## 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 \(b = 8 \).

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.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.