Geometry and measures worksheet — GCSE Foundation

1.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.

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

3.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.

4.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

5.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

6.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.

7.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.

8.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.

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

10.A cube has all of its edges the same length. How many planes of symmetry does it have?

11.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

12.Work out the exact value of (sin 30°)² + (cos 30°)².

13.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.

14.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

15.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.