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

MathsUKwww.geekhero.co.uk

1.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
(a)60°
(b)20°
(c)120°
(d)80°
2.A student says the reverse of the translation vector $(- 9 4)$ is $(9 4)$ . Write down the correct reverse translation vector.
(a) $(- 9 - 4)$
(b) $(- 9 4)$
(c) $(9 - 4)$
(d) $(9 4)$
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.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.
(a)Congruent circles
(b)Tangential circles
(c)Similar circles
(d)Concentric circles
5.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.
(a)28 cm
(b)48 cm²
(c)80 cm²
(d)32 cm²
6.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
7.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
(a)3
(b)7
(c)14
(d)5
8.A water tank holds 2.5 m³. Work out this volume in cm³.
(a)2500 cm³
(b)2 500 000 cm³
(c)25 000 cm³
(d)250 cm³
9.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.
(a)27 cm
(b)45 cm
(c)15 cm
(d)11 cm
10.How many edges does a triangular prism have?
(a)9
(b)5
(c)6
(d)12
11.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
12.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.
(a)1.5
(b)−10
(c)−1.5
(d)−24
13.A sector of a circle has radius 9 cm and angle 60°. Using π = 3.14, work out the area of the sector, to 1 decimal place.
(a)9.4 cm²
(b)4.7 cm²
(c)254.3 cm²
(d)42.4 cm²
14.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.
(a)£157.00
(b)£31.40
(c)£7.85
(d)£15.70
15.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?
(a)opposite angles of a parallelogram are equal
(b)co-interior angles add up to 180°
(c)alternate angles are equal
(d)angles on a straight line add up to 180°

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