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.How many vertices does a cuboid have?

3.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

4.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

5.What does the statement AB = CD mean, where A, B, C and D are all points?

6.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.

7.Work out the distance between the point (0, 0) and the point (5, 12).

8.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.

9.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?

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

11.A straight line is drawn from the centre of a circle to a point on the circle. Write down the name of this line.

12.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.

13.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

14.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?

15.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.