Geometry and measures worksheet — GCSE Foundation

1.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.

2.A jug holds 750 ml of water. Work out what fraction of a litre this is.

3.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

4.A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.

5.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

6.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

7.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

8.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?

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

10.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

11.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?

12.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

13.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

14.A square tile has sides of length 6 cm. Work out the area of the tile.

15.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.