هذه المجموعة متاحة بلغتها الأصلية.

1. الموضوع: Indices

   1. Simplify (2³ × 2⁴) ÷ 2⁵.

   A2B4C8D16
   الحل

   B. 4

   • Add the powers when multiplying: 2³ × 2⁴ = 2⁷.
   • Subtract when dividing: 2⁷ ÷ 2⁵ = 2².
   • 2² = 4.

2. الموضوع: Standard form

   2. Express 0.000356 in standard form.

   A3.56 × 10⁻⁴B3.56 × 10⁻³C35.6 × 10⁻⁵D3.56 × 10⁴
   الحل

   A. 3.56 × 10⁻⁴

   • Move the decimal point 4 places to the right to get 3.56.
   • Moving right for a small number gives a negative power: 3.56 × 10⁻⁴.

3. الموضوع: Linear equations

   3. Solve 3x − 7 = 2x + 5.

   Ax = 2Bx = 12Cx = −2Dx = −12
   الحل

   B. x = 12

   • Subtract 2x from both sides: x − 7 = 5.
   • Add 7 to both sides: x = 12.

4. الموضوع: Logarithms

   4. Evaluate log₁₀ 1000 + log₁₀ 0.01.

   A1B5C−1D0.5
   الحل

   A. 1

   • log₁₀ 1000 = 3 because 10³ = 1000.
   • log₁₀ 0.01 = −2 because 10⁻² = 0.01.
   • 3 + (−2) = 1.

5. الموضوع: Ratio and angles

   5. The angles of a triangle are in the ratio 2 : 3 : 4. Find the largest angle.

   A40°B60°C80°D100°
   الحل

   C. 80°

   • The angles of a triangle add up to 180°.
   • Total parts: 2 + 3 + 4 = 9, so one part is 180° ÷ 9 = 20°.
   • Largest angle: 4 × 20° = 80°.

6. الموضوع: Percentages

   6. A trader buys an item for ₦2,000 and sells it for ₦2,500. Find the percentage profit.

   A20%B25%C50%D500%
   الحل

   B. 25%

   • Profit = 2,500 − 2,000 = ₦500.
   • Percentage profit = 500 ÷ 2,000 × 100 = 25%.
   • Always divide by the cost price.

7. الموضوع: Statistics

   7. Find the mean of 4, 6, 8, 10 and 12.

   A6B8C10D40
   الحل

   B. 8

   • Sum: 4 + 6 + 8 + 10 + 12 = 40.
   • There are 5 numbers: 40 ÷ 5 = 8.

8. الموضوع: Factorisation

   8. Factorise x² − 9.

   A(x − 9)(x + 1)B(x − 3)²C(x − 3)(x + 3)Dx(x − 9)
   الحل

   C. (x − 3)(x + 3)

   • x² − 9 is a difference of two squares: x² − 3².
   • a² − b² = (a − b)(a + b), so x² − 9 = (x − 3)(x + 3).

9. الموضوع: Simple interest

   9. Calculate the simple interest on ₦5,000 at 4% per annum for 3 years.

   A₦200B₦600C₦5,600D₦6,000
   الحل

   B. ₦600

   • Simple interest = P × R × T ÷ 100.
   • 5,000 × 4 × 3 ÷ 100 = ₦600.

10. الموضوع: Probability

    10. A fair die is thrown once. Find the probability of getting a number greater than 4.

    A1/6B1/3C1/2D2/3
    الحل

    B. 1/3

    • Numbers greater than 4: 5 and 6, so 2 favourable outcomes.
    • Total outcomes: 6.
    • Probability = 2/6 = 1/3.