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Year 10 Maths practice questions

Five free Year 10 maths questions covering the big topics before senior maths, with the answer and full working for each.

Name ____________________Date ______________
  1. 1.Solve x² − 5x + 6 = 0.
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    Answer: x = 2 or x = 3
    Factorise: find two numbers that multiply to 6 and add to −5: −2 and −3. So (x − 2)(x − 3) = 0, which gives x = 2 or x = 3.
  2. 2.Solve the simultaneous equations x + y = 10 and x − y = 4.
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    Answer: x = 7, y = 3
    Add the equations: 2x = 14, so x = 7. Substitute into x + y = 10: 7 + y = 10, so y = 3.
  3. 3.In a right-angled triangle, the hypotenuse is 12 cm and one angle is 30°. How long is the side opposite the 30° angle?
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    Answer: 6 cm
    sin 30° = opposite ÷ hypotenuse, so opposite = 12 × sin 30° = 12 × 0.5 = 6 cm.
  4. 4.Simplify √50.
    25√25√22√510√5
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    Answer: 5√2
    50 = 25 × 2, so √50 = √25 × √2 = 5√2.
  5. 5.Two fair coins are tossed. What is the probability of getting two heads?
    1/21/31/43/4
    Show answer
    Answer: 1/4
    The outcomes are HH, HT, TH, TT: 4 equally likely outcomes, and 1 is HH. So the probability is 1/4.

Answers: Year 10 Maths practice questions

  1. x = 2 or x = 3. Factorise: find two numbers that multiply to 6 and add to −5: −2 and −3. So (x − 2)(x − 3) = 0, which gives x = 2 or x = 3.
  2. x = 7, y = 3. Add the equations: 2x = 14, so x = 7. Substitute into x + y = 10: 7 + y = 10, so y = 3.
  3. 6 cm. sin 30° = opposite ÷ hypotenuse, so opposite = 12 × sin 30° = 12 × 0.5 = 6 cm.
  4. 5√2. 50 = 25 × 2, so √50 = √25 × √2 = 5√2.
  5. 1/4. The outcomes are HH, HT, TH, TT: 4 equally likely outcomes, and 1 is HH. So the probability is 1/4.

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StudyHop is not affiliated with or endorsed by ACARA, NESA, the NSW Department of Education or any curriculum or exam authority. Names such as NAPLAN, Selective, OC, HSC and VCE describe the style of practice only. All questions here are original StudyHop questions, not official papers.