Geometry and measures worksheet — GCSE Foundation

1.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

2.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

3.Triangle ABC has AB = (2x + 3) cm, BC = 11 cm and angle B = 90°. Triangle DEF has DE = 13 cm, EF = 11 cm and angle E = 90°. Given that the two triangles are congruent by SAS, work out the value of x.

4.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

5.Lines PQ and RS are parallel. A straight line crosses PQ at point X and crosses RS at point Y. Angle PXY = 63°. Angle PXY and angle XYS are co-interior (allied) angles, which add up to 180°. Work out the size of angle XYS.

6.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.

7.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

8.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

9.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

10.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.

11.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.

12.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

13.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

14.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

15.Work out the distance between the point (0, 0) and the point (5, 12).