Geometry and measures worksheet — GCSE Foundation

1.A vertical line passes through the point (5, 2). Write down the equation of this line.

2.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

3.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

4.Write down the name given to a triangle whose three sides are all the same length.

5.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.

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

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

8.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.

9.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

10.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

11.In geometry, which of the following best describes a 'plane'?

12.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

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

14.Write down the column vector, from the options given, that would move a point to the right and downwards.

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