Year 10 maths questions with answers, including 10A and optional content

The daily Year 10 Maths (10A) paper has 8 original questions worth 25 to 35 marks. It covers quadratics, simultaneous equations, inequalities, indices and surds, straight-line and quadratic graphs, Pythagoras and trigonometry, similarity, proportion, probability, statistics and circle theorems. Skip its vectors questions: vectors aren't in the Australian Curriculum for Year 10.

Year 10 maths and 10A in each state

• Australian Curriculum (version 9.0): Year 10 covers number, algebra, measurement, space, statistics and probability. ACARA's optional content for students heading to Mathematical Methods adds surds and fractional indices, completing the square and the quadratic formula, sine and cosine graphs, logarithms, rates of change, circle geometry and measures of spread.
• Victoria: Mathematics Version 2.0 runs from Foundation to Level 10A. Level 10A is extension content with no achievement standard of its own.
• NSW: the Mathematics K to 10 Syllabus (2022), taught in Years 7 to 10 from 2024, splits Stage 5 into a mandatory Core and Paths that add further algebra, graphing, geometric proof, networks, statistics and probability. Year 10 grades go on your Record of School Achievement (RoSA).

There is no state-wide Year 10 maths exam in NSW or Victoria: your school sets its own end-of-year exam. If you plan to take Maths Advanced or Maths Methods in Year 11, the 10A questions below are the ones to master.

Year 10 maths questions with answers

We wrote these for this page. Try each before you read the answer.

1. The quadratic formula (10A)

Question: Solve 2x² − 3x − 4 = 0, giving answers to 2 decimal places. Answer: a = 2, b = −3 and c = −4, so the discriminant is b² − 4ac = 9 + 32 = 41. It is positive and not a perfect square, so there are two irrational roots: x = (3 ± √41) ÷ 4, which gives x ≈ 2.35 or x ≈ −0.85.

Try a quadratic formula question in our Algebra course, then press Mark.

2. Surds (10A)

Question: Simplify √72 + √50 − √8, then rationalise the denominator of 6 ÷ √3. Answer: √72 = 6√2, √50 = 5√2 and √8 = 2√2, so the sum is 9√2. Multiply 6 ÷ √3 by √3 ÷ √3 to get 6√3 ÷ 3 = 2√3.

3. Simultaneous equations

Question: Solve 3x + 2y = 16 and x − y = 2. Answer: from the second equation, x = y + 2. Substitute: 3(y + 2) + 2y = 16, so 5y = 10, y = 2 and x = 4. Check in the first: 12 + 4 = 16. The Simultaneous Equations Calculator shows both lines crossing at (4, 2).

4. Trigonometry

Question: Standing 40 m from the foot of a tree, you measure the angle of elevation to its top as 32°. How tall is the tree? Answer: you know the side adjacent to the angle and want the opposite side, so use tan: height = 40 × tan 32° = 25.0 m (to 1 decimal place). Check it with the Trigonometry Calculator.

5. Probability without replacement

Question: A bag holds 5 red and 3 blue counters. Two are taken out without replacement. Find the probability that both are red, and that they are different colours. Answer: P(both red) = 5/8 × 4/7 = 20/56 = 5/14. For different colours, add red then blue and blue then red: 5/8 × 3/7 + 3/8 × 5/7 = 30/56 = 15/28. A tree diagram keeps the second-draw fractions straight.

6. Circle geometry (10A)

Question: O is the centre of the circle. The angle APB at the circumference is 35°. Find the angle AOB at the centre. Answer: an angle at the centre is double any angle at the circumference that stands on the same arc, so ∠AOB = 2 × 35° = 70°. Triangle AOB is isosceles (OA and OB are radii), so each base angle is (180° − 70°) ÷ 2 = 55°.

Use the daily paper as a practice exam

1. Open today's Year 10 Maths paper and work to the suggested time, 35 to 40 minutes.
2. Skip any vectors question.
3. Show every step: most marks in a written exam are for working.
4. Mark it and list the topics you lost marks on, then redo the matching question on this page.

Common Year 10 maths mistakes

• Dropping the negative sign on b in the quadratic formula: −b with b = −3 is +3.
• Adding surds that aren't alike. √2 + √3 is not √5; simplify first and only combine like surds.
• Keeping the same denominator on the second draw of a without-replacement probability.
• Using sin when the side is adjacent. Label opposite, adjacent and hypotenuse from the angle first.
• Halving instead of doubling between the angle at the circumference and the angle at the centre.

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