Unit 9

The graph below shows the temperature (in °C) of a liquid as it cools over time.

Write down the algebraic equation for the graph that results from stretching by a scale factor of 4 in the y-direction.

Find the gradient and y-intercept of the straight line with equation .

Below are graphs of , , and .

Explain how each of the following transformations affects the graph of :

(i) Replacing x with x-1

(ii) Replacing x with x+3

The diagram below shows a cuboid ABCDEFGH with AB = 4 cm, BC = 5 cm, and BF = 12 cm.

Work out the length of the space diagonal AE.

A pyramid has a square base PQRS, with PQ = QR = 6 cm. The vertex T is vertically above the centre of the base TSQ. The height VT = 9 cm.

Calculate the length of the edge VP from the vertex to a base corner.

A cuboid has dimensions 6 cm × 8 cm × 10 cm. Using Pythagoras’ theorem, explain how to find the length of its longest diagonal.

The diagram shows a rectangular box. The base AB = 9 cm, BC = 5 cm, and the height is BE = 12 cm. Point F is directly above C.

For a square-based pyramid with base edge of 10 cm and height of 15 cm (vertex directly above the centre), work out the vertical angle (angle between a side face and the base).

A right triangular prism has end triangle sides 3 cm, 4 cm and 5 cm, and height (length perpendicular to end) of 10 cm.

Calculate the length of the longest diagonal from one vertex to the opposite vertex on the other end.