Printable · GCSE Higher · ages 14-16
Geometry and measures worksheet — GCSE Higher
Fifteen questions across the geometry and measures statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
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Geometry and measures worksheet — GCSE Higher
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- 1.Work out the exact value of (cos 45°)² + (sin 45°)².
- 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 hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?
- 4.Triangle ABC is extended so that side BC is extended beyond C to a point D, forming exterior angle ACD. Angle BAC = 48° and angle ABC = 67°. Which single angle fact gives angle ACD = 115° in one step, without first working out the interior angle at C?
- 5.Triangle T has vertices (1, 1), (3, 1) and (1, 4). It is mapped onto triangle T′ with vertices (5, −1), (3, −1) and (5, −4). Which single composition of two transformations maps T onto T′?
- 6.A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.
- 7.An enlargement with scale factor 5 maps the point (4, 1) to the point (12, 9). Which of these points is invariant (does not move) under this enlargement?
- 8.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?
- 9.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.
- 10.A cube has all of its edges the same length. How many planes of symmetry does it have?
- 11.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.
- 12.Two spheres are similar solids. Their radii are in the ratio 3 : 4. Write down the ratio of their surface areas.
- 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.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.
- 15.In triangle OAB, OA = a and OB = b. M is the midpoint of OA, and N is the midpoint of OB. Express the vector MN in terms of a and b.
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