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 window is made from a rectangle with a semicircle on top. The rectangle is 40 cm wide and 60 cm tall. The semicircle has the same width as the rectangle. Work out the total area of the window. Use π = 3.14. Give your answer to the nearest whole number.
(a)4912 cm²
(b)2400 cm²
(c)3028 cm²
(d)3656 cm²
2.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°
3.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.
(a)150 cm
(b)24 cm
(c)30 cm
(d)6 cm
4.A pin on a map is at grid reference (5, 2). It is moved by the vector $(4 - 3)$ . Write down its new grid reference.
(a)(2, 6)
(b)(8, 6)
(c)(9, −1)
(d)(2, 2)
5.A circular table mat has diameter 20 cm. Yasmin has a 70 cm length of ribbon and sews it around the edge of the mat with no overlap. Using π = 3.14, work out how much ribbon is left over after going around the mat once.
(a)7.2 cm
(b)50 cm
(c)20 cm
(d)62.8 cm
6.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.
(a)16 m
(b)22.42 m
(c)17.71 m
(d)20.71 m
7.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.
(a)90°
(b)45°
(c)30°
(d)60°
8.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?
(a)65
(b)0.65
(c)650
(d)6.5
9.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.
(a)2.5 cm
(b)10 cm
(c)5 cm
(d)15.7 cm
10.A triangle has vertices X, Y and Z, with a right angle at Y. Side XY is twice as long as side YZ. Which of the following correctly describes this triangle?
(a)A right-angled isosceles triangle
(b)A right-angled triangle
(c)An isosceles triangle
(d)An equilateral triangle
11.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?
(a)Wrong: 1 litre = 100 ml, so his number is off.
(b)Wrong: 1 litre = 1000 ml, so 3.2 l = 3200 ml.
(c)Wrong, but only because 3.2 should round to 3.
(d)Correct: ×100 converts litres to millilitres.
12.A flower bed in the shape of a parallelogram has a base of 3.5 m and a perpendicular height of 2 m. Compost costs £4.80 per m². Work out the total cost of covering the flower bed with compost.
(a)£7.00
(b)£33.60
(c)£26.40
(d)£16.80
13.To construct a perpendicular to a line at a given point P on the line, compasses are first opened to draw two arcs crossing the line, one on each side of P. What is the correct next step?
(a)Join the two crossing points with a straight line.
(b)Draw wider arcs from each crossing point, meeting above.
(c)Draw an arc centred at P through only one crossing point.
(d)Draw a circle centred at P through both crossing points.
14.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?
(a)a cone
(b)a cylinder
(c)a sphere
(d)a square-based pyramid
15.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

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