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 sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.
(a)5 cm
(b)30 cm
(c)7.5 cm
(d)15 cm
2.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
3.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.
(a)59.0 cm²
(b)82.6 cm²
(c)144.0 cm²
(d)118.0 cm²
4.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.
(a)150°
(b)300°
(c)42°
(d)157°
5.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.
(a)444 m
(b)44.4 m
(c)0.77 m
(d)4.44 m
6.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector $(- 9 6)$ to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
(a) $(- 2 8)$
(b) $(- 7 - 2)$
(c) $(7 2)$
(d) $(- 7 4)$
7.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.
(a)The angles are not necessarily equal
(b)Similar triangles are never congruent
(c)The scale factor is 2, not 1, so the sides are not equal
(d)Congruent triangles must have a right angle
8.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.
(a)6.3 cm
(b)12.6 cm
(c)11.2 cm
(d)12.1 cm
9.Point P has coordinates (6, 4). P is rotated 90° clockwise about the point (1, 2), and the image is then translated by the vector (−3, 5). Work out the coordinates of the final image of P.
(a)(8, 0)
(b)(0, 2)
(c)(3, −3)
(d)(−4, 12)
10.In triangle ABC, AB = 13 cm, AC = 9 cm and angle ABC = 35°. Given that angle ACB is obtuse, work out its size. Give your answer to 1 decimal place.
(a)23.4°
(b)124.1°
(c)89.1°
(d)55.9°
11.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.
(a)(−5, 1)
(b)(5, 4)
(c)(−4, 7)
(d)(−2, 6)
12.Two cylindrical storage tins are geometrically similar. The smaller tin has height 4 cm and the larger tin has height 6 cm. Work out the ratio of the surface area of the smaller tin to the surface area of the larger tin, giving your answer in the form a : b in its simplest form.
(a)9 : 4
(b)4 : 9
(c)2 : 3
(d)8 : 27
13.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.
(a)£112
(b)£157
(c)£143
(d)£129
14.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.
(a)3.6 m³
(b)2.88 m³
(c)1.44 m³
(d)0.48 m³
15.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?
(a)335°
(b)025°
(c)155°
(d)065°

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