Algebra

Simplify 3a + 2b + a - b.

• A4a + b✓
• B3a + 2b
• C5ab
• D4a + 3b

Answer: Collect like terms: 3a + a = 4a, and 2b - b = b. So 3a + 2b + a - b = 4a + b.

Expand 3(x + 4).

• A3x + 4
• B3x + 12✓
• Cx + 12
• D3x + 7

Answer: Multiply each term inside the bracket by 3: 3 × x + 3 × 4 = 3x + 12.

Solve x + 5 = 12.

• Ax = 17
• Bx = 7✓
• Cx = -7
• Dx = 2.4

Answer: Subtract 5 from both sides: x + 5 - 5 = 12 - 5, so x = 7.

Solve 2x = 16.

• Ax = 8✓
• Bx = 18
• Cx = 14
• Dx = 32

Answer: Divide both sides by 2: 2x ÷ 2 = 16 ÷ 2, so x = 8.

If y = 3x + 2, what is y when x = 4?

• A10
• B12
• C14✓
• D9

Answer: Substitute x = 4: y = 3(4) + 2 = 12 + 2 = 14.

Simplify 5x × 2y.

• A7xy
• B10xy✓
• C10x + y
• D5xy × 2

Answer: 5x × 2y = (5 × 2) × (x × y) = 10xy.

Expand 2(3x - 5).

• A6x - 5
• B6x - 10✓
• C5x - 5
• D3x - 10

Answer: 2 × 3x = 6x, and 2 × (-5) = -10. So 2(3x - 5) = 6x - 10.

Solve 3x - 2 = 10.

• Ax = 4✓
• Bx = 2.67
• Cx = 8
• Dx = 12

Answer: Add 2 to both sides: 3x = 12. Divide by 3: x = 4.

Factorise 6a + 9.

• A3(2a + 3)✓
• B3(a + 3)
• C6(a + 1.5)
• D2(3a + 4.5)

Answer: Find the highest common factor: HCF(6, 9) = 3. So 6a + 9 = 3(2a + 3).

What is the next term in the sequence 2, 5, 8, 11, ...?

• A12
• B13
• C14✓
• D15

Answer: The sequence increases by 3 each time (2→5, 5→8, 8→11). So the next term is 11 + 3 = 14.

What is the nth term formula for the sequence 3, 6, 9, 12, ...?

• An + 3
• B3n✓
• Cn + 2
• D3n + 3

Answer: Each term is 3 times its position: 1st term = 3(1) = 3, 2nd term = 3(2) = 6, 3rd term = 3(3) = 9. The nth term is 3n.

Expand (x + 2)(x + 3).

• Ax² + 5x + 6✓
• Bx² + 6x + 5
• Cx² + 6
• D2x + 5

Answer: x(x+3) + 2(x+3) = x² + 3x + 2x + 6 = x² + 5x + 6.