Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

2.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.

3.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

4.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

5.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².

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

7.A tank holds 3.2 m³ of water. Work out this volume in litres.

8.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).

9.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.

11.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

12.A submarine travels due south. What is the three-figure bearing for this direction?

13.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.

14.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

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