Home / iGCSE Mathematics (0580) – C1.3 Powers and roots- Exam Style Questions Paper 3

iGCSE Mathematics (0580) - C1.3 Powers and roots- Exam Style Questions Paper 3- New Syllabus

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

Question

(a) Find the value of

(i) $\sqrt{1.96}$

(ii) $17^3$

(iii) $-0.8 \times -1.2$

(b) Write these numbers in order, starting with the smallest.

$\frac{11}{19} \quad 58\% \quad \frac{27}{47} \quad 0.574$

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

• C1.3 Powers and roots (a)
• C1.5 Ordering (b)
▶️ Answer/Explanation

(a)
(i) Compute the square root directly: $\sqrt{1.96} = 1.4$
(ii) Calculate the cube: $17 \times 17 \times 17 = 4913$
(iii) Multiply the two negative decimals (result will be positive): $-0.8 \times -1.2 = 0.96$
✅ Answers: (i) $1.4$, (ii) $4913$, (iii) $0.96$

(b)
Convert all numbers to decimals for easy comparison:
$\frac{11}{19} \approx 0.5789$
$58\% = 0.58$
$\frac{27}{47} \approx 0.5744$
$0.574$
Comparing these: $0.574 < 0.5744 < 0.5789 < 0.58$.
✅ Answer: $0.574 < \frac{27}{47} < \frac{11}{19} < 58\%$

Question

(a) From the list of numbers: 6, 7, 10, 12, 18, 49, 63, write down:

(i) a factor of 21

(ii) a square number

(iii) a prime number

(b) Find the value of:

(i) the cube root of 1728

(ii) \(2^5\)

(iii) \(5^0\)

(iv) \(36^{\frac{1}{2}}\)

(c) Put one pair of brackets into this calculation to make it correct:

$$3 \times 2 – 6 – 2 \div 2 = 4$$

(d) Find the lowest common multiple (LCM) of 30 and 68.

▶️ Answer/Explanation
Solution

(a)(i) Ans: 7

Factors of 21: 1, 3, 7, 21. From the list, only 7 is present.

(a)(ii) Ans: 49

Square numbers in list: 49 (since \(7 \times 7 = 49\)).

(a)(iii) Ans: 7

Prime numbers in list: 7 (only divisible by 1 and itself).

(b)(i) Ans: 12

\(\sqrt[3]{1728} = 12\) because \(12 \times 12 \times 12 = 1728\).

(b)(ii) Ans: 32

\(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\).

(b)(iii) Ans: 1

Any non-zero number to the power of 0 is 1: \(5^0 = 1\).

(b)(iv) Ans: 6

\(36^{\frac{1}{2}} = \sqrt{36} = 6\).

(c) Ans: \(3 \times 2 – (6 – 2) \div 2 = 4\)

Working: \(3 \times 2 – (6 – 2) \div 2 = 6 – 4 \div 2 = 6 – 2 = 4\)

(d) Ans: 1020

Prime factors: \(30 = 2 \times 3 \times 5\) \(68 = 2^2 \times 17\) LCM = \(2^2 \times 3 \times 5 \times 17 = 1020\)

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