Home / iGCSE Mathematics (0580) – C1.8 Standard form- Exam Style Questions Paper 3

iGCSE Mathematics (0580) - C1.8 Standard form- Exam Style Questions Paper 3- New Syllabus

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

Question

Calculate

$\frac{4.6 \times 10^3}{1.84 \times 10^5}$

Give your answer in standard form.

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

• C1.8 Standard form
▶️ Answer/Explanation

Divide the numerical parts and subtract the powers of $10$ separately:
$\frac{4.6}{1.84} = 2.5$
$\frac{10^3}{10^5} = 10^{3 – 5} = 10^{-2}$
Combine them to get the final answer in standard form.
✅ Answer: $2.5 \times 10^{-2}$

Question

Calculate $(5.6 \times 10^{-3}) \div (2.4 \times 10^{-5})$.
Write your answer in standard form.

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

• C1.8 Standard form
▶️ Answer/Explanation

You can directly input this into a scientific calculator or process the numbers and indices separately.
$(5.6 \div 2.4) \times 10^{-3 – (-5)}$
$= 2.333… \times 10^{2}$
Rounding to an appropriate standard form gives $2.33 \times 10^2$.
✅ Answer: $2.33 \times 10^2$

Question

(a) Work out \(48\div 3-5\times 2\).

(b) Insert one pair of brackets to make this statement correct.

3 + 2 × 12 – 4 = 19

(c) Write the following in order, starting with the smallest.

\(\frac{3}{4}\)  0.749  76%

(d) Find the value of: [1 each]

(i) \(\sqrt{265.69}\)

(ii) 83

(e) Write down the smallest prime number.

(f) Write down all the factors of 18.

(g) Write down a common factor of 16 and 72 that is greater than 2.

(h) Write \(\frac{28}{140}\) as a fraction in its simplest form.

(i) Jeff and his friends win a prize. Jeff’s share is \$160 which is \(\frac{5}{11}\) of the prize.

Work out the value of the prize.

▶️ Answer/Explanation
Solution

(a) Ans: 6

Using order of operations (BIDMAS):
\(48 ÷ 3 = 16\)
\(5 × 2 = 10\)
\(16 – 10 = 6\)

(b) Ans: 3 + 2 × (12 – 4) = 19

Brackets make the calculation:
\(12 – 4 = 8\)
\(2 × 8 = 16\)
\(3 + 16 = 19\)

(c) Ans: 0.749, \(\frac{3}{4}\), 76%

Convert all to decimals:
\(\frac{3}{4} = 0.75\)
76% = 0.76
Order: 0.749, 0.75, 0.76

(d)(i) Ans: 16.3

\(\sqrt{265.69} = 16.3\) (since \(16.3 × 16.3 = 265.69\))

(d)(ii) Ans: 512

\(8^3 = 8 × 8 × 8 = 512\)

(e) Ans: 2

2 is the smallest number with exactly two distinct factors (1 and itself).

(f) Ans: 1, 2, 3, 6, 9, 18

Numbers that divide 18 exactly: 1 × 18, 2 × 9, 3 × 6.

(g) Ans: 4 or 8

Common factors of 16 (1,2,4,8,16) and 72 (1,2,3,4,6,8,9,12,18,24,36,72) >2: 4, 8.

(h) Ans: \(\frac{1}{5}\)

Simplify \(\frac{28}{140}\): divide numerator and denominator by 28.

(i) Ans: \$352

Let total prize be \(x\):
\(\frac{5}{11}x = 160\)
\(x = 160 × \frac{11}{5} = 352\)

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