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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 · 15 questions

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1.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?
(a)A triangle-based pyramid standing on its triangular base
(b)A triangular prism standing on its triangular end
(c)A cuboid standing on a rectangular face
(d)A triangular prism lying on one of its rectangular faces
2.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?
(a)A perpendicular of AB
(b)A plane of AB
(c)The midpoint of AB
(d)The vertex of AB
3.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.
(a)12√3 cm
(b)6 cm
(c)4√3 cm
(d)6√3 cm
4.Write down the column vector that describes a translation of 5 units to the left and 3 units down.
(a) $(- 5 - 3)$
(b) $(- 3 5)$
(c) $(3 - 5)$
(d) $(- 3 - 5)$
5.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)
6.A regular nonagon has 9 sides. Work out the sum of its interior angles.
(a)1260°
(b)1620°
(c)1440°
(d)140°
7.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
8.A robotic arm's tip starts at the point (12.5, −4.25) on a grid measured in centimetres. It moves by the vector $(6.5 - 3.75)$ to pick up a component, then by the vector $(- 1.5 2.25)$ to place it. Work out the coordinates of the tip after both moves.
(a)(0.75, 11)
(b)(8.75, 2.25)
(c)(6.5, 3.75)
(d)(11, 0.75)
9.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?
(a)(−6, −8)
(b)(6, −8)
(c)(6, −4)
(d)(9, −8)
10.A triangular prism has two triangular end faces and three rectangular faces joining them. How many faces does it have in total?
(a)5
(b)6
(c)3
(d)9
11.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)
(a)28.6 m
(b)20.6 m
(c)12.6 m
(d)41.1 m
12.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
13.Rectangle ABCD has vertices A(−1, 2), B(4, 2), C(4, 5) and D(−1, 5). The rectangle is translated so that C moves to (0, −1). Write down the coordinates of the image of A.
(a)(3, 8)
(b)(−5, 8)
(c)(0, −1)
(d)(−5, −4)
14.Shape S has a vertex at (9, 6). It is enlarged by a scale factor of 1/3, centre the origin. Work out the coordinates of the image of this vertex.
(a)(6, 4)
(b)(27, 18)
(c)(3, 2)
(d)(3, 6)
15.Write down the exact value of cos 60°.
(a)0
(b)1
(c)1/2
(d)1/3

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