Table of Contents
IGCSE Mathematics – Questions and Answers | 20 Questions
Section A – Recall (Questions 1–6) #
1. Write down the value of $5^2$.
Answer: 25
$5^2 = 5 \times 5 = 25$
Revision note: Squaring means multiplying the number by itself. You must know all squares from $1^2$ to $15^2$ from memory.
2. Write down the value of $\sqrt{144}$.
Answer: 12
Ask: which number squared gives 144?
$12 \times 12 = 144$ ✓
$\sqrt{144} = 12$
Revision note: Finding a square root is the reverse of squaring. If you know your squares table, you can always find square roots quickly.
3. Write down the value of $3^3$.
Answer: 27
$3^3 = 3 \times 3 \times 3$
$= 9 \times 3 = 27$
Revision note: Cubing means multiplying the number by itself three times. You must know the cubes of 1, 2, 3, 4, 5, and 10.
4. Write down the value of $\sqrt[3]{125}$.
Answer: 5
Ask: which number cubed gives 125?
$5^3 = 5 \times 5 \times 5 = 125$ ✓
$\sqrt[3]{125} = 5$
Revision note: The cube root is the reverse of cubing. The symbol $\sqrt[3]{\phantom{x}}$ means cube root.
5. Write down the value of $12^2$.
Answer: 144
$12^2 = 12 \times 12 = 144$
Revision note: $12^2 = 144$ is a key square to memorise. Notice that $\sqrt{144} = 12$ — squaring and square roots are opposites.
6. Write down the value of $\sqrt{196}$.
Answer: 14
Ask: which number squared gives 196?
$14 \times 14 = 196$ ✓
$\sqrt{196} = 14$
Revision note: $14^2 = 196$ is one of the squares from 1–15 that you must know. Practice the full table regularly.
Section B – Application (Questions 7–16) #
7. Work out $7^2 – \sqrt{49}$.
Answer: 42
Step 1: $7^2 = 49$
Step 2: $\sqrt{49} = 7$
Step 3: $49 – 7 = 42$
Revision note: When a calculation has both a power and a root, work each one out separately first, then combine.
8. Work out $2^3 + 3^2$.
Answer: 17
Step 1: $2^3 = 2 \times 2 \times 2 = 8$
Step 2: $3^2 = 3 \times 3 = 9$
Step 3: $8 + 9 = 17$
Revision note: $2^3$ is a cube (multiply three times). $3^2$ is a square (multiply twice). Don’t mix them up.
9. Work out $\sqrt{169} \times \sqrt[3]{8}$.
Answer: 26
Step 1: $\sqrt{169} = 13$ (since $13^2 = 169$)
Step 2: $\sqrt[3]{8} = 2$ (since $2^3 = 8$)
Step 3: $13 \times 2 = 26$
Revision note: This question tests both your squares and cubes tables. Always work out each root separately before multiplying.
10. Work out $4^3 \div \sqrt{16}$.
Answer: 16
Step 1: $4^3 = 4 \times 4 \times 4 = 64$
Step 2: $\sqrt{16} = 4$
Step 3: $64 \div 4 = 16$
Revision note: Work out the power and the root first, then divide. Follow the order of operations.
11. Write down all the square numbers that are between 50 and 120.
Answer: 64, 81, 100
$7^2 = 49$ — too small (not between 50 and 120)
$8^2 = 64$ ✓
$9^2 = 81$ ✓
$10^2 = 100$ ✓
$11^2 = 121$ — too large (not between 50 and 120)
Revision note: “Between 50 and 120” means you do not include 50 or 120 themselves. Go through your squares table and check each one.
12. Work out $\sqrt[3]{1000} + 11^2$.
Answer: 131
Step 1: $\sqrt[3]{1000} = 10$ (since $10^3 = 1000$)
Step 2: $11^2 = 121$
Step 3: $10 + 121 = 131$
Revision note: $10^3 = 1000$ is one of the key cubes to memorise. So $\sqrt[3]{1000} = 10$.
