Geometry and measures worksheet — GCSE Foundation

1.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?

2.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

3.Which of these describes an obtuse angle?

4.How many edges does a triangular prism have?

5.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?

6.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

7.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

8.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.

9.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).

10.The diagram shows a prism resting on a table. Which shape is its front elevation, the view looking at it from directly in front?

11.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

12.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

13.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

14.Which of the following correctly describes what it means for two lines to be perpendicular?

15.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.