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.

Calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Geometry and measures worksheet — GCSE Higher

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

MathsUKwww.geekhero.co.uk

1.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
2.Shape S is enlarged by a scale factor of −3 about a fixed centre. Which statement correctly describes the image compared to the original shape?
(a)3 times the size, opposite side, rotated 180°
(b)3 times the size, same side as the original
(c)3 times the size, same orientation, just further away
(d)1/3 the size, opposite side of the centre
3.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?
(a)6
(b)5
(c)12
(d)3
4.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
5.A triangular sail for a small boat has two sides of 4.2 m and 3.6 m, with an angle of 115° between them. One litre of waterproofing paint covers 3 m² of sail. Work out the least number of whole tins of paint (1 litre each) needed to cover the sail.
(a)3
(b)2
(c)5
(d)7
6.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
(a)£24.00
(b)£2.94
(c)£29.40
(d)£2940.00
7.In triangle PQR, PQ = 8 cm and QR = 11 cm. Angle QPR = 50°. A student calculates the area of the triangle as Area = 1/2 × 8 × 11 × sin 50°. Is the student's method correct?
(a)Yes — any angle works with any two sides.
(b)Yes — PQ and QR are the arms of angle QPR.
(c)No — 50° is angle P, not between PQ and QR.
(d)No — the formula needs all three sides.
8.A parallelogram-shaped tile has two sides of 6 cm and 9 cm, with an angle of 60° between them. Work out the area of the tile. Give your answer to 1 decimal place.
(a)27.0 cm²
(b)46.8 cm²
(c)13.0 cm²
(d)23.4 cm²
9.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.
(a)90°
(b)45°
(c)30°
(d)60°
10.In triangle ABC, angle ABC = 47°, AC = 12.5 cm and BC = 9.2 cm. Work out the size of angle BAC. Give your answer to 1 decimal place.
(a)57.4°
(b)147.4°
(c)32.6°
(d)83.6°
11.A line joins the points A(0, 0, 0) and B(9, 12, 8) in a three-dimensional coordinate system in which the z-axis is vertical. Work out the angle this line makes with the horizontal (the xy-plane). Give your answer correct to 1 decimal place.
(a)28.1°
(b)41.6°
(c)61.9°
(d)33.7°
12.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
13.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)
14.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)
15.A kite ABCD is symmetrical about the diagonal AC, with AB = AD = 6 cm and CB = CD = 9 cm. Angle ABC = 100°. By splitting the kite into two congruent triangles along AC, work out the area of the whole kite. Give your answer to 1 decimal place.
(a)106.4 cm²
(b)26.6 cm²
(c)54.0 cm²
(d)53.2 cm²

Build your own mix at the worksheet builder.