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

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1.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.
(a)20
(b)22
(c)18
(d)16
2.Three of these are rational numbers and one is irrational. Write down the one that is irrational.
(a)sin 30°
(b)tan 0°
(c)cos 45°
(d)sin 90°
3.A robotic arm's tip starts at the point (12.5, −4.25) on a grid measured in centimetres. It moves by the vector $(6.5 - 3.75)$ to pick up a component, then by the vector $(- 1.5 2.25)$ to place it. Work out the coordinates of the tip after both moves.
(a)(0.75, 11)
(b)(8.75, 2.25)
(c)(6.5, 3.75)
(d)(11, 0.75)
4.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?
(a)The length must be written as |AB|, not AB
(b)A different symbol is needed for the length
(c)AB means the segment or its length, shown by context
(d)AB can only mean the segment, never a length
5.A shape is translated by the vector $(- 7 4)$ and then by the vector $(3 - 9)$ . Write down the single column vector that has the same effect as those two translations together.
(a) $(- 4 - 5)$
(b) $(- 10 13)$
(c) $(- 4 - 13)$
(d) $(- 10 - 5)$
6.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.
(a)(−5, 2)
(b)(5, −2)
(c)(2, 5)
(d)(−5, −2)
7.In parallelogram ABCD the vertices are labelled in order round the shape, so angle A and angle B are at the two ends of the same side. Angle A is 70°. Work out the size of angle B.
(a)110°
(b)20°
(c)290°
(d)70°
8.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
(a)a rounded rectangle: 5 m by 4 m with semicircular ends
(b)a circle of radius 2 m
(c)a rectangle, 9 m by 4 m
(d)a rectangle, 5 m by 2 m
9.How many edges does a cube have?
(a)12
(b)6
(c)8
(d)4
10.Write down the exact value of tan 60°.
(a)1/√3
(b)3
(c)√3/2
(d)√3
11.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°
12.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
13.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°
14.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.
(a)Horizontal, because both points have a y-coordinate
(b)Neither, because both coordinates differ
(c)Horizontal, because the x-coordinates increase from A to B
(d)Vertical, because both points have an x-coordinate
15.Every point on a circle is exactly the same distance from one particular point. Write down the name of that point.
(a)The arc
(b)The chord
(c)The diameter
(d)The centre

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