Geometry and measures worksheet — GCSE Foundation

1.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?

2.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

3.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

4.Write down the exact value of tan 0°.

5.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

6.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?

7.Two metal window frames are checked before installation. Frame A has edges of 40 cm and 65 cm, with a marked angle of 35° at the far end of the 65 cm edge, away from where the two given edges meet. Frame B has matching edges of 40 cm and 65 cm, with a matching 35° angle in the same position. The fitter wants to know if these measurements alone guarantee the two frames are congruent. What should the fitter be told?

8.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

9.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

10.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?

11.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

12.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

13.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

14.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°.

15.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.