Geometry and measures worksheet — GCSE Foundation

1.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

2.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.

3.Lines AB and CD cross at a point, forming four right angles where they meet. Which notation correctly describes the relationship between AB and CD?

4.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

5.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

6.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

7.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

8.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

9.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

10.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

11.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.

12.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

13.Write down the exact value of sin 60°.

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

15.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.