Geometry and measures worksheet — GCSE Foundation

1.Write down the exact value of cos 30°.

2.In geometry, which of the following best describes a 'plane'?

3.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

4.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

5.A bus journey takes 2.5 hours. Work out how many minutes this is.

6.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).

7.A trapezium has parallel sides of 5 cm and 11 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

8.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

9.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.

10.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

11.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

12.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.

13.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

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

15.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.