Geometry and measures worksheet — GCSE Higher

1.A photocopier enlarges a document so that every length is multiplied by the same scale factor. A line on the original document is 3.2 cm long, and the same line measures 11.2 cm on the enlarged copy. A second line on the original document is 2.5 cm long. Work out the length of the second line on the enlarged copy, giving your answer to 2 decimal places.

2.Two coastguard stations A and B are 18 km apart, with B due east of A. A boat at C is on a bearing of 062° from A and on a bearing of 315° from B. Work out the distance of the boat from station B. Give your answer to 1 decimal place.

3.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

4.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).

5.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.

6.A cube has edges of length 5 cm. Work out the length of the diagonal that runs from one corner of the cube to the opposite corner. Give your answer as a surd in its simplest form.

7.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

8.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

9.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

10.Triangle T has a vertex A at (3, 1). It is enlarged by a scale factor of −2, centre (1, 1). Work out the coordinates of the image of point A.

11.ABCD is a convex quadrilateral field with diagonal AC = 20 m. In triangle ABC, AB = 14 m and angle BAC = 35°. In triangle ACD, AD = 16 m and angle DAC = 40°. Work out the total area of the field. Give your answer to 1 decimal place.

12.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.

13.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

14.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?

15.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.