Geometry and measures worksheet — GCSE Higher

1.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

2.Two traffic cones are geometrically similar. The smaller cone has height 6 m and the larger cone has height 9 m. Work out the ratio of the volume of the smaller cone to the volume of the larger cone, giving your answer in the form a : b in its simplest form.

3.A drinks company sells a novelty giant bottle that is geometrically similar to its standard 500 ml bottle, scaled up by a length factor of 1.5. Work out the capacity of the giant bottle, in ml.

4.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

5.A zip-wire is fixed at an angle of 60° to the horizontal ground. The zip-wire is 12 m long. Using the exact value of cos 60°, work out the exact horizontal distance it covers.

6.In triangle ABC the angle at C is 90° and the hypotenuse AB is 12 cm. H is the point on AB for which CH is perpendicular to AB, and AH = 3 cm. Work out the length of AC.

7.A trundle wheel has a diameter of 0.5 m. It is rolled along the ground and makes 20 complete turns. Using π = 3.14, work out the total distance rolled, in metres.

8.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.

9.A, B, C and D are points on a circle with centre O, in that order around the circle. B lies on the major arc AC, and angle AOC = 152°. In triangle ACD, angle ACD = 30°. Work out the size of angle DAC.

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

11.A rotation of 180° about the point (3, 2) can be written as a reflection in the line x = 3, followed by a reflection in a second line, for every point in the plane. Which line is the second line?

12.Shape T has a vertex at (5, 3). T is enlarged by scale factor −1, centre (2, 1). Work out the coordinates of the image of the vertex (5, 3).

13.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?

14.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.

15.A picture frame is a rhombus with a diagonal of 16 cm and a diagonal of 12 cm. The two diagonals meet at right angles at their midpoints. Work out the length of one side of the rhombus.