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.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?
(a)∠YZW
(b)∠WXY
(c)∠XYZ
(d)∠ZWX
2.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
3.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?
(a)Yes - SSS, the three side lengths all match
(b)Yes - SAS, two sides and an angle match
(c)Cannot be determined without the angles
(d)No - the sides are listed in a different order
4.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.
(a)70°
(b)140°
(c)50°
(d)20°
5.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.
(a)£2.50
(b)£5.00
(c)£325.00
(d)£3.25
6.Here are four trigonometric ratios of special angles. Write down the one that does not have a value.
(a)sin 90°
(b)tan 90°
(c)tan 0°
(d)cos 90°
7.A quadrilateral has angles of 100°, 85° and 95° at three of its vertices. Work out the fourth angle.
(a)260°
(b)280°
(c)70°
(d)80°
8.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
9.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
(a)60°
(b)240°
(c)110°
(d)120°
10.Triangles ABE and CDE share the vertex E, where lines AC and BD cross at E. AE equals CE, and BE equals DE. Angle AEB and angle CED are formed as vertically opposite angles where the lines cross. Which condition proves that triangle ABE is congruent to triangle CDE?
(a)ASA, vertically opposite angle at E
(b)Cannot prove — no angle measured
(c)SSS, three equal side pairs
(d)SAS, vertically opposite angle included
11.How many vertices does a cuboid have?
(a)12
(b)6
(c)4
(d)8
12.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.
(a)280 cm²
(b)140 cm²
(c)168 cm²
(d)47 cm
13.Write down the exact value of tan 60°.
(a)1/√3
(b)3
(c)√3/2
(d)√3
14.After a translation by the vector $(6 - 2)$ , a point lands on (4, 1). Write down the coordinates of the point before the translation.
(a)(2, −5)
(b)(2, 7)
(c)(6, −5)
(d)(6, 7)
15.A bottle holds 2 litres of water. A glass holds 250 ml. Work out how many of these glasses can be filled from one full bottle.
(a)8
(b)80
(c)0.8
(d)125

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