Geometry and measures worksheet — GCSE Foundation

1.A designer enlarges a drawing of a model car for a poster. She first enlarges the drawing by a scale factor of 1.5, and then enlarges that result by a further scale factor of 2. On the original drawing, the position of a wheel relative to the front bumper is given by the column vector with top number 4 and bottom number −3, in centimetres. What is the corresponding column vector on the poster, in centimetres?

2.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.

3.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

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

5.A parallelogram has a base of 20 cm and a sloping side of 13 cm. The perpendicular drawn from the top of that sloping side down to the base meets the base 5 cm from the foot of the sloping side, so the perpendicular, the 5 cm and the 13 cm sloping side form a right-angled triangle. Work out the area of the parallelogram.

6.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

7.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).

8.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

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

10.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.

11.A square has sides of length 7 cm. Work out its area.

12.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.

13.Write down the exact value of tan 60°.

14.Quadrilateral WXYZ has WX parallel to ZY, and WZ = XY (the two non-parallel sides are equal in length). Give a reason why angle W = angle X.

15.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.