Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.

1.

GCSE Higher

At depths below 900 metres, the temperature of the water in the sea is given by the formula:

$$T=\frac{4500}{x}$$

Where $$x$$ is the depth in metres and the temperature of the water is T °C.

(a) A fish swims downwards from a depth of 1000 metres to a depth of 1500 metres. How many degrees colder is the sea water at 1500m than 1000m?

(b) Roughly sketch the shape of a graph that shows that T is inversely proportional to $$x$$.

2.

GCSE Higher

The graph gives information about how the charging time in hours of an electric car relates to its range given as a distance in kilometres.

(a) Find the gradient of the graph.

(b) Interpret what the gradient of the graph represents.

3.

GCSE Higher

(a) Sketch a graph on the axes below left that shows that $$y$$ is directly proportional to $$x$$.

(b) Sketch the graph of $$y = -x^3$$ on the axes above right.

(c) It is possible to draw many rectangles that have area $$48 cm^2$$.

Draw a graph to show the relationship between length and width for rectangles with area $$48 cm^2$$ and sides less than $$50cm$$.

4.

GCSE Higher

At a constant temperature, the volume of a gas $$V$$ is inversely proportional to its pressure $$p$$. By what percentage will the pressure of a gas change if its volume increases by 15% ?

5.

GCSE Higher

The graph shows the temperature ($$T$$) of an unidentified flying object over a period of 10 seconds ($$t$$).

Use the graph to work out an estimate of the rate of decrease of temperature at 7 seconds. You must show your working.

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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.

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