Geometry and measures worksheet — GCSE Higher

1.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

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

3.ABCD is a cyclic quadrilateral, with its vertices in that order around the circle. Angle DAB = (2x + 10)° and angle DCB = (3x − 5)°. Work out the size of angle DAB.

4.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

5.Triangle T has a vertex A at (4, 6). It is enlarged by a scale factor of −1/2, centre (2, 2). Work out the coordinates of the image of point A.

6.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.

7.The perimeter of a square is 20 cm. Work out the area of the square.

8.A shape is reflected in the line y = −x. Which of these points is invariant under this reflection?

9.u is the column vector with top number 5 and bottom number 1. v is the column vector with top number 2 and bottom number 4. Work out u − v, giving your answer as a column vector in the form (top, bottom).

10.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

11.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.

12.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

13.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

14.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?

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