Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.

2.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

3.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

4.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

5.Write down the name given to a triangle whose three sides are all the same length.

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

7.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

8.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

9.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

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 is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).

12.Write down the exact value of tan 0°.

13.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

14.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?