Geometry and measures worksheet — GCSE Higher

1.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

2.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

3.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.

4.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?

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

6.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.

7.A regular octagonal tabletop has centre O. Each vertex is 30 cm from O. Work out the area of the tabletop. Give your answer to the nearest square centimetre.

8.In triangle ABC, AB = 7 cm, AC = 6 cm and angle ABC = 40°. Two different lengths of BC are possible. Given that BC is the longer of them, work out the length of BC. Give your answer to 1 decimal place.

9.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

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 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?

12.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.

14.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

15.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².