CAMBRIDGE IGCSE MATHS (0580)

Question 1: Write the following in order of size, smallest first.
\( 0.47, \frac{8}{17}, \sqrt{0.22}, \tan 25^\circ \)

Question 2: For this question, \(1 < x < 2\).
Write the following in order of size, smallest first:
\( \frac{5}{x}, 5x, \frac{x}{5}, x - 5 \)

Question 3: Use your calculator to find the value of:
\[ \frac{8.1^2 + 6.2^2 - 4.3^2}{2 \cdot 8.1 \cdot 6.2} \]

Question 4: Work out:
\[ 11.3139 - 2.28 \times \sqrt[3]{9^2} \]
Give your answer correct to one decimal place.

Question 5:
(a) Use your calculator to work out: \[ \sqrt{65} - 1.7^2 \] Write down all the numbers displayed on your calculator.

(b) Write your answer to part (a) correct to 2 significant figures.

Question 6:
(a) Use a calculator to find: \[ \sqrt{5 \frac{5}{24}} \]
(b) Use a calculator to find: \[ \frac{\cos 40^\circ}{7} \]

Question 7:
Write the following in order of size, smallest first:
\[ (1.5)^{\frac{2}{3}}, \quad \left(\frac{2}{3}\right)^{1.5}, \quad \left(\frac{2}{3}\right)^{-1.5}, \quad \left(-\frac{2}{3}\right)^{\frac{2}{3}} \]

Question 8:
Write the following numbers correct to one significant figure:
(a) 7682
(b) 0.07682

Question 9:
Find the value of: \[ \frac{7.2}{11.8 - 10.95} \]
Give your answer correct to 4 significant figures.

Question 10:
(a) Calculate: \[ \sqrt{5.7} - (1.03)^2 \]
Write down all the numbers displayed on your calculator.
(b) Write your answer to part (a) correct to 3 decimal places.

Question 11:
Calculate: \[ \frac{(5.27 - 0.93)}{(4.89 - 4.07)} \]
Give your answer correct to 4 significant figures.

Question 12:
Write the following in order of size, smallest first:

• 19%
• \(\frac{1}{5}\)
• \(\sqrt{0.038}\)
• \(\sin 11.4^\circ\)
• 0.719⁵

Question 13:
Use a calculator to work out the following:

• (a) \(3 \left( -4 \times 6^2 - 5 \right)\)
• (b) \(\sqrt{3} \times \tan 30^\circ + \sqrt{2} \times \sin 45^\circ\)

Question 14:
Write 3.5897 correct to 4 significant figures.

Question 15:
Calculate: \[ \sqrt[3]{16} \div 1.3^2 \]

Question 16:
(a) Write 569,000 correct to 2 significant figures.
(b) Write 569,000 in standard form.

Question 17:
(a) Write 209,802 correct to the nearest thousand.
(b) Write 4,123 correct to 3 significant figures.

Question 18:
Write 23.4571 correct to:
(a) 4 significant figures
(b) the nearest 10

Question 19:
Write 0.07164 correct to 2 significant figures.

Question 20:
Calculate: \[ \sqrt{120} + 3.8^2 - 25 \]

Question 21:
(a) Use a calculator to work out: \[ \frac{5^{0.4} - \sqrt{3}}{0.13 - 0.015} \] Write down all the digits in your calculator display.
(b) Write your answer to part (a) correct to 2 significant figures.

Question 22:
Write these numbers correct to 2 significant figures.
(a) 0.076499
(b) 10,100

Question 23:
Write the following in order of size, smallest first:
\[ \cos 100^\circ, \tan 100^\circ, \frac{1}{100}, 100^{-0.1} \]

Question 24:
Use your calculator to work out: \[ \sqrt{\frac{3}{4}} + 2^{-1} \] Give your answer correct to 2 decimal places.

Question 25: \[ p = \frac{4.8 \times 1.98276}{16.83} \] (a) In the spaces provided, write each number in this calculation correct to 1 significant figure.


(b) Use your answer to part (a) to estimate the value of p.