Geometry and measures worksheet — GCSE Foundation

1.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?

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

3.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

4.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.

5.A chord divides a circle into two segments of different sizes. Write down the name given to the smaller of the two segments.

6.Triangle XYZ has angle X = 90°. Angle Y = 34°. Work out angle Z.

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

8.Three angles meet at a single point on one side of a straight line. Two of the angles are 48° and 65°. Work out the third angle.

9.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

10.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.

11.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

12.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

13.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

14.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

15.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.