Surface area and volume of spheres
- FF.7 Introduction to similar solids
- FF.8 Surface area and volume of similar solids
- FF.9 Surface area and volume review

## Circles

- GG.1 Parts of a circle
- GG.2 Central angles
- GG.3 Arc measure and arc length
- GG.4 Area of sectors
- GG.5 Circle measurements: mixed review
- GG.6 Arcs and chords
- GG.7 Tangent lines
- GG.8 Perimeter of polygons with an inscribed circle
- GG.9 Inscribed angles
- GG.10 Angles in inscribed right triangles
- GG.11 Angles in inscribed quadrilaterals

## Circles in the coordinate plane

- HH.1 Find the centre of a circle
- HH.2 Find the radius or diameter of a circle
- HH.3 Write equations of circles in standard form from graphs
- HH.4 Write equations of circles in standard form using properties
- HH.5 Convert equations of circles from general to standard form
- HH.6 Find properties of circles from equations in general form
- HH.7 Graph circles