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 · 15 questions

MathsUKwww.geekhero.co.uk

1.A cube has all of its edges the same length. How many planes of symmetry does it have?
(a)9
(b)6
(c)12
(d)3
2.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
3.In geometry, which of the following best describes a 'plane'?
(a)A flat surface extending infinitely in two directions
(b)A straight line extending in one direction
(c)A single, fixed position with no size
(d)A flat, bounded face on a 3D shape
4.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
5.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.
(a)0.14 cm
(b)1008 cm
(c)3.5 cm
(d)7 cm
6.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.
(a)228°
(b)48°
(c)66°
(d)132°
7.Triangle ABC is translated by the column vector with top number 3 and bottom number −5 to form triangle A′B′C′. Triangle A′B′C′ is then translated by the column vector with top number −7 and bottom number 2 to form triangle A″B″C″. Work out the single column vector that translates triangle ABC directly to triangle A″B″C″.
(a)(10, −7)
(b)(4, −3)
(c)(−4, 3)
(d)(−4, −3)
8.A solid is built from centimetre cubes standing on a table. Seen from the front, the left-hand column is 2 cubes high, the middle column is 2 cubes high and the right-hand column is 1 cube high. Work out how many squares make up the front elevation.
(a)3
(b)6
(c)5
(d)4
9.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.
(a)3 cm
(b)6 cm
(c)8 cm
(d)30 cm
10.Write down the exact value of cos 45°.
(a)1/2
(b)√2/2
(c)√3/2
(d)√2
11.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.
(a)432
(b)18
(c)10368
(d)1.8
12.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.
(a)40 cm²
(b)80 cm²
(c)20 cm²
(d)13 cm²
13.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.
(a)A tangent always passes through the centre of the circle
(b)A tangent is always parallel to the radius it touches
(c)The angle in a semicircle is 90°
(d)The angle between a tangent and a radius is 90°
14.A scale drawing of a rectangular lawn uses a scale of 1 : 125. On the drawing, the lawn measures 4 cm by 2.4 cm. Work out the perimeter of the real lawn, in metres.
(a)1600
(b)500
(c)8
(d)16
15.What does the statement AB = CD mean, where A, B, C and D are all points?
(a)AB is parallel to CD
(b)A, B, C and D all lie on one line
(c)AB and CD are equal in length
(d)AB is perpendicular to CD

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