Geometry and measures worksheet — GCSE Higher

1.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

2.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

3.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?

4.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

5.In cyclic quadrilateral ABCD, with vertices in that order around the circle, the diagonal BD is drawn. In triangle ABD, angle ABD = 35° and angle ADB = 65°. Side DC is extended beyond C to a point E. Work out the size of angle BCE.

6.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

7.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

8.Each of these has an exact value. Write down the one whose value is the greatest.

10.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

11.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

12.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

13.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.

14.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?

15.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.