## 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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