Home / iGCSE Mathematics (0580) – C1.1 Types of number- Exam Style Questions Paper 3

iGCSE Mathematics (0580) - C1.1 Types of number- Exam Style Questions Paper 3- New Syllabus

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

Question

From the list of numbers, write down

(a) a square number

(b) the value of $39^0$

(c) a prime number.

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

• TOPIC C1.1 Number: Identify primes, prime factors, and square numbers (Core)
▶️ Answer/Explanation

(a)
A square number is the result of multiplying an integer by itself. In this list, $1 \times 1 = 1$ and $9 \times 9 = 81$.
✅ Answer: 1 or 81

(b)
Any non-zero number raised to the power of 0 is always equal to 1.
✅ Answer: 1

(c)
A prime number has only two distinct factors: 1 and itself. In this list, 59 is the only prime number because 39 (3×13) and 51 (3×17) can be divided by 3.
✅ Answer: 59

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 \( 16^{-\frac{1}{2}} = \frac{1}{16^{\frac{1}{2}}} = \frac{1}{4} \))

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