Geometry and measures worksheet — GCSE Foundation

1.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

2.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.

3.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

4.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

5.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

6.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

7.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

8.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.

9.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

10.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.

11.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

12.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.

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

14.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).

15.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.