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

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1.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?
(a)radius
(b)diameter
(c)circumference
(d)chord
2.Triangle ABC has AB = 8 cm, BC = 10 cm and CA = 6 cm. Triangle LMN has LM = 10 cm, MN = 6 cm and NL = 8 cm. The two triangles are congruent by SSS. Which of the following correctly matches the corresponding vertices?
(a)A↔L, B↔M, C↔N (ABC≅LMN)
(b)A↔N, B↔M, C↔L (ABC≅NML)
(c)A↔N, B↔L, C↔M (ABC≅NLM)
(d)A↔M, B↔N, C↔L (ABC≅MNL)
3.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?
(a)080°
(b)100°
(c)180°
(d)440°
4.A translation is described by the column vector $(- 5 6)$ . Write down the column vector of the translation that undoes it.
(a) $(6 - 5)$
(b) $(- 5 - 6)$
(c) $(5 - 6)$
(d) $(5 6)$
5.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.
(a)−32
(b)48
(c)32
(d)37
6.Write down the exact value of cos 60°.
(a)0
(b)1
(c)1/2
(d)1/3
7.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.
(a)4700 cm²
(b)2000 cm²
(c)7200 cm²
(d)2700 cm²
8.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
9.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.
(a)(5, 2)
(b)(−5, −2)
(c)(−5, 2)
(d)(2, 5)
10.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.
(a)44
(b)22
(c)10
(d)5.5
11.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
12.Which of these describes an obtuse angle?
(a)An angle between 180° and 360°
(b)An angle between 90° and 180°
(c)An angle of exactly 90°
(d)An angle between 0° and 90°
13.A sector of a circle has radius 9 cm and angle 60°. Using π = 3.14, work out the area of the sector, to 1 decimal place.
(a)9.4 cm²
(b)4.7 cm²
(c)254.3 cm²
(d)42.4 cm²
14.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.
(a)9.42 cm²
(b)113.04 cm²
(c)18.84 cm²
(d)452.16 cm²
15.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.
(a)40 cm
(b)12 cm
(c)88 cm
(d)768 cm

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