Geometry and measures worksheet — GCSE Higher

1.In triangle ABC, AB = 8 cm, AC = 5 cm and angle BAC = 60°. Work out the value of BC².

2.A jug holds 750 ml of water. Work out what fraction of a litre this is.

3.A cuboid has a rectangular base measuring 6 cm by 8 cm, and a height of 4 cm. Work out the angle between the diagonal from a base corner to the opposite top corner, and the base of the cuboid. Give your answer correct to 1 decimal place.

4.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

5.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.

6.A triangular flower bed ABC has AB = 14 m, BC = 9 m and AC = 11 m. Work out the area of the flower bed. Give your answer to 1 decimal place.

7.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

8.O is the centre of a circle, and PT is a tangent to the circle at the point T. A is a point on the circle, with OA and OT both radii and angle AOT = 122°. At the point T, the chord TA lies between the radius TO and the tangent TP. Work out the size of angle ATP, the angle between the chord and the tangent.

9.Work out the exact value of sin 30° + cos 60°.

10.In triangle ABC, angle ABC = 58°, angle ACB = 47° and BC = 14 cm. Work out the area of triangle ABC. Give your answer to 1 decimal place.

11.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.

12.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.

13.A rhombus has all four sides equal in length, but it is not a square — its angles are not all 90°. How many lines of symmetry does this rhombus have?

14.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.

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.