Geometry and measures worksheet — GCSE Foundation

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

2.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

3.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

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

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

6.A vertical line passes through the point (5, 2). Write down the equation of this line.

7.Write down the name given to a quadrilateral with exactly one pair of parallel sides.

8.A solid pyramid has a square base of side 10 cm and four identical triangular faces. Its apex is directly above the centre of the base, at a vertical height of 12 cm, and the slant height of each triangular face — the distance from the apex to the midpoint of a base edge — is 13 cm. Work out the total surface area of the pyramid.

9.Triangle A has a vertex at (1, 2). Triangle A is enlarged, centre (1, 1), to give triangle B, whose corresponding vertex is at (1, 5). Work out the scale factor of the enlargement.

11.Work out the exact value of (sin 30°)² + (cos 30°)².

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

13.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

14.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.

15.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.