# 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 view a sample question. 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

## Solve equations

- D.1Model and solve equations using algebra tiles
- D.2Write and solve equations that represent diagrams
- D.3Solve one-step linear equations
- D.4Solve two-step linear equations
- D.5Solve advanced linear equations
- D.6Solve equations with variables on both sides
- D.7Identities and equations with no solutions
- D.8Solve linear equations: word problems
- D.9Solve linear equations: mixed review

## Single-variable inequalities

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

## Relations and functions

- F.1Relations: convert between tables, graphs, mappings and lists of points
- F.2Domain and range of relations
- F.3Identify independent and dependent variables
- F.4Identify functions
- F.5Complete a function table from an equation
- F.6Evaluate function rules
- F.7Graph a function
- F.8Write a function rule: word problems
- F.9Find points on a function graph
- F.10Write a rule for a function table
- F.11Find values using function graphs
- F.12Complete a function table from a graph

## Linear functions

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

## Simultaneous equations

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

## Inequalities and linear programming

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

## Matrices

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

## Exponents

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

## Logarithms

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

## Exponential and logarithmic functions

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

## Monomials

## Polynomials

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

## Factorising

## Quadratic equations

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

## Functions: linear, quadratic, exponential

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

## Parabolas

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

## Hyperbolas

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

## Rational exponents

## Radical functions and expressions

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

## Rational functions and expressions

## Two-dimensional figures

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

## Introduction to congruent figures

## Congruent triangles

## Similarity

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

## Right triangles

## Trigonometry

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

## Surface area and volume

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

## Circles

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

## Circles in the coordinate plane

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