Geometry and measures worksheet — GCSE Foundation

1.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

2.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

3.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

4.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

5.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.

6.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?

7.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

8.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

9.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?

10.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

11.Write down the exact value of tan 0°.

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

13.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

14.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

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