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Year 12 Maths practice questions (HSC, VCE and QCE-style)

Five free Year 12 maths questions in the style of senior exams across Australia, with the answer and full working for each.

Name ____________________Date ______________
  1. 1.Differentiate y = 3x⁴ − 2x.
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    Answer: dy/dx = 12x³ − 2
    Bring the power down and reduce it by 1: 3 × 4x³ = 12x³. The derivative of −2x is −2.
  2. 2.Evaluate ∫₀² (2x + 3) dx.
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    Answer: 10
    The antiderivative is x² + 3x. At x = 2: 4 + 6 = 10. At x = 0: 0. So the answer is 10 − 0 = 10.
  3. 3.Solve 2ˣ = 32.
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    Answer: x = 5
    Write 32 as a power of 2: 32 = 2⁵. So x = 5.
  4. 4.Differentiate y = e²ˣ.
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    Answer: dy/dx = 2e²ˣ
    Chain rule: the derivative of e^(f(x)) is f′(x)e^(f(x)). Here f′(x) = 2.
  5. 5.A and B are independent events with P(A) = 0.3 and P(B) = 0.5. Find P(A and B).
    Show answer
    Answer: 0.15
    For independent events, P(A and B) = P(A) × P(B) = 0.3 × 0.5 = 0.15.

Answers: Year 12 Maths practice questions (HSC, VCE and QCE-style)

  1. dy/dx = 12x³ − 2. Bring the power down and reduce it by 1: 3 × 4x³ = 12x³. The derivative of −2x is −2.
  2. 10. The antiderivative is x² + 3x. At x = 2: 4 + 6 = 10. At x = 0: 0. So the answer is 10 − 0 = 10.
  3. x = 5. Write 32 as a power of 2: 32 = 2⁵. So x = 5.
  4. dy/dx = 2e²ˣ. Chain rule: the derivative of e^(f(x)) is f′(x)e^(f(x)). Here f′(x) = 2.
  5. 0.15. For independent events, P(A and B) = P(A) × P(B) = 0.3 × 0.5 = 0.15.

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