1. Expand: (2x − 3)(x + 5). (3 marks)
Edexcel GCSEworksheethard
Higher Algebra Manipulation
Expanding products, factorising quadratics, and algebraic fractions — GCSE Higher.
Mathematics · Algebra · Higher · 35 mins · 24 marks · 10 questions
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Expand: (2x − 3)(x + 5). (3 marks)
Factorise: x² − 7x + 12. (2 marks)
Simplify: (x² − 9)/(x − 3) for x ≠ 3. (2 marks)
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2. Factorise: x² − 7x + 12. (2 marks)
- (x − 3)(x − 4)
- (x − 2)(x − 6)
- (x + 3)(x + 4)
- (x − 1)(x − 12)
3. Simplify: (x² − 9)/(x − 3) for x ≠ 3. (2 marks)
4. Solve: x² − 4x − 5 = 0. (3 marks)
5. Complete the square: x² − 8x + 10 = (x − 4)² + k. Find k. (2 marks)
6. The discriminant of 2x² − 3x + 1 is: (2 marks)
- 1
- 9
- 17
- −7
7. Simplify: (3x/4) × (8/9x) for x ≠ 0. (2 marks)
8. Solve simultaneously: x + y = 7 and 2x − y = 5. (3 marks)
9. Expand fully: (x − 2)³. (3 marks)
10. If f(x) = x² − 2x, find f(−3). (2 marks)
- 3
- 15
- 9
- −15
Show answer key
- 1. 2x² + 7x − 15
- 2. (x − 3)(x − 4)
- 3. x + 3
- 4. x = 5 or x = −1
- 5. −6
- 6. 1
- 7. 2/3
- 8. x = 4, y = 3
- 9. x³ − 6x² + 12x − 8
- 10. 15
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