Geometry and measures worksheet — GCSE Foundation

1.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.

2.A regular nonagon has 9 sides. Work out the sum of its interior angles.

3.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

4.A submarine travels due south. What is the three-figure bearing for this direction?

5.A composite solid is made from a cylinder of radius 3 cm and height 10 cm, with a cone of the same radius and vertical height 4 cm fixed on top, apex upward. Work out the total volume of the solid. Use π = 3.14 and give your answer correct to 1 decimal place.

6.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

7.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

8.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

9.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

10.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

11.Write down the name given to a quadrilateral with exactly one pair of parallel sides.

12.Write down the number of lines of symmetry a rhombus has.

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

14.Triangles PQS and RQS share the common side QS. PQ equals RQ, and PS equals RS. Which condition proves that triangle PQS is congruent to triangle RQS?

15.A square-based pyramid has a square base and four identical triangular sloping faces, with its apex directly above the centre of the base. How many planes of symmetry does it have?