Geometry and measures worksheet — GCSE Foundation

1.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.

2.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.

3.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

4.How many vertices does a cuboid have?

5.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?

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

7.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.

8.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

9.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

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

11.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.

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

13.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.

14.Which of these correctly compares a 'line' with a 'line segment'?

15.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.