Geometry and measures worksheet — GCSE Higher

1.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

2.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

4.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.

5.A, B and C are points on a circle with centre O, and AB is a diameter. Prove that angle ACB = 90°, using the fact that triangle OAC and triangle OBC are both isosceles. In the proof, angle OAC = angle OCA = x and angle OBC = angle OCB = y. Which equation correctly expresses the angle sum of triangle ABC in terms of x and y, and leads to the required proof?

6.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?

7.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

8.In triangle ABC, AB = 8 cm, AC = 5 cm and angle BAC = 60°. Work out the value of BC².

9.A sector of a circle has radius 10 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector, to 1 decimal place.

10.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

11.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.

12.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?

13.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

14.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

15.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.