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 kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.
(a)100°
(b)260°
(c)80°
(d)50°
2.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.
(a)64°
(b)32°
(c)58°
(d)122°
3.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?
(a)kite
(b)trapezium
(c)rhombus
(d)parallelogram
4.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?
(a)8.5
(b)10.5
(c)3.5
(d)14
5.A robot on a grid moves by the vector $(- 2 3)$ , then by the vector $(5 - 7)$ , then by the vector $(1 4)$ . Write down the single column vector that has the same overall effect as these three moves.
(a) $(- 6 14)$
(b) $(0 4)$
(c) $(3 - 4)$
(d) $(4 0)$
6.A shop sells a scale model of a van. The model and the real van are similar shapes, with lengths in the ratio 1 : 24. The model is 18.5 cm long. Work out the length of the real van, giving your answer in metres.
(a)444 m
(b)44.4 m
(c)0.77 m
(d)4.44 m
7.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
8.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.
(a)36 cm
(b)12 cm
(c)7 cm
(d)4 cm
9.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.
(a)Q, since OQ = 5 and OP = 6
(b)P, since OP = 5 and OQ = 6
(c)P, since OP = 6 and OQ = 5
(d)They are equally distant from the origin
10.Triangle ABC is right-angled at B. Triangle DEF is right-angled at E. AB = DE = 6 cm and AC = DF = 10 cm (AC and DF are the hypotenuses of their triangles). A student says this is not enough information to prove the triangles are congruent, because only two sides are given. Which reason shows the student is wrong?
(a)AAA applies, because both triangles have a right angle
(b)The triangles cannot be proved congruent from this information
(c)RHS applies: the right angle, hypotenuse and one matching side are all equal
(d)SSS applies, because all three sides must be equal in any right-angled triangle
11.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
12.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
13.The diagram shows the plan view and the front elevation of a cuboid-shaped box, each drawn as a rectangle. Work out the area of the box's side elevation, in square centimetres.
(a)40 cm²
(b)120 cm²
(c)24 cm²
(d)15 cm²
14.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°
15.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.
(a)750
(b)0.00075
(c)75
(d)7500

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