Geometry and measures worksheet — GCSE Foundation

1.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

2.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

3.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

4.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.

5.How many edges does a cube have?

6.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

7.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

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

9.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.

10.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

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

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

13.Work out the exact value of cos 0° − sin 30°.

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

15.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?