Geometry and measures worksheet — GCSE Foundation

1.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

2.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

3.Write down the exact value of cos 45°.

4.A square tile has sides of length 6 cm. Work out the area of the tile.

5.Write down how many right angles a rectangle has.

6.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

7.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

8.An angle is measured with a protractor as 47°. What type of angle is this?

9.Write down the exact value of cos 60°.

10.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

11.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

12.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

13.A square tile has sides of length 4.5 cm. Work out the perimeter of the tile.

14.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?

15.Write down which one of these statements about quadrilaterals is true.