Geometry and measures worksheet — GCSE Foundation

1.A kitchen scale is marked in equal divisions of 20 g. The pointer rests three divisions past the 400 g mark. Work out the reading on the scale.

2.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

3.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

4.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.

5.In this question, a curved surface counts as a face. How many faces does a cone have?

6.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.

7.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.

8.A parallelogram has an area of 136 cm² and a base of 17 cm. Work out the perpendicular height of the parallelogram.

9.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

10.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

11.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?

12.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

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

14.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

15.Work out the exact value of sin 30° + cos 60°.