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 plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?
(a)0.85 m
(b)8.5 m
(c)850 m
(d)3.4 m
2.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?
(a)No, because 45 ÷ 360 = 1/6, not 1/8.
(b)Yes, but only because the radius happens to make 45° exactly one eighth of a full turn in this particular circle.
(c)No, because the fraction of the area also depends on the radius, so it is not fixed.
(d)Yes, because 45 ÷ 360 = 1/8, and this fraction applies to any radius.
3.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?
(a)A smaller circle
(b)A triangle
(c)The same size circle as the base
(d)An ellipse
4.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.
(a)22
(b)28
(c)35
(d)63
5.A party hat is in the shape of a cone with a base radius of 6 cm and a slant height of 10 cm. Work out the curved surface area of the party hat. Use π = 3.14 and the formula curved surface area = πrl.
(a)188.4 cm²
(b)376.8 cm²
(c)113.04 cm²
(d)60 cm²
6.Write down the name given to a quadrilateral with exactly one pair of parallel sides.
(a)Trapezium
(b)Kite
(c)Rhombus
(d)Parallelogram
7.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.
(a)37.68 cm²
(b)1808.64 cm²
(c)150.72 cm²
(d)452.16 cm²
8.Triangle ABC has AB = 8 cm, angle B = 50° and BC = 6 cm. Triangle DEF has DE = 8 cm, angle E = 50° and EF = 6 cm. Which condition proves the two triangles are congruent?
(a)AAS - two angles and a non-included side equal
(b)SSS - three sides equal
(c)SAS - two sides and the included angle equal
(d)ASA - two angles and the included side equal
9.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.
(a)7
(b)3
(c)5
(d)27
10.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°
11.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
12.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
13.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
(a)30°
(b)150°
(c)15°
(d)36°
14.Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm and 5 cm. The shortest side of the second triangle is 9 cm. Work out the scale factor from the first triangle to the second.
(a)1/3
(b)3
(c)6
(d)1.8
15.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
(a)133
(b)47
(c)227
(d)142

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