Cette série est proposée dans sa langue d’origine.

1. Notion: Numbers

   1. Evaluate (−8 + 3 × 4) ÷ 2.

   A−10B2C10D20
   Correction

   B. 2

   • Multiplication comes before addition: 3 × 4 = 12.
   • −8 + 12 = 4, then 4 ÷ 2 = 2.

2. Notion: Algebra

   2. Simplify (x² − 4) ÷ (x + 2).

   Ax + 2Bx − 2Cx² − 2Dx − 4
   Correction

   B. x − 2

   • Factorise the top as a difference of two squares: (x − 2)(x + 2).
   • Cancel (x + 2): the answer is x − 2.

3. Notion: Indices

   3. Solve 3^(2x) = 81.

   Ax = 1Bx = 2Cx = 4Dx = 27
   Correction

   B. x = 2

   • Write 81 as a power of 3: 81 = 3⁴.
   • So 2x = 4 and x = 2.

4. Notion: Commercial arithmetic

   4. A radio is marked at Ksh 4,000. A discount of 15% is given. Find the selling price.

   AKsh 600BKsh 3,400CKsh 3,850DKsh 4,600
   Correction

   B. Ksh 3,400

   • Discount = 15% of 4,000 = Ksh 600.
   • Selling price = 4,000 − 600 = Ksh 3,400.

5. Notion: Straight lines

   5. Find the gradient of the line 2y − 6x = 8.

   A−3B2C3D4
   Correction

   C. 3

   • Make y the subject: 2y = 6x + 8, so y = 3x + 4.
   • The gradient is the coefficient of x: 3.

6. Notion: Area

   6. Find the area of a triangle with base 10 cm and height 6 cm.

   A16 cm²B30 cm²C60 cm²D120 cm²
   Correction

   B. 30 cm²

   • Area = ½ × base × height.
   • ½ × 10 × 6 = 30 cm².

7. Notion: Geometry

   7. What is the sum of the interior angles of a hexagon?

   A360°B540°C720°D1080°
   Correction

   C. 720°

   • Sum of interior angles = (n − 2) × 180°.
   • A hexagon has 6 sides: (6 − 2) × 180° = 720°.

8. Notion: Logarithms

   8. Find x if log₂ x = 5.

   A10B25C32D64
   Correction

   C. 32

   • log₂ x = 5 means 2⁵ = x.
   • x = 32.

9. Notion: Rates

   9. Convert 72 km/h to metres per second.

   A7.2 m/sB20 m/sC36 m/sD259.2 m/s
   Correction

   B. 20 m/s

   • 72 km/h = 72,000 m in 3,600 s.
   • 72,000 ÷ 3,600 = 20 m/s. A quick rule is to divide by 3.6.

10. Notion: Volume

    10. Find the volume of a cylinder of radius 7 cm and height 10 cm. (Take π = 22/7)

    A440 cm³B1,540 cm³C3,080 cm³D4,620 cm³
    Correction

    B. 1,540 cm³

    • Volume = πr²h.
    • 22/7 × 7 × 7 × 10 = 22 × 7 × 10 = 1,540 cm³.