Geometry and measures worksheet — GCSE Foundation

1.A locus is described as the set of points exactly 4 cm from a fixed point O. What shape is this locus?

2.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

3.In this question, a curved surface counts as a face. How many faces does a cone have?

4.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

5.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.

6.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?

7.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

8.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

9.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

10.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

11.A window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.

12.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

13.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

14.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

15.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?