Geometry and measures worksheet — GCSE Foundation

1.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

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

3.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?

4.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

5.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.

6.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

7.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

8.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

9.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

10.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

11.How many vertices does a square-based pyramid have?

12.What does the statement AB = CD mean, where A, B, C and D are all points?

13.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

14.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

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