هذه المجموعة متاحة بلغتها الأصلية.

1. الموضوع: Simplifying

   1. Simplify 3a + 5b − a + 2b.

   A4a + 7bB2a + 7bC2a + 3bD9ab
   الحل

   B. 2a + 7b

   • Collect the a terms: 3a − a = 2a.
   • Collect the b terms: 5b + 2b = 7b.

2. الموضوع: Expanding

   2. Expand 4(x − 3).

   A4x − 12B4x − 3C4x + 12Dx − 12
   الحل

   A. 4x − 12

   • Multiply each term in the bracket by 4.
   • 4 × x = 4x and 4 × −3 = −12.

3. الموضوع: Equations

   3. Solve 3x + 5 = 20.

   Ax = 15Bx = 7Cx = 25/3Dx = 5
   الحل

   D. x = 5

   • Subtract 5 from both sides: 3x = 15.
   • Divide by 3: x = 5.

4. الموضوع: Factorising

   4. Factorise fully 6x + 9.

   A3(2x + 9)B6(x + 9)C3(2x + 3)D3(x + 3)
   الحل

   C. 3(2x + 3)

   • The highest common factor of 6x and 9 is 3.
   • 6x + 9 = 3(2x + 3). Check by expanding.

5. الموضوع: Substitution

   5. Work out 2p + q² when p = 4 and q = −3.

   A−1B17C2D14
   الحل

   B. 17

   • 2p = 2 × 4 = 8.
   • q² = (−3)² = 9, because a negative squared is positive.
   • 8 + 9 = 17.

6. الموضوع: Sequences

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

   A3n + 2Bn + 3C3n + 5D5n + 3
   الحل

   A. 3n + 2

   • The terms go up by 3, so the nth term starts 3n.
   • When n = 1, 3n = 3, and the first term is 5, so add 2: 3n + 2.

7. الموضوع: Rearranging

   7. Make t the subject of v = u + at.

   At = v − u − aBt = (v + u)/aCt = a(v − u)Dt = (v − u)/a
   الحل

   D. t = (v − u)/a

   • Subtract u from both sides: v − u = at.
   • Divide by a: t = (v − u)/a.

8. الموضوع: Equations

   8. Solve 2(x + 4) = 18.

   Ax = 7Bx = 11Cx = 5Dx = 9
   الحل

   C. x = 5

   • Divide both sides by 2: x + 4 = 9.
   • Subtract 4: x = 5.

9. الموضوع: Inequalities

   9. Solve 4x − 1 < 11.

   Ax < 2.5Bx < 3Cx > 3Dx < 12
   الحل

   B. x < 3

   • Add 1 to both sides: 4x < 12.
   • Divide by 4: x < 3.

10. الموضوع: Straight-line graphs

    10. What is the gradient of the line y = 4x − 7?

    A4B−7C7D1/4
    الحل

    A. 4

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