هذه المجموعة متاحة بلغتها الأصلية.

1. الموضوع: Algebra

   1. Solve x² − 5x + 6 = 0.

   Ax = −2 or x = −3Bx = 2 or x = 3Cx = 1 or x = 6Dx = −1 or x = 6
   الحل

   B. x = 2 or x = 3

   • Factorise: (x − 2)(x − 3) = 0.
   • So x = 2 or x = 3.

2. الموضوع: Exponents

   2. Simplify 2^(x + 2) ÷ 2^x.

   A2B4C2^(2x + 2)Dx + 2
   الحل

   B. 4

   • Subtract the exponents: 2^(x + 2 − x) = 2².
   • 2² = 4.

3. الموضوع: Sequences

   3. For the arithmetic sequence 3, 7, 11, ..., find T₁₀.

   A39B40C43D36
   الحل

   A. 39

   • a = 3 and d = 4.
   • Tₙ = a + (n − 1)d, so T₁₀ = 3 + 9 × 4 = 39.

4. الموضوع: Series

   4. Find the sum of the first 20 terms of 3, 7, 11, ...

   A790B820C800D860
   الحل

   B. 820

   • Sₙ = n/2 [2a + (n − 1)d].
   • S₂₀ = 10 × (6 + 19 × 4) = 10 × 82 = 820.

5. الموضوع: Calculus

   5. If f(x) = 2x², find f′(x).

   A2xB4xC4x²Dx²
   الحل

   B. 4x

   • Bring the power down and reduce it by 1.
   • f′(x) = 2 × 2x = 4x.

6. الموضوع: Analytical geometry

   6. Find the gradient of the line through (1; 2) and (3; 8).

   A2B3C4D6
   الحل

   B. 3

   • m = (y₂ − y₁) ÷ (x₂ − x₁).
   • m = (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.

7. الموضوع: Trigonometry

   7. What is the exact value of sin 30°?

   A1/2B√3/2C√2/2D1
   الحل

   A. 1/2

   • sin 30° = 1/2 is a special angle value.
   • Learn it with sin 45° = √2/2 and sin 60° = √3/2.

8. الموضوع: Analytical geometry

   8. Find the midpoint of the line joining (2; 4) and (6; 10).

   A(4; 7)B(8; 14)C(2; 3)D(3; 7)
   الحل

   A. (4; 7)

   • Midpoint = ((x₁ + x₂)/2 ; (y₁ + y₂)/2).
   • ((2 + 6)/2 ; (4 + 10)/2) = (4; 7).

9. الموضوع: Finance

   9. R5,000 is invested at 10% per year compounded annually. What is it worth after 2 years?

   AR5,500BR6,000CR6,050DR6,100
   الحل

   C. R6,050

   • A = P(1 + i)ⁿ.
   • A = 5,000 × 1.1² = 5,000 × 1.21 = R6,050.

10. الموضوع: Sequences

    10. For the geometric sequence 2, 6, 18, ..., find T₅.

    A54B108C162D486
    الحل

    C. 162

    • a = 2 and r = 3.
    • Tₙ = arⁿ⁻¹, so T₅ = 2 × 3⁴ = 2 × 81 = 162.