Geometry and measures worksheet — GCSE Foundation

1.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?

2.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.

3.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

4.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

5.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

6.Work out the distance between the point (0, 0) and the point (5, 12).

7.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.

8.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

9.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

10.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

11.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

12.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

13.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

14.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.

15.Write down the name given to a triangle whose three sides are all the same length.