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Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.


GCSE Higher

A number, \(n\), when rounded to two decimal places is 7.32

Express the error interval for \(n\) using inequalities.


GCSE Higher

The Glacier Ski Resort has this sign showing the safety limit for each cable car:


Eddie and some other people are in one of the cable cars. Their total mass is 570 kg to the nearest 5 kg

Eddie gets out. He has a mass of 74 kg to the nearest kg.

Is the cable car now safe to use? You must show your working.


GCSE Higher

Ayden is marking out the pitch for a ball game in a large field.

He measures the length of the pitch, which needs to be at least ten metres long, by pacing. Ayden knows that his stride length is 0.7 metres, rounded to the nearest tenth of a metre. Find the minimum number of strides Ayden will need to take to guarantee that the pitch is no shorter than ten metres long.


GCSE Higher

The height of a tree is 9 metres to the nearest metre.


(a) Complete the error interval for the height of the tree.

$$ ........ m \le height \lt ........ m $$

The height of a different tree is 7 metres to the nearest metre.

Mr Schneebly says "The sum of the heights of the two trees is 17 metres to the nearest metre."

(b) Give an example to show that he could be correct.


GCSE Higher

Ralph used his calculator to work out the value of C, the circumference of a circle. Unfortunately he put his banana down on his desk so that it covered most of the calculator screen. All that can be seen are the first two digits of the answer.

Banana on calculator


Complete the error interval for C

$$. . . . . . . . . . \le C \lt . . . . . . . . . .$$


GCSE Higher

Minerva's Revenge, the longest rollercoaster in the Funville Theme Park, takes 95 seconds (to the nearest 5 seconds) to complete one circuit of the 2280 metre long track.


(a) Mr Finklestein assumes that the track has been measured to the nearest 10m. What is the greatest possible speed of the rollercoaster train if his assumption is correct?

(b) Mr Finklestein finds out that in fact the track was measured to the nearest 5m. With this new information recalculate the greatest possible speed.

(c) Comment on the effect this new information had on the results of the calculations.


GCSE Higher

Calculate the upper bound for the length of an edge of the cube if the long diagonal (connecting opposite vertices) is 62 metres correct to the nearest metre. You must show all your working.



GCSE Higher

(a) Calculate the upper bound for the value of A giving your answer correct to 6 significant figures if:

$$ A = \frac{3b}{2c^2} $$

\(b = 7.4\) correct to 2 significant figures and \(c = 4.38\) correct to 3 significant figures.


(b)The lower bound for the value of A is 0.573376 correct to 6 significant figures.

By considering bounds, write down the value of A to a suitable degree of accuracy. You must give a reason for your answer.

If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.


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