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.Each of these has an exact value. Write down the one whose value is the greatest.
(a)cos 60°
(b)sin 45°
(c)tan 45°
(d)cos 30°
2.A polygon has 9 sides. What is the name of this polygon?
(a)Octagon
(b)Nonagon
(c)Heptagon
(d)Decagon
3.A submarine travels due south. What is the three-figure bearing for this direction?
(a)270
(b)090
(c)018
(d)180
4.Lines GH and JK are parallel. A straight line crosses GH at point M and crosses JK at point N. Angle HMN = 71°. Angle HMN and angle MNK are alternate angles. Work out angle MNK.
(a)142°
(b)19°
(c)109°
(d)71°
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.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.
(a)arc
(b)segment
(c)chord
(d)sector
7.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
8.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.
(a)7 cm³
(b)70 cm³
(c)35 cm³
(d)140 cm³
9.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
(a)142°
(b)40°
(c)38°
(d)398°
10.Write down the exact value of tan 45°.
(a)0
(b)√3
(c)√3/3
(d)1
11.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.
(a)the lens-shaped region where the two circles overlap
(b)the whole smaller circle, since it fits inside the larger one
(c)no overlap — 30 km and 20 km don't add to 40 km
(d)a straight strip, exactly halfway between the two
12.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.
(a)200√3 cm
(b)√3 cm
(c)100√3 cm
(d)50√3 cm
13.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.
(a)Co-interior angles add up to 180°
(b)Angles on a straight line add up to 180°
(c)Corresponding angles are equal
(d)Alternate angles are equal
14.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)
15.The vector $(- 2 5)$ describes a translation. A student writes it as $(5 - 2)$ by mistake. Write down what error the student has made.
(a)Doubled the x component
(b)Reversed both signs
(c)Swapped the x and y components
(d)Reversed only the y sign

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