Geometry and measures worksheet — GCSE Foundation

1.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.

2.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).

3.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?

4.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

5.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

6.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

7.How many edges does a cube have?

8.Write down the exact value of tan 0°.

9.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

10.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.

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

12.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

13.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

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

15.Which of these describes an obtuse angle?