Geometry and measures worksheet — GCSE Foundation

1.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.

2.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

3.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

4.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

5.Write down the column vector that describes a translation of 5 units to the left and 3 units down.

6.How many vertices does a square-based pyramid have?

7.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.

8.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

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

10.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

11.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.

12.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.

13.Which of the following is the correct definition of a regular polygon?

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

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