AQA GCSE · Mathematics 8300

Structure and calculation: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Structure and calculation.

10 questions23 marksFree, no account

Question 1

1 mark

Which of the following mathematical statements is true?

Question 2

1 mark

Find the highest common factor (HCF) of 48 and 72.

Question 3

1 mark

Evaluate the expression \( \left( \frac{27}{8} \right)^{-\frac{2}{3}} \).

Question 4

1 mark

Calculate the following value using the correct order of operations:

\( 8 + 12 \div (6 - 2) \)

Question 5

1 mark

Calculate the value of the following expression using the priority of operations:

\( 5^2 - \sqrt{144} \div (7 - 4) \)

Question 6

3 marks

Using the correct order of operations, calculate the value of:
\(10 + 4 \times (3^2 - 5)\)

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

Using product notation, express 720 as a product of its prime factors.
Give your answer in index form.

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Work out the exact value of \(\left( \frac{125}{64} \right)^{-\frac{2}{3}}\).
Give your answer as a fraction in its simplest form.

Write your answer out first, then check it against the worked solution.

Question 9

3 marks

Calculate the following, showing your working at each step:

(a) \(4^3 - \sqrt{144}\)
(b) \(2 + 3 \times (10 - 2^2)\)

Write your answer out first, then check it against the worked solution.

Question 10

4 marks

A rectangular playground has a length of \( 45.4 \text{ m} \) and a width of \( 28.7 \text{ m} \). Both measurements are given to the nearest 10 cm.

(a) Write down the lower bound and upper bound for the length of the playground.
(b) Calculate the upper bound for the area of the playground. Give your answer to 2 decimal places.

Write your answer out first, then check it against the worked solution.

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