Geometry and measures worksheet — GCSE Foundation

1.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?

2.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?

3.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.

4.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

5.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

6.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

7.Write down the exact value of cos 30°.

8.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

9.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?

10.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

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.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.

13.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.

14.A polygon has 12 straight sides. What is the mathematical name for this polygon?

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