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 · 15 questions

MathsUKwww.geekhero.co.uk

1.A shape is translated by the vector $(3 - 8)$ , and one vertex of the image is at the point (1, 6). The original shape is instead translated by the vector $(- 5 2)$ . Work out the coordinates of the image of that same vertex under this second translation.
(a)(7, 8)
(b)(11, 3)
(c)(3, 1)
(d)(11, −2)
2.In triangle ABC, AB = 9 cm, AC = 6 cm, and angle BAC = 65°. Work out the length of BC. Give your answer to 1 decimal place.
(a)9.7 cm
(b)8.4 cm
(c)12.8 cm
(d)4.4 cm
3.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
4.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?
(a)Its rotational symmetry order is always 4
(b)Its diagonals cross at right angles
(c)Its diagonals are always equal in length
(d)It always has four right angles
5.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?
(a)x = 2
(b)y = 3
(c)y = x
(d)y = 2
6.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.
(a)32
(b)28
(c)24
(d)20
7.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.
(a)49°
(b)41°
(c)82°
(d)98°
8.A triangle has one unknown side or angle, marked x. In which one of these situations should the sine rule, rather than the cosine rule, be used to find x?
(a)Two sides and the included angle; x is the third side
(b)Two sides and the included angle; x is another angle
(c)Two angles and one side are known; x is another side
(d)All three sides are known; x is one of the angles
9.An enlargement has a scale factor of −2. Priti says the image must be a mirror image of the original shape. Is Priti correct?
(a)No — it's a 180° rotation, not a reflection.
(b)Yes — negative numbers always mean a reflection.
(c)Yes — upside down is the same thing as mirrored.
(d)No — negative factors change size, not orientation.
10.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?
(a)Kite
(b)Rhombus
(c)Trapezium
(d)Parallelogram
11.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
(a)2
(b)−2
(c)8
(d)0.5
12.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.
(a)12 cm
(b)768 cm
(c)104 cm
(d)24 cm
13.In triangle ABC, BC = 8 cm, AC = 10 cm and angle BAC = 40°. Given that angle ABC is acute, work out its size. Give your answer to 1 decimal place.
(a)53.5°
(b)126.5°
(c)73.2°
(d)30.9°
14.In triangle OAB, OA = a and OB = b. P is the point on OA such that OP = (1/3)a, and Q is the point on OB such that OQ = (1/3)b. Express the vector PQ in terms of a and b.
(a)(1/3)a − (1/3)b
(b)b − a
(c)(1/3)b − (1/3)a
(d)(2/3)b − (2/3)a
15.Two traffic cones are geometrically similar. The smaller cone has height 6 m and the larger cone has height 9 m. Work out the ratio of the volume of the smaller cone to the volume of the larger cone, giving your answer in the form a : b in its simplest form.
(a)4 : 9
(b)8 : 27
(c)2 : 3
(d)27 : 8

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