Find the median of 3, 8, 5, 12, 9, 7.

In order 3, 5, 7, 8, 9, 12, so 7.5

Year 10 · Australian Curriculum

Year 10 maths: what's covered and how to help

Year 10 finishes the core algebra of secondary school and sets up senior maths. Here's every Year 10 and 10A topic in the Australian Curriculum, where students get stuck, and free worksheets and tests for each one.

Year 10 worksheets Year 10 maths test Every topic ↓

What’s new in Year 10

Algebra comes together: simultaneous equations, solving and factorising quadratics, algebraic fractions and inequalities.
Trigonometry is applied to elevation, depression and bearings.
Statistics adds quartiles, box plots, scatterplots and two-way tables.
Year 10A adds the extension topics for the harder senior maths subjects: surds, logarithms, polynomials and the sine and cosine rules.

Where students get stuck

Factorising quadratics, especially with a negative constant. Practise it →
Choosing between elimination and substitution for simultaneous equations. Practise it →
Flipping the inequality sign when dividing by a negative. Practise it →
Algebraic fractions with different denominators. Practise it →

Every Year 10 maths topic

Grouped by strand, as in the Australian Curriculum. Each topic has worked examples, a question to try and a free worksheet.

Number

2 topics

Surds and fractional indices (10A)Master surds, irrational numbers and fractional indices, the foundation of senior Methods maths.
Logarithms and log laws (10A)Understanding the definition: log base b of x = y means b^y = x

Algebra

19 topics

Simultaneous equationsSubstitution, elimination, graphical: all three methods.
Quadratic equationsNull factor law, factorising, completing the square preview.
Quadratic factorisingExpand, factorise, difference of squares: the building blocks.
Linear equationsMulti-step equations, equations from formulas, applied problems.
Linear inequalitiesSolve, graph on number line, handle sign flips from negatives.
Algebraic fractionsAdd, subtract, multiply, divide: and simplify cleanly.
Exponential equationsSame-base solving, index manipulation, growth/decay setup.
Coordinate geometryParallel, perpendicular, equations of lines from conditions.
Compound interestGrowth, decay, compound interest in applied contexts.
Factorising by common factorSpot the common factor, write the brackets, check your answer.
Index laws with algebraMultiplying algebraic terms using the product law (aᵐ × aⁿ = aᵐ⁺ⁿ)
Substituting and rearranging formulasWork with real formulas, substitute values, and solve for any variable.
Linear equations with algebraic fractionsClear the fractions, solve with confidence.
Graphs of parabolas, circles, hyperbolas and exponentialsSketching parabolas from equations in the form y = ax² + bx + c and identifying the turning point, axis of symmetry and intercepts
Polynomials and factor theorem (10A)Identifying degree, leading coefficient and type of a polynomial
Exponential and logarithmic equations (10A)Converting between exponential and logarithmic form (e.g. 2³ = 8 ↔ log₂8 = 3)
Factorising non-monic quadratics (10A)Master factorising and solving quadratics with a leading coefficient, ready for senior Methods maths.
Function notation (10A)Read, write and evaluate functions with confidence before senior Methods maths begins.
Linear and non-linear simultaneous equations (10A)Solving two linear simultaneous equations by substitution and elimination

Measurement

5 topics

TrigonometryPythagoras + SOHCAHTOA in applied contexts, including bearings.
Surface area and volumeComposite objects, real-world capacity, optimisation flavours.
Direct and inverse proportionModel real-world relationships with proportion.
Logarithmic scalesRead, interpret and use log scales in real contexts.
Surface area and volume of pyramids, cones and spheres (10A)Tackle curved and pointed solids with confidence.

Space

6 topics

Geometric reasoning and proofsCongruence proofs using the four triangle tests (SSS, SAS, AAS, RHS)
NetworksIdentifying vertices, edges and the degree of each vertex
Circle theorems (10A)Prove and apply angle relationships in circles.
Sine rule, cosine rule and area (10A)Solve any triangle, not just right-angled ones.
Solving trigonometric equations (10A)Reading exact trigonometric values from the unit circle
Pythagoras and trigonometry in 3D (10A)Identifying right-angled triangles embedded in 3D solids

Statistics

4 topics

StatisticsQuartiles, IQR, boxplots, comparing distributions.
Scatterplots and lines of good fitRead, draw and interpret scatterplots.
Two-way tablesRead, construct and interpret two-way tables to explore relationships between categories.
Mean and standard deviation (10A)Calculate, interpret and investigate spread.

Probability

3 topics

ProbabilityConditional probability, independence, multi-step events.
Multi-step probability and tree diagramsMap out two- and three-step chance experiments, assign probabilities and test for independence.
Counting principles and arrangements (10A)Master factorial notation and systematic counting, the foundation of senior probability.

Quick check

7 Year 10 questions

One from each of these topics. Try each one, then open the answer.

Quadratic equations
Solve $(x - 5)(x + 2) = 0$ .
Answer
$x = 5$ or $x = -2$
Trigonometry
In a right-angled triangle the hypotenuse is $15$ cm and one angle is $40^\circ$ . Find the side opposite the angle, to 2 decimal places.
Answer
$15\sin 40^\circ \approx 9.64$ cm
Linear equations
Solve $7x - 4 = 3x + 16$ .
Answer
$x = 5$
Linear inequalities
Solve $x + 7 > 12$ .
Answer
$x > 5$
Algebraic fractions
Simplify $\dfrac{12y}{18}$ .
Answer
$\dfrac{2y}{3}$
Compound interest
Find the final amount when $8000 is invested at $5\%$ per annum, compounded annually, for $2$ years.
Answer
$8820
Statistics
Find the median of 3, 8, 5, 12, 9, 7.
Answer
In order 3, 5, 7, 8, 9, 12, so $7.5$

Try the full Year 10 sample test →

How to help with Year 10 maths at home

Year 10 results usually decide which senior maths a student can take, so close gaps from Years 8 and 9 early in the year.
If they're heading for the harder senior maths, make sure the Year 10A topics get proper practice, not just the core ones.
Before each test, do a timed practice exam and redo every question they got wrong.
Algebra is the foundation for everything in senior maths, so a little regular algebra practice pays off most.

Year 10 maths questions

What maths do Year 10 students learn in Australia?

Algebra (simultaneous equations, quadratics, algebraic fractions, inequalities, exponential equations and graphs), measurement (trigonometry, surface area and volume, proportion), space (geometric reasoning and networks), statistics (box plots, scatterplots and two-way tables) and probability (tree diagrams).

What is Year 10A maths?

Year 10A is optional extension content in the Australian Curriculum, for students heading to the harder senior maths courses. It includes surds, logarithms, polynomials, circle theorems, the sine and cosine rules and standard deviation.

How should my child prepare for senior maths?

Make sure Year 10 algebra is automatic: expanding, factorising, solving equations and working with indices. Those skills are assumed from the first week of the harder senior courses.

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.

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