Geometry and measures worksheet — GCSE Foundation

1.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).

2.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

3.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

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

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

6.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.

7.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

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

9.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.

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

11.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

12.A regular nonagon has 9 sides. Work out the sum of its interior angles.

13.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.

14.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.

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