Geometry and measures worksheet — GCSE Foundation

1.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?

2.e is the column vector with top number 5 and bottom number k. f is the column vector with top number 15 and bottom number 6. Given that f is 3 times e, work out the value of k.

3.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

4.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

5.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

6.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

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

8.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.

9.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

10.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?

11.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

12.A cylindrical water tank has a solid hemispherical dome on top, both with radius 2 m. Work out the volume of the hemispherical dome alone. Use π = 3.14 and give your answer correct to 3 decimal places.

13.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

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

15.A sector of a circle is bounded by two straight edges and one curved edge. Write down the mathematical term for each of the two straight edges.