Geometry and measures worksheet — GCSE Foundation

1.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

2.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

3.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

4.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.

5.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

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

7.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

8.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?

9.How many vertices does a cylinder have?

10.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

11.A jug holds 750 ml of water. Work out what fraction of a litre this is.

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

13.Work out the exact value of (sin 30°)² + (cos 30°)².

14.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

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