Printable · GCSE Foundation · ages 14-16

Geometry and measures worksheet — GCSE Foundation

Fifteen questions across the geometry and measures statements at Foundation 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 Foundation

Maths · GCSE Foundation · Geometry and measures · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.
(a)10 cm
(b)20 cm
(c)3.2 cm
(d)40 cm
2.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?
(a)an arc of the same radius, centred at the midpoint of AB
(b)an arc of the same radius, centred at B
(c)a smaller arc, centred at A again
(d)a straight line joining the ends of the first arc
3.A solid is built from five centimetre cubes, standing side by side on a table in a single straight row. Looking down from directly above (the plan view), how many squares are visible?
(a)5
(b)25
(c)10
(d)1
4.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
5.p is the column vector with top number 5 and bottom number 1. q is the column vector with top number −2 and bottom number 3. Work out p − 2q, giving your answer as a column vector in the form (top, bottom).
(a)(9, −5)
(b)(1, 7)
(c)(12, −1)
(d)(7, −2)
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.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.
(a)121.8
(b)58.2
(c)116.4
(d)63.6
8.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.
(a)tan θ = adjacent/opposite
(b)cos θ = opposite/adjacent
(c)tan θ = opposite/adjacent
(d)sin θ = opposite/adjacent
9.Triangle ABC has AB = 10 cm, BC = 7 cm and angle A = 40°. Triangle DEF has DE = 10 cm, EF = 7 cm and angle D = 40°. Sam says the two triangles are congruent by SAS. Which statement about Sam's claim is correct?
(a)Wrong - none of the sides or angles match
(b)Correct, but by ASA rather than SAS
(c)Correct - two sides and an angle match
(d)Wrong - the given angle is not the included angle
10.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?
(a)a cone
(b)a cylinder
(c)a sphere
(d)a square-based pyramid
11.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.
(a)(6, 1)
(b)(6, 3)
(c)(2, 3)
(d)(5, 4)
12.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.
(a)12π + 16 cm
(b)12π cm
(c)12π + 8 cm
(d)4π + 16 cm
13.The diagram shows a solid resting on its side on a table. Work out which shape is its plan view, the view looking straight down from above.
(a)A rectangle with rounded ends
(b)An oval
(c)A circle
(d)A rectangle
14.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?
(a)ASA (two angles and the included side)
(b)SAS (two sides and the included angle)
(c)RHS (right angle, hypotenuse, one side)
(d)SSS (three sides)
15.How many vertices does a cuboid have?
(a)12
(b)6
(c)4
(d)8

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