Cette série est proposée dans sa langue d’origine.

1. Notion: Percentages

   1. Work out 15% of 240.

   A24B36C16D40
   Correction

   B. 36

   • 10% of 240 = 24 and 5% = 12.
   • 15% = 24 + 12 = 36.

2. Notion: Algebra

   2. Simplify 6a + 3b − 2a + b.

   A4a + 4bB8a + 4bC4a + 2bD8ab
   Correction

   A. 4a + 4b

   • Collect the a terms: 6a − 2a = 4a.
   • Collect the b terms: 3b + b = 4b.

3. Notion: Equations

   3. Solve 4(x − 2) = 20.

   Ax = 3Bx = 5.5Cx = 7Dx = 22
   Correction

   C. x = 7

   • Divide both sides by 4: x − 2 = 5.
   • Add 2: x = 7.

4. Notion: Number

   4. Write 72 as a product of its prime factors.

   A2 × 36B2³ × 3²C2² × 3³D8 × 9
   Correction

   B. 2³ × 3²

   • 72 = 2 × 36 = 2 × 2 × 18 = 2 × 2 × 2 × 9 = 2 × 2 × 2 × 3 × 3.
   • In index form: 2³ × 3².

5. Notion: Sequences

   5. Find the nth term of the sequence 5, 8, 11, 14, ...

   An + 3B3n + 2C5nD3n + 5
   Correction

   B. 3n + 2

   • The sequence goes up by 3, so it starts with 3n.
   • When n = 1, 3n = 3, but the first term is 5, so add 2: 3n + 2.

6. Notion: Geometry

   6. Find the area of a circle with radius 3 cm, to 1 decimal place.

   A9.4 cm²B18.8 cm²C28.3 cm²D113.1 cm²
   Correction

   C. 28.3 cm²

   • Area = πr² = π × 3² = 9π.
   • 9π = 28.27..., which is 28.3 cm² to 1 decimal place.

7. Notion: Ratio

   7. Share £60 in the ratio 2 : 3.

   A£20 and £40B£24 and £36C£30 and £30D£12 and £48
   Correction

   B. £24 and £36

   • Total parts: 2 + 3 = 5, so one part is £60 ÷ 5 = £12.
   • 2 × 12 = £24 and 3 × 12 = £36.

8. Notion: Graphs

   8. What is the gradient of the line y = 4x − 1?

   A−1B1C4D−4
   Correction

   C. 4

   • In y = mx + c, m is the gradient.
   • Here m = 4.

9. Notion: Algebra

   9. Expand and simplify (x + 4)(x − 2).

   Ax² − 8Bx² + 2x − 8Cx² + 6x − 8Dx² − 2x + 8
   Correction

   B. x² + 2x − 8

   • x × x = x², x × (−2) = −2x, 4 × x = 4x, 4 × (−2) = −8.
   • Collect terms: x² + 2x − 8.

10. Notion: Probability

    10. The probability of picking a red counter is 0.35. What is the probability of not picking a red counter?

    A0.35B0.65C0.75D1.35
    Correction

    B. 0.65

    • Probabilities of an event and its opposite add up to 1.
    • 1 − 0.35 = 0.65.