Home / CIE iGCSE Maths C2.2 Algebraic manipulation – Exam Style Practice Questions- Paper 3

CIE iGCSE Maths C2.2 Algebraic manipulation - Exam Style Practice Questions- Paper 3- New Syllabus

IGCSE Mathematics(0580) Practice Questions Paper 3 - All Chapters

Question

(a) Factorise.
$8x^{2} – 2x$

(b) Expand the brackets and simplify.
$5(2m – 1) + 3(m + 7)$

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• TOPIC C2.2 Algebra and graphs: Algebraic manipulation, expansion and factorisation (Core)
▶️ Answer/Explanation

(a)
Identify the greatest shared numerical and literal factor between the terms $8x^2$ and $2x$. Both can be divided by $2x$:
$8x^2 – 2x = 2x(4x – 1)$
✅ Answer: $2x(4x – 1)$

(b)
First, expand each bracket by distributing the numerical values outside across the inner terms:
$5 \times 2m – 5 \times 1 = 10m – 5$
$3 \times m + 3 \times 7 = 3m + 21$
Combine them together:
$10m – 5 + 3m + 21$
Group matching variables and constant coefficients to simplify:
$(10m + 3m) + (-5 + 21) = 13m + 16$
✅ Answer: $13m + 16$

Question

(a) Write in figures six million three thousand and seventy six.

(b) (i) Work out the value of p when p = –0.6 ÷ 1.6.

(ii) Work out the value of q when q = –0.6 – 1.6.

(iii) Use one of the symbols >, <, ≥, ≤, = to complete this statement.

(c) Mount Robson in Canada has a height of 3950 metres, correct to the nearest 10 metres.
Complete the following statement about the height, h m, of Mount Robson.

(d) Calculate \(2\frac{1}{12}\div 1\frac{1}{4}.\)
Give your answer as a decimal, correct to 4 significant figures.

(e) (i) Write down the value of 80.

(ii) Work out 5–3.
Write your answer as a fraction.

(iii) Simplify the expression.
8x5 × 3x4

▶️ Answer/Explanation
Solution

(a) 6,003,076 – Six million = 6,000,000; three thousand = 3,000; seventy-six = 76.

(b)(i) –0.375 – \( p = \frac{-0.6}{1.6} = -0.375 \).

(b)(ii) –2.2 – \( q = -0.6 – 1.6 = -2.2 \).

(b)(iii) > – Since –0.375 > –2.2.

(c) 3945 ≤ h < 3955 – Nearest 10m means height rounds to 3950m, so range is 3945m to 3955m.

(d) 1.667 – Convert to improper fractions: \( \frac{25}{12} ÷ \frac{5}{4} = \frac{25}{12} × \frac{4}{5} = \frac{100}{60} ≈ 1.6667 \) (4 s.f.).

(e)(i) 1 – Any non-zero number to the power of 0 is 1.

(e)(ii) \(\frac{1}{125}\) – \( 5^{-3} = \frac{1}{5^3} = \frac{1}{125} \).

(e)(iii) 24x9 – Multiply coefficients: \(8 × 3 = 24\); add exponents: \(x^{5+4} = x^9\).

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