Year 10 Maths practice questions

Lock in’s Year 10 Maths course has 7 units with 117 flashcards and 128 practice questions, plus timed exams built fresh each time.

• Algebraic techniques, indices and surdsExpanding binomial products; Factorising quadratic expressions; Algebraic fractions; Index laws, negative and fractional indices; Surds (10A)
• Linear, simultaneous and quadratic equationsLinear equations and inequalities; Simultaneous equations; Quadratic equations by factorising; Quadratic formula and completing the square; Formulas and problem solving
• Non-linear graphs, growth and decayParabolas; Exponential graphs and equations; Circles and hyperbolas; Compound interest; Depreciation, growth and decay models
• TrigonometryRight-angled trigonometry; Elevation, depression and bearings; Three-dimensional problems; The sine rule (10A); The cosine rule and area of a triangle (10A)
• Surface area and volumePrisms and cylinders; Pyramids and cones; Spheres and hemispheres; Composite solids; Units, capacity and accuracy
• Statistics and probabilityBox plots, quartiles and outliers; Standard deviation (10A); Bivariate data and lines of best fit; Conditional probability and independence; Multi-stage experiments; Statistical reports and bias
• Geometric reasoning, circles and networksCongruence and proof; Similarity; Polygons and deductive reasoning; Circle geometry (10A); Networks

Try each question before you open the answer. Written answers show what a full-marks response needs to include.

1. Question 1. Algebraic techniques, indices and surdsMultiple choice

   Expand (x − 4)(x + 4)

   1. Ax^² + 16
   2. Bx^² − 8
   3. Cx^² − 16
   4. Dx^² − 8x − 16
   Show answer

   C. x^² − 16

   Difference of two squares.

2. Question 2. Linear, simultaneous and quadratic equationsMultiple choice

   Solve 2(x − 5) = 3x + 1

   1. Ax = 6
   2. Bx = −9
   3. Cx = −11
   4. Dx = 11
   Show answer

   C. x = −11

   2x − 10 = 3x + 1.

3. Question 3. Linear, simultaneous and quadratic equations: quadratic formula and completing the square3 marks

   Solve 2x^² − 3x − 4 = 0 using the quadratic formula. Give exact answers and answers correct to 2 decimal places.

   Show model answer and marking criteria

   Model answer. a = 2, b = −3, c = −4. x = (3 ± √((−3)^² − 4 × 2 × (−4)))/(2 × 2) = (3 ± √41)/4. So x = (3 + √41)/4 ≈ 2.35 or x = (3 − √41)/4 ≈ −0.85.

   A full-marks answer:

   • Substitutes a = 2, b = −3, c = −4: x = (3 ± √(9 + 32))/4
   • Exact solutions x = (3 ± √41)/4
   • Decimal solutions x ≈ 2.35 and x ≈ −0.85
4. Question 4. Non-linear graphs, growth and decayMultiple choice

   $1000 at 10% p.a. compounded annually for 2 years grows to…

   1. A$1100
   2. B$1210
   3. C$1200
   4. D$1221
   Show answer

   B. $1210

   1000 × 1.1^².

5. Question 5. Non-linear graphs, growth and decay: compound interest3 marks

   $8000 is invested for 5 years at 4.8% p.a. compounded monthly. Find the final value and the interest earned.

   Show model answer and marking criteria

   Model answer. Rate per month = 4.8% ÷ 12 = 0.4% = 0.004 and there are 5 × 12 = 60 periods. A = 8000 × 1.004^⁶⁰ ≈ $10,165.13. Interest = $10,165.13 − $8,000 = $2,165.13.

   A full-marks answer:

   • r = 0.048 ÷ 12 = 0.004 and n = 60
   • A = 8000 × 1.004^⁶⁰ ≈ $10,165.13
   • Interest ≈ $2,165.13
6. Question 6. TrigonometryMultiple choice

   Area of a triangle with sides 6 and 7 and included angle 90°

   1. A13
   2. B42
   3. C21
   4. D84
   Show answer

   C. 21

   1/2 × 6 × 7 × 1.

Write every line of working, not just the answer. Most marks in a Maths exam are for method, so a correct final number with no working can lose marks, and a small slip with clear working usually keeps most of them. When you get one wrong, redo it from a blank page a day later.

In Lock in, every Maths topic has short notes, then flashcards that use spaced repetition: rate each card Again, Hard, Good or Easy and it comes back just before you would forget it. Practice questions come in three levels, Foundation, Standard and Complex. Three right in a row moves you up a level, and two wrong moves you back.

Press Study for me and the app builds a 15 to 20 minute session from the cards that are due, the mistakes that are due and questions on your weakest topics. Anything you get wrong comes back 1, 3 and 7 days later until you get it right. When an exam is close, sit a timed practice exam with AI marking.

More Year 10 subjects

Year 10 English practice questions, Year 10 Science practice questions, Year 10 History practice questions, Year 10 Geography practice questions, Year 10 PDHPE practice questions.

Maths in other years

Year 7 Maths practice questions, Year 8 Maths practice questions, Year 9 Maths practice questions.