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

Maths · GCSE Higher · Geometry and measures · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A shape is translated by the vector (5, −3), and the image is then translated by the vector (−5, 3). Which single transformation has the same overall effect as this combination, for every point?
(a)A reflection in the x-axis
(b)A translation by the vector (10, −6)
(c)A rotation of 180° about the origin
(d)No transformation — every point stays exactly where it was
2.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.
(a)11.4 cm
(b)4.8 cm
(c)14.7 cm
(d)58.8 cm
3.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?
(a)It is a trapezium
(b)It must be a rhombus
(c)It is a parallelogram but not a rectangle
(d)It must be a rectangle
4.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.
(a)33
(b)11
(c)36
(d)35
5.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.
(a)432
(b)18
(c)10368
(d)1.8
6.The area of triangle ABC is 42 cm². AB = 9.5 cm and angle BAC = 61°. Work out the length of AC. Give your answer to 1 decimal place.
(a)10.1 cm
(b)7.7 cm
(c)18.2 cm
(d)5.1 cm
7.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.
(a)10 cm
(b)20 cm
(c)100 cm
(d)5 cm
8.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?
(a)The length must be written as |AB|, not AB
(b)A different symbol is needed for the length
(c)AB means the segment or its length, shown by context
(d)AB can only mean the segment, never a length
9.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.
(a)5.4 m
(b)4 m
(c)9 m
(d)7.2 m
10.In triangle OAB, OA = a and OB = b. P lies on AB such that AP is twice PB. Express the vector OP in terms of a and b.
(a)a + (2/3)b
(b)(1/2)a + (1/2)b
(c)(1/3)a + (2/3)b
(d)(2/3)a + (1/3)b
11.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
(a)65 cm²
(b)1,000 cm²
(c)500 cm²
(d)2,000 cm²
12.Which of these statements about the area formula Area = 1/2ab sin C is correct?
(a)AB, BC and angle ABC: Area = 1/2 × AB × BC × sin(BAC)
(b)Three sides, no angle: Area still = 1/2 AB×AC×sin(BAC)
(c)AB, AC and angle BAC: Area = 1/2 × AB × AC × sin(BAC)
(d)AB, AC and angle ABC: Area = 1/2 × AB × AC × sin(ABC)
13.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.
(a)15.7 cm
(b)21.7 cm
(c)27.7 cm
(d)31.4 cm
14.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.
(a)150 cm
(b)24 cm
(c)30 cm
(d)6 cm
15.In triangle ABC, AB = 9 cm, AC = 6 cm and angle BAC = 110°. Work out the length of BC. Give your answer to 1 decimal place.
(a)11.6 cm
(b)153.9 cm
(c)12.4 cm
(d)8.9 cm

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