Geometry and measures worksheet — GCSE Foundation

1.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

2.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

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

4.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

5.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

6.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.

7.Which pair of points lies on a horizontal line when the points are plotted on a coordinate grid?

8.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

9.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?

10.A trapezium-shaped garden bed has parallel sides of 2.5 m and 4.5 m, and a perpendicular width of 3 m. A gardener wants to know the area of the bed before ordering topsoil. Work out the area of the garden bed.

11.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

12.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

13.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?

14.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

15.A hiker walks due west. What is the three-figure bearing for this direction?