Geometry and measures worksheet — GCSE Foundation

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

2.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.

3.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?

4.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

5.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?

6.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

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

8.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

9.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

10.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

11.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.

12.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.

13.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?

14.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

15.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?