Geometry and measures worksheet — GCSE Higher

1.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

2.Shape S is enlarged by a scale factor of −3 about a fixed centre. Which statement correctly describes the image compared to the original shape?

3.Triangle 1 has sides of 10 cm and 13 cm with an angle of 64° between them. Triangle 2 has sides of 11 cm and 12 cm with an angle of 70° between them. Which triangle has the greater area, and by how much? Give your answer to 1 decimal place.

4.A regular nonagon has 9 sides. Work out the sum of its interior angles.

5.Triangle ABC has AB = 10 cm, BC = 7 cm and angle A = 40°. Triangle DEF has DE = 10 cm, EF = 7 cm and angle D = 40°. Sam says the two triangles are congruent by SAS. Which statement about Sam's claim is correct?

6.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.

7.A vertical line passes through the point (5, 2). Write down the equation of this line.

8.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

9.PT is a tangent to a circle with centre O, touching the circle at T. C is a point on the circle such that C lies inside angle OTP (the right angle between the radius OT and the tangent PT), and OC is a radius. Angle TOC = 130°. Work out the size of angle PTC, the angle between the tangent PT and the chord TC.

10.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

11.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

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

13.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?

14.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

15.Two coastguard stations A and B are 18 km apart, with B due east of A. A boat at C is on a bearing of 062° from A and on a bearing of 315° from B. Work out the distance of the boat from station B. Give your answer to 1 decimal place.