Geometry and measures worksheet — GCSE Foundation

1.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

2.Write down the exact value of tan 45°.

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

4.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

5.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?

6.Work out the exact value of tan 30° + tan 30°.

7.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?

8.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

9.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

10.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

11.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?

12.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

13.A gardener wants to plant a tree so that it is the same distance from two straight garden walls that meet at a corner, and also the same distance from two ornamental posts standing 4 m apart. Which construction locates this point?

14.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

15.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?