Geometry and measures worksheet — GCSE Foundation

1.A composite solid is made from a cylinder of radius 3 cm and height 10 cm, with a cone of the same radius and vertical height 4 cm fixed on top, apex upward. Work out the total volume of the solid. Use π = 3.14 and give your answer correct to 1 decimal place.

2.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

3.A ship's radar can detect other ships up to 20 km away, over a sector-shaped area with angle 90°. A monitoring company charges £0.50 per square kilometre covered by one radar sweep. Using π = 3.14, work out the total charge for one sweep.

4.Write down how many right angles a rectangle has.

5.A postcard measuring 10 cm by 15 cm is enlarged by a scale factor of 2 to make a poster. Work out the area of the poster, in cm².

6.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

7.Two straight lines cross at a point. To find the points that are the same distance from both lines, which construction should be used?

8.In parallelogram ABCD the vertices are labelled in order round the shape, so angle A and angle B are at the two ends of the same side. Angle A is 70°. Work out the size of angle B.

9.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

10.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.

11.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.

12.Triangle PQR and triangle XYZ have angle P = angle X, angle Q = angle Y and angle R = angle Z, with no side lengths given for either triangle. Which of the following correctly describes the relationship between the two triangles?

13.Two triangles are congruent to each other. What does this tell you about their angles and sides?

14.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

15.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.