Geometry and measures worksheet — GCSE Foundation

1.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

2.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

3.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

4.Write down how many right angles a right-angled triangle has.

5.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

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 has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

8.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.

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

10.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

11.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.

12.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

13.A circle has a diameter of 4 cm. Work out the radius of the circle.

14.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

15.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?