Geometry and measures worksheet — GCSE Foundation

1.Write down the exact value of cos 45°.

2.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.

3.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?

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

5.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

6.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

7.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.

8.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.

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

10.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.

11.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

12.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

13.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

14.A plan of a car park is drawn to a scale of 1 : 500. A parking bay is drawn as a rectangle measuring 1.2 cm by 0.6 cm. The real width of the bay corresponds to the 0.6 cm side. What is the real width of the bay, in metres?

15.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.