# Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

GCSE Higher

The following table shows corresponding values for two variables $$x$$ and $$y$$.

 x 1 2 3 4 y 5 $$1 \frac14$$ $$\frac{5}{9}$$ $$\frac{5}{16}$$

(a) If $$y$$ is inversely proportional to the square of $$x$$ find an equation for $$y$$ in terms of $$x$$.

(b) Find the positive value for $$x$$ when $$y = 20$$.

### 2.

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 $$50cm$$.

### 3.

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% ?

### 4.

GCSE Higher

Which of the following statements are correct if $$xy = c$$ and $$c$$ is a constant.

• (a) $$y$$ is directly proportional to $$x$$
• (b) $$y$$ is directly proportional to $$\frac{1}{x}$$
• (c) $$y$$ is inversely proportional to $$\frac{1}{x}$$
• (d) $$x$$ is directly proportional to $$y$$

### 5.

GCSE Higher

If $$a$$ is inversely proportional to $$b$$ and $$b$$ is directly proportional to $$c^2$$ find a formula for $$a$$ in terms of $$c$$ given that $$a=20$$ and $$c = 4$$ when $$b = 8$$.

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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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