Algebraic Manipulation (Copy)

IGCSE Mathematics 0580 – Algebraic Expressions Practice Exam
Divided into Paper 1 (Non-Calculator) and Paper 2 (Calculator Allowed)
Full Worked Solutions Provided

PAPER 1 – NON-CALCULATOR SECTION

Simplify Expressions

Q1. Simplify:
5x + 7y – 3x + 2y

Solution:
Group like terms:
(5x – 3x) + (7y + 2y) = 2x + 9y
Answer: 2x + 9y

Q2. Simplify:
8a² – 3a + 5a² + 7a

Solution:
(8a² + 5a²) + (–3a + 7a) = 13a² + 4a
Answer: 13a² + 4a

Expand Single Bracket

Q3. Expand:
4(x – 5)

Solution:
4 × x = 4x
4 × (–5) = –20
Answer: 4x – 20

Q4. Expand:
–3(2a – 7)

Solution:
–3 × 2a = –6a
–3 × (–7) = +21
Answer: –6a + 21

Expand Two Brackets

Q5. Expand:
(x + 3)(x – 2)

Solution:
First: x × x = x²
Outside: x × (–2) = –2x
Inside: 3 × x = 3x
Last: 3 × (–2) = –6
Combine: x² + (–2x + 3x) – 6 = x² + x – 6
Answer: x² + x – 6

Q6. Expand:
(2y – 5)(y + 4)

Solution:
First: 2y × y = 2y²
Outside: 2y × 4 = 8y
Inside: (–5) × y = –5y
Last: (–5) × 4 = –20
Combine: 2y² + (8y – 5y) – 20 = 2y² + 3y – 20
Answer: 2y² + 3y – 20

Factorise by Taking Out Common Factors

Q7. Factorise:
6x + 9

Solution:
Common factor = 3
3(2x + 3)
Answer: 3(2x + 3)

Q8. Factorise:
10m² – 15m

Solution:
Common factor = 5m
5m(2m – 3)
Answer: 5m(2m – 3)

PAPER 2 – CALCULATOR ALLOWED SECTION

Simplify Expressions

Q9. Simplify:
12a – 7b + 4a + 3b

Solution:
(12a + 4a) + (–7b + 3b) = 16a – 4b
Answer: 16a – 4b

Q10. Simplify:
3x² + 2xy – 5x² + 6xy

Solution:
(3x² – 5x²) + (2xy + 6xy) = –2x² + 8xy
Answer: –2x² + 8xy

Expand Single Bracket

Q11. Expand:
5(2x – 7y)

Solution:
5 × 2x = 10x
5 × (–7y) = –35y
Answer: 10x – 35y

Q12. Expand:
–7(x – 3)

Solution:
–7 × x = –7x
–7 × (–3) = +21
Answer: –7x + 21

Expand Two Brackets

Q13. Expand:
(3x + 2)(x – 5)

Solution:
First: 3x × x = 3x²
Outside: 3x × (–5) = –15x
Inside: 2 × x = 2x
Last: 2 × (–5) = –10
Combine: 3x² + (–15x + 2x) – 10 = 3x² – 13x – 10
Answer: 3x² – 13x – 10

Q14. Expand:
(2a – 3)(4a + 5)

Solution:
First: 2a × 4a = 8a²
Outside: 2a × 5 = 10a
Inside: (–3) × 4a = –12a
Last: (–3) × 5 = –15
Combine: 8a² + (10a – 12a) – 15 = 8a² – 2a – 15
Answer: 8a² – 2a – 15

Factorise by Taking Out Common Factors

Q15. Factorise:
14x – 21y

Solution:
Common factor = 7
7(2x – 3y)
Answer: 7(2x – 3y)

Q16. Factorise:
18p² – 24pq

Solution:
Common factor = 6p
6p(3p – 4q)
Answer: 6p(3p – 4q)

Q17. Factorise Fully:
4x² + 6xy

Solution:
Common factor = 2x
2x(2x + 3y)
Answer: 2x(2x + 3y)

Q18. Expand and Simplify:
(2x + 3)(x – 2)

Solution:
First: 2x × x = 2x²
Outside: 2x × (–2) = –4x
Inside: 3 × x = 3x
Last: 3 × (–2) = –6
Combine: 2x² + (–4x + 3x) – 6 = 2x² – x – 6
Answer: 2x² – x – 6

Q19. Factorise Fully:
15x² – 20x

Solution:
Common factor = 5x
5x(3x – 4)
Answer: 5x(3x – 4)

Q20. Expand:
(x – 5)(x + 7)

Solution:
First: x × x = x²
Outside: x × 7 = 7x
Inside: (–5) × x = –5x
Last: (–5) × 7 = –35
Combine: x² + (7x – 5x) – 35 = x² + 2x – 35
Answer: x² + 2x – 35