Geometry and measures worksheet — GCSE Foundation

1.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

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

3.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.

4.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

5.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

6.An angle measures 108°. Write down the name given to an angle of this size.

7.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.

8.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?

9.A quadrilateral has two pairs of parallel sides. All four of its interior angles are right angles, but its sides are not all the same length. Which quadrilateral is this?

10.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

11.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

12.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

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

14.A cylindrical tin has a curved surface, a flat circular base and a flat circular lid. A label is stuck around the curved surface only. How many of the tin's faces are NOT covered by the label?

15.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.