Geometry and measures worksheet — GCSE Foundation

1.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

2.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

3.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

4.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

5.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

6.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

7.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

8.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?

9.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

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

11.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

12.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?

13.Triangle LMN has a right angle at M, with hypotenuse LN = 15 cm and LM = 9 cm. Triangle PQR has a right angle at Q, with hypotenuse PR = 15 cm and PQ = 9 cm. Which condition proves the two triangles are congruent?

14.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

15.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.