Algebra

Factorise x² + 5x + 6.

• A(x + 2)(x + 3)✓
• B(x + 1)(x + 6)
• C(x − 2)(x − 3)
• D(x + 6)(x − 1)

Answer: Find two numbers that multiply to 6 and add to 5: 2 and 3. So x² + 5x + 6 = (x + 2)(x + 3).

Solve x² = 49.

• Ax = 7 only
• Bx = 7 or x = −7✓
• Cx = 24.5
• Dx = ±49

Answer: Square rooting gives two solutions: x = 7 or x = −7 (since (−7)² = 49).

Expand and simplify (x + 3)(x − 2).

• Ax² + x − 6✓
• Bx² − 6
• Cx² + 5x − 6
• Dx² − x − 6

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

Solve the simultaneous equations x + y = 10 and x − y = 4.

• Ax = 7, y = 3✓
• Bx = 3, y = 7
• Cx = 6, y = 4
• Dx = 5, y = 5

Answer: Add the equations: 2x = 14, so x = 7. Then y = 10 − 7 = 3.

Make x the subject of y = 3x − 5.

• Ax = (y + 5)/3✓
• Bx = (y − 5)/3
• Cx = 3y − 5
• Dx = (y + 5)·3

Answer: Add 5: y + 5 = 3x. Divide by 3: x = (y + 5)/3.

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

• A−7
• B4✓
• C7
• D−4

Answer: In y = mx + c, the gradient m is the coefficient of x, which is 4.

Solve the inequality 2x + 1 > 9.

• Ax > 4✓
• Bx < 4
• Cx > 5
• Dx > 8

Answer: Subtract 1: 2x > 8. Divide by 2: x > 4.

The nth term of a sequence is 3n + 2. What is the 10th term?

• A30
• B32✓
• C35
• D23

Answer: Substitute n = 10: 3(10) + 2 = 32.

Solve 3(x − 2) = 2x + 4.

• Ax = 10✓
• Bx = 2
• Cx = −10
• Dx = 6

Answer: 3x − 6 = 2x + 4 → x = 10.

Simplify (3x²y)(2xy³).

• A6x³y⁴✓
• B5x³y⁴
• C6x²y³
• D6x³y³

Answer: Multiply coefficients (3×2=6) and add indices: x²·x = x³, y·y³ = y⁴, giving 6x³y⁴.

Solve the quadratic x² − 5x + 6 = 0.

• Ax = 2 or 3✓
• Bx = −2 or −3
• Cx = 1 or 6
• Dx = 5 or 6

Answer: Factorise to (x − 2)(x − 3) = 0, so x = 2 or x = 3.