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.

Calculator

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Geometry and measures worksheet — GCSE Foundation

Maths · GCSE Foundation · Geometry and measures · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.
(a)3.6 m³
(b)2.88 m³
(c)1.44 m³
(d)0.48 m³
2.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.
(a)2π cm²
(b)9π cm²
(c)81π cm²
(d)18π cm²
3.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.
(a)The angles are not necessarily equal
(b)Similar triangles are never congruent
(c)The scale factor is 2, not 1, so the sides are not equal
(d)Congruent triangles must have a right angle
4.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.
(a)third quadrant
(b)second quadrant
(c)first quadrant
(d)fourth quadrant
5.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.
(a)75°
(b)105°
(c)37°
(d)146°
6.A cylinder has a volume of 942 cm³ and a height of 12 cm. Using π = 3.14, work out the radius of the cylinder.
(a)25 cm
(b)8.9 cm
(c)5 cm
(d)17.3 cm
7.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.
(a)20 cm
(b)10 cm
(c)5 cm
(d)2.5 cm
8.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
9.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?
(a)50
(b)5
(c)0.5
(d)0.05
10.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.
(a)12 cm
(b)486 cm
(c)6 cm
(d)45 cm
11.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.
(a)9.42 cm²
(b)452.16 cm²
(c)56.52 cm²
(d)4.71 cm²
12.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
13.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.
(a)7.0 cm
(b)14.0 cm
(c)9.9 cm
(d)5.0 cm
14.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.
(a)150°
(b)300°
(c)42°
(d)157°
15.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?
(a)radius
(b)diameter
(c)circumference
(d)chord

Build your own mix at the worksheet builder.