Geometry and measures worksheet — GCSE Foundation

1.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

2.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?

3.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

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

5.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

6.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).

7.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?

8.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.

9.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

10.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.

11.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

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

13.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

14.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

15.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.