13. Work out $2^6$.
Answer: 64
$2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 4 \times 4 \times 4$
$= 16 \times 4 = 64$
Revision note: For powers greater than 3, multiply step by step. Break it into smaller multiplications to avoid errors.
14. Work out $\sqrt[3]{27} \times 5^2$.
Answer: 75
Step 1: $\sqrt[3]{27} = 3$ (since $3^3 = 27$)
Step 2: $5^2 = 25$
Step 3: $3 \times 25 = 75$
Revision note: Work out the root and the power separately first, then multiply.
15. Work out $10^3 – 15^2$.
Answer: 775
Step 1: $10^3 = 1000$
Step 2: $15^2 = 225$
Step 3: $1000 – 225 = 775$
Revision note: $10^3 = 1000$ and $15^2 = 225$ are both key values to have memorised.
16. Work out $\sqrt{81} + \sqrt[3]{64}$.
Answer: 13
Step 1: $\sqrt{81} = 9$ (since $9^2 = 81$)
Step 2: $\sqrt[3]{64} = 4$ (since $4^3 = 64$)
Step 3: $9 + 4 = 13$
Revision note: Be careful not to confuse $\sqrt{\phantom{x}}$ (square root) with $\sqrt[3]{\phantom{x}}$ (cube root). The small 3 inside the root sign is the key difference.
Section C – Multi-Step (Questions 17–20) #
17. Work out $5^2 \times \sqrt[3]{8}$.
Answer: 50
Step 1: $5^2 = 25$
Step 2: $\sqrt[3]{8} = 2$ (since $2^3 = 8$)
Step 3: $25 \times 2 = 50$
Revision note: This is a direct example from the IGCSE syllabus. Always evaluate the power and root separately before combining.
18. Given that $x^2 = 225$, find the positive value of $x$.
Answer: $x = 15$
$x^2 = 225$
$x = \sqrt{225}$
Ask: which number squared gives 225?
$15 \times 15 = 225$ ✓
$x = 15$
Revision note: To find $x$ when you know $x^2$, you take the square root of both sides. Since the question asks for the positive value, the answer is $15$.
19. Work out $\dfrac{6^2 + \sqrt{64}}{\sqrt[3]{8}}$.
Answer: 22
Step 1: Work out the numerator (top):
$6^2 = 36$
$\sqrt{64} = 8$
$36 + 8 = 44$
Step 2: Work out the denominator (bottom):
$\sqrt[3]{8} = 2$
Step 3: Divide: $44 \div 2 = 22$
Revision note: For fraction calculations, fully work out the top and bottom separately first, then divide. This avoids errors.
20. Work out $13^2 – \sqrt[3]{1000} \times \sqrt{25}$.
Answer: 119
Step 1: $13^2 = 169$
Step 2: $\sqrt[3]{1000} = 10$
Step 3: $\sqrt{25} = 5$
Step 4: Multiply before subtracting (BIDMAS): $10 \times 5 = 50$
Step 5: $169 – 50 = 119$
Revision note: Remember BIDMAS — multiplication comes before subtraction. Work out $\sqrt[3]{1000} \times \sqrt{25}$ first, then subtract from $13^2$.
Final Revision Tips for Powers and Roots:
• Memorise squares 1–15 and cubes of 1, 2, 3, 4, 5, and 10 — many questions depend on this
• Powers and roots are opposites: squaring and square root cancel each other out
• Always work out powers and roots before adding, subtracting, or multiplying
• For fraction questions, simplify the top and bottom separately first
• Memorise squares 1–15 and cubes of 1, 2, 3, 4, 5, and 10 — many questions depend on this
• Powers and roots are opposites: squaring and square root cancel each other out
• Always work out powers and roots before adding, subtracting, or multiplying
• For fraction questions, simplify the top and bottom separately first
