Geometry and measures worksheet — GCSE Foundation

1.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

2.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.

3.Write down which one of these statements about quadrilaterals is true.

4.Each of these has an exact value. Write down the one whose value is the greatest.

5.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.

6.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

7.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

8.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

9.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

10.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

11.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

12.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.

13.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.

14.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

15.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.