Geometry and measures worksheet — GCSE Foundation

1.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.

2.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.

3.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).

4.Write down which one of these statements about quadrilaterals is true.

5.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.

6.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?

7.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.

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

9.Write down the exact value of sin 60°.

10.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

11.A circular clock face has a diameter of 18 cm. Work out the circumference of the clock face. Use π = 3.14.

12.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.

13.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

14.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

15.A polygon has one more side than a heptagon. What is the polygon called?