Home / iGCSE Mathematics (0580) : C1.1 Identify and use natural numbers, integers, prime numbers,square and cube numbers, common factors, real numbers. iGCSE Style Questions Paper 3

iGCSE Mathematics (0580) : C1.1 Identify and use natural numbers, integers, prime numbers,square and cube numbers, common factors, real numbers. iGCSE Style Questions Paper 3

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

(a) 14,   17,   25,   27,   30,   36,   48

From the list, write down:

(i) the square root of 289,
(ii) a factor of 81,
(iii) a common multiple of 3 and 5.

(b) A, B and C are three consecutive whole numbers.

  • A is a prime number
  • B is a cube number
  • C is a square number
  • A + B + C is less than 40

Find A, B and C.

(c) Put one pair of brackets into each calculation to make them correct:

(i) \( 4 \times 3 + 7 \div 2 = 20 \)

(ii) \( 51 – 12 \div 3 + 6 = 19 \)

(d) Write down:

(i) the reciprocal of 8,
(ii) the value of \( 14^0 \).

(e) Calculate:

(i) \( 5^4 \)
(ii) \( \sqrt[3]{6859} \)
(iii) \( 16^{-\frac{1}{2}} \)

▶️ Answer/Explanation
Solution

1(a)(i): 17 (since 17 × 17 = 289)

1(a)(ii): 27 (because 81 ÷ 3 = 27)

1(a)(iii): 30 (divisible by both 3 and 5)

1(b): A = 7, B = 8, C = 9 (7 is prime, 8 is 2³, 9 is 3², and 7+8+9=24<40)

1(c)(i): \( 4 \times (3 + 7) \div 2 = 20 \)

1(c)(ii): \( (51 – 12) \div 3 + 6 = 19 \)

1(d)(i): \( \frac{1}{8} \) or 0.125 (reciprocal means 1 divided by the number)

1(d)(ii): 1 (any number to the power of 0 equals 1)

1(e)(i): 625 (5 × 5 × 5 × 5)

1(e)(ii): 19 (19 × 19 × 19 = 6859)

1(e)(iii): \( \frac{1}{4} \) (since \( 16^{-\frac{1}{2}} = \frac{1}{16^{\frac{1}{2}}} = \frac{1}{4} \))

Question

(a) 8 15 18 33 39 41 51 57 60 81
From this list, write down
(i) a factor of 54,
(ii) a multiple of 19,
(iii) a prime number.
(b) Write down the reciprocal of 64.
(c) (i) Write 4.81×10−3 as an ordinary number.
(ii) Write 75000 in standard form.
(iii) Calculate (6.3×102)/(7×10−3).
Write your answer in standard form.
(d) (i)
E = {2, 4, 8, 16, 32, 64}
A = {square numbers}
B = {cube numbers}
Use this information to complete the Venn diagram.

Venn diagram

(ii) On this Venn diagram, shade the region P∪Q.

Venn diagram
▶️ Answer/Explanation
Answer:
(a)(i) 18
(ii) 57
(iii) 41
(b) 1/64
(c)(i) 0.00481
(ii) 7.5×104
(iii) 9×104
(d)(i) Venn solution
(ii) Shaded Venn
Detailed Solution:
1. (a)(i) 18 is a factor of 54 because 54 ÷ 18 = 3 exactly.
2. (a)(ii) 57 is divisible by 19 (19×3=57).
3. (a)(iii) 41 is prime – only divisible by 1 and itself.
4. (b) Reciprocal of 64 is 1/64 (flip the number).
5. (c)(i) 4.81×10-3 = 0.00481 (move decimal left 3 places).
6. (c)(ii) 75000 = 7.5×104 (decimal after first digit, count remaining places).
7. (c)(iii) (6.3×102)/(7×10-3) = 0.9×105 = 9×104 (divide numbers, subtract exponents).
8. (d)(i) In set E: 4,16,64 are squares; 8,64 are cubes; 64 is both; 2,32 are neither.
9. (d)(ii) P∪Q means all elements in P or Q or both (shade both circles entirely).
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