Geometry and measures worksheet — GCSE Foundation

1.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

2.Write down how many right angles a rectangle has.

3.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.

4.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

5.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

6.How many vertices does a cylinder have?

7.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

8.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

9.Write down the exact value of sin 0°.

10.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

11.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

12.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

13.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

14.A tank holds 3.2 m³ of water. Work out this volume in litres.

15.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.