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.
Geometry and measures worksheet — GCSE Higher
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- 1.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.
- 2.In triangle ABC, angle BAC = 42°, angle ABC = 63° and BC = 8.4 cm. Work out the length of AC. Give your answer to 1 decimal place.
- 3.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?
- 4.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.
- 5.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
- 6.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.
- 7.From an external point P, two tangents PA and PB touch a circle with centre O at the points A and B. Angle APB = 46°. C is a point on the major arc AB, the arc on the opposite side of AB from P. Work out the size of angle ACB.
- 8.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?
- 9.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.
- 10.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
- 11.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.
- 12.A shape is reflected in the line y = −x. Which of these points is invariant under this reflection?y = −x
- 13.In triangle ABC, AB = x cm, AC = (x + 3) cm, BC = 7 cm and angle BAC = 60°. Work out the value of x.
- 14.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.
- 15.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.
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