Geometry and measures worksheet — GCSE Foundation

1.Write down the column vector that describes a translation of 4 units to the right and 4 units up.

2.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?

3.A rectangular photograph is 12 cm long and 5 cm wide. Work out the perimeter of the photograph.

4.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

5.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

6.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

7.Work out the exact value of (cos 45°)² + (sin 45°)².

8.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.

9.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

10.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.

11.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.

12.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

13.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

14.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

15.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.