Geometry and measures worksheet — GCSE Higher

1.Two spheres are similar solids. Their radii are in the ratio 3 : 4. Write down the ratio of their surface areas.

2.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

3.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.

4.A, B, C and D are points on a circle, with B and D both on the same major arc AC. E lies on the straight line through A and B, beyond B, so that angle CBE = 145°. Work out the size of angle ADC.

5.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.

6.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?

7.In triangle ABC, AB = 10 cm, BC = 7 cm and angle ACB = 35°. Given that angle BAC is acute, work out the length of AC. Give your answer to 1 decimal place.

8.ABCD is a cyclic quadrilateral, with its vertices in that order around the circle. Angle DAB = (2x + 10)° and angle DCB = (3x − 5)°. Work out the size of angle DAB.

9.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

10.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².

11.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

12.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?

13.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

14.In triangle OAB, OA = a and OB = b. P lies on AB such that AP is twice PB. Express the vector OP in terms of a and b.

15.In triangle ABC, BC = 8 cm, AC = 10 cm and angle BAC = 40°. Given that angle ABC is acute, work out its size. Give your answer to 1 decimal place.