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SHS Core Mathematics · Year 2

Number Sets (Advanced) practice questions

Surds (pure, mixed, compound), rationalisation, the laws of indices and logarithms, and modular arithmetic, with their applications in banking, population growth and calendar/duty-roster systems.

34 questions in this topic: 11 recall, 14 applying skills and concepts, 8 strategic thinking and 1 extended thinking. Every one carries a written explanation.

Sample questions

5 of 34 questions in this topic. Sign up to answer them and see the explanations.

  1. Question 1Strategic thinking

    You invest GH¢1000 at 10% annual interest compounded yearly for 3 years, using A = P(1+r)ᵗ. This gives A = 1000(1.1)³ = 1000 × 1.331, so the final amount is

    • aGH¢1331
    • bGH¢1300
    • cGH¢1100
    • dGH¢1000
  2. Question 2Strategic thinking

    Given log₂3 = 1.58 and log₂5 = 2.32, using the product law log₂15 = log₂(3×5) = log₂3 + log₂5, the value of log₂15 is

    • a3.90
    • b0.74
    • c5.48
    • d1.58
  3. Question 3Extended thinking

    Simplifying 3√8 + 2√18 − 6√2 requires first rewriting √8 = 2√2 and √18 = 3√2, giving 6√2 + 6√2 − 6√2, which equals

    • a6√2
    • b18√2
    • c0
    • d12√2
  4. Question 4Skills & concepts

    Like surds (surds with the same radicand, such as √6 and √6) can be added or subtracted much like algebraic like terms; for example, 3√6 + 6√6 equals

    • a9√6
    • b9√12
    • c18√6
    • d3√12
  5. Question 5Skills & concepts

    Simplifying √32 by factoring out the largest perfect square (16) gives √32 = √16 × √2, which equals

    • a4√2
    • b2√16
    • c16√2
    • d8√2

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