Geometry and measures worksheet — GCSE Foundation

1.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

2.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.

3.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

4.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

5.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

6.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

7.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

8.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?

9.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.

10.A submarine travels due south. What is the three-figure bearing for this direction?

11.An angle measures 108°. Write down the name given to an angle of this size.

12.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?

13.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

14.Work out the exact value of (cos 45°)² + (sin 45°)².

15.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?