Geometry and measures worksheet — GCSE Foundation

1.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

2.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?

3.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

4.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

5.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.

6.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.

7.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

8.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder. Give your answer to the nearest whole number of cubic centimetres.

9.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

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 garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

12.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

13.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

14.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.

15.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.