Geometry and measures worksheet — GCSE Higher

1.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?

2.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

3.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?

4.Point A(1, 2) is enlarged to give image point A′(7, −4). The centre of enlargement lies on the x-axis. Work out the scale factor of the enlargement.

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

6.Triangle ABC has a right angle at B, hypotenuse AC = 13 cm and AB = 5 cm. Triangle DEF has a right angle at E, hypotenuse DF = 13 cm and DE = 5 cm. Which condition proves the two triangles are congruent?

7.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.

8.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.

9.Work out the distance between the point (0, 0) and the point (5, 12).

10.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.

11.Points A, B, C and D lie on a circle with centre O, in that order around the circle, and AC is a diameter. Which of the following circle facts does NOT apply to this diagram?

12.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

13.a is the column vector with top number 3 and bottom number −2. b is the column vector with top number −1 and bottom number 5. Work out 2a + b, giving your answer as a column vector in the form (top, bottom).

14.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

15.A shape is reflected in the line y = 1, and the image is then reflected in the line y = 4. Which single transformation is equivalent to this combination, for every point?