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.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.
(a)65
(b)25
(c)115
(d)245
2.A pop-up canopy has two sloping supports that meet at the top. Each support makes an angle of 30° with the ground and is 6 m long. Using the exact value of cos 30°, work out the total width of the canopy's base.
(a)3√3 m
(b)6√3 m
(c)12 m
(d)6 m
3.Triangle ABC is extended so that side BC is extended beyond C to a point D, forming exterior angle ACD. Angle BAC = 48° and angle ABC = 67°. Which single angle fact gives angle ACD = 115° in one step, without first working out the interior angle at C?
(a)angles in a triangle add up to 180°
(b)angles on a straight line add up to 180°
(c)exterior angle = sum of the two interior opposite angles
(d)exterior angle is always double the smallest angle
4.A cylindrical tin has a curved surface, a flat circular base and a flat circular lid. A label is stuck around the curved surface only. How many of the tin's faces are NOT covered by the label?
(a)0
(b)4
(c)2
(d)1
5.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
(a)2
(b)−2
(c)8
(d)0.5
6.A quadrilateral has vertices A(1, 1), B(5, 1), C(6, 4) and D(2, 4). By comparing the y-coordinates of A, B and of D, C, write down whether the sides AB and DC are parallel, and give a reason for your answer.
(a)Parallel, since A and D have the same x-coordinate
(b)Parallel, since AB and DC are both horizontal lines
(c)Not parallel, since AB is horizontal and DC is vertical
(d)Not parallel, since AB and DC have different lengths
7.How many faces does a cuboid have?
(a)8
(b)4
(c)6
(d)12
8.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.
(a)a line parallel to both, 3 cm from each
(b)the perpendicular bisector of the gap
(c)a line parallel to both, 6 cm from each
(d)a circle of radius 3 cm, centred midway
9.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.
(a)7 cm
(b)17 cm
(c)13 cm
(d)60 cm
10.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?
(a)∠QRS
(b)∠PQR
(c)∠TRP
(d)∠RST
11.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?
(a)Triangular-based pyramid (tetrahedron)
(b)Square-based pyramid
(c)Cube
(d)Triangular prism
12.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
13.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.
(a)106°
(b)16°
(c)74°
(d)148°
14.Write down the term for the distance all the way around the edge of a circle.
(a)diameter
(b)circumference
(c)area
(d)radius
15.A cylindrical drum and a cuboid box are being wrapped for a display. A shop assistant wraps only the flat faces of each item, not any curved surface. How many flat faces in total does the assistant wrap across both items?
(a)8
(b)9
(c)3
(d)6

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