Geometry and measures worksheet — GCSE Foundation

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

2.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?

3.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

4.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

5.Triangle ABC has AB = 5 cm, BC = 7 cm and CA = 9 cm. Triangle DEF has DE = 5 cm, EF = 7 cm and FD = 9 cm. Which condition proves the two triangles are congruent?

6.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.

7.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?

8.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

9.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

10.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?

11.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

12.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

13.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?

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 sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.