Geometry and measures worksheet — GCSE Foundation

1.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.

2.A tank holds 3.2 m³ of water. Work out this volume in litres.

3.Write down the exact value of cos 60°.

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

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

6.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

7.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?

8.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

9.u is the column vector with top number 7 and bottom number 3. v is the column vector with top number 2 and bottom number 5. Work out u − v, giving your answer as a column vector in the form (top, bottom).

10.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

11.A hiker walks due west. What is the three-figure bearing for this direction?

12.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.

13.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

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.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.