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 straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?
(a)118°
(b)180°
(c)62°
(d)236°
2.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.
(a)8,000,000 cm³
(b)8,000 cm³
(c)8 cm³
(d)80,000 cm³
3.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.
(a)105°
(b)55°
(c)108°
(d)210°
4.The point M(3, 8) is translated by the vector $(2 - 5)$ . Write down the coordinates of the image of M.
(a)(−2, 8)
(b)(5, 3)
(c)(−2, 10)
(d)(3, 10)
5.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)
6.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.
(a)441 cm
(b)21 cm
(c)35 cm
(d)9 cm
7.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.
(a)65°
(b)115°
(c)25°
(d)295°
8.A right-angled triangle has its two shorter sides equal to 8 cm and 15 cm. Work out the value of cos θ, where θ is the angle opposite the 8 cm side. Give your answer as a fraction.
(a)17/15
(b)8/17
(c)15/17
(d)8/15
9.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.
(a)Parallel, since both gradients are 2
(b)Not parallel, since the gradients are 2 and 4
(c)Parallel, since both lines pass through positive coordinates
(d)Not parallel, since the two lines cross the y-axis at different points
10.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?
(a)RHS - right angle, hypotenuse and one side equal
(b)SAS - two sides and the included angle equal
(c)AAS - two angles and a non-included side equal
(d)ASA - two angles and the included side equal
11.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.
(a)1 hour 15 minutes
(b)1 hour 35 minutes
(c)2 hours 15 minutes
(d)2 hours 25 minutes
12.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?
(a)y
(b)z
(c)x
(d)X
13.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.
(a)SSS – all three corresponding sides are equal
(b)RHS – a right angle, hypotenuse and one other side are equal
(c)SAS – two sides and the included angle are equal
(d)ASA – two angles and the included side are equal
14.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.
(a)chord
(b)radius
(c)diameter
(d)tangent
15.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.
(a)13 cm
(b)16 cm
(c)21 cm
(d)24 cm

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