Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher 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 Higher

Maths · GCSE Higher · Geometry and measures · 15 questions

MathsUKwww.geekhero.co.uk

1.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?
(a)Square-based pyramid
(b)Cube
(c)Cuboid
(d)Triangular prism
2.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².
(a)120 m²
(b)12 m²
(c)4.6 m²
(d)1.2 m²
3.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
4.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.
(a)200√3 cm
(b)√3 cm
(c)100√3 cm
(d)50√3 cm
5.In triangle ABC, angle ABC = 72° and angle ACB = 48°. Side AB = (2x + 1) cm and side AC = (3x − 2) cm. Work out the value of x. Give your answer to 1 decimal place.
(a)4.7
(b)7.4
(c)1.9
(d)3.0
6.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?
(a)4
(b)0
(c)2
(d)1
7.A regular octagonal tabletop has centre O. Each vertex is 30 cm from O. Work out the area of the tabletop. Give your answer to the nearest square centimetre.
(a)1909 cm²
(b)5091 cm²
(c)318 cm²
(d)2546 cm²
8.The point R(−6, 9) is translated by the vector $(- 11 5)$ . Write down the coordinates of the image of R.
(a)(−1, 9)
(b)(−1, −2)
(c)(−6, −2)
(d)(−11, 20)
9.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
(a)£24.00
(b)£2.94
(c)£29.40
(d)£2940.00
10.In triangle ABC, angle ABC = 47°, AC = 12.5 cm and BC = 9.2 cm. Work out the size of angle BAC. Give your answer to 1 decimal place.
(a)57.4°
(b)147.4°
(c)32.6°
(d)83.6°
11.A, B, C and D are points on a circle, and ABCD is a cyclic quadrilateral with the vertices in that order around the circle. Angle ABC = 108° and angle ADC = 72°. Which circle theorem is the reason that angle ABC + angle ADC = 180°?
(a)The angle at the centre is twice the circumference angle
(b)The angle between a tangent and a radius is 90°
(c)The angle in a semicircle is 90°
(d)Opposite angles in a cyclic quadrilateral sum to 180°
12.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?
(a)a triangle
(b)a triangle with a rectangle attached
(c)two triangles joined at their bases
(d)a rectangle
13.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.
(a)64 cm²
(b)32 cm²
(c)20 cm²
(d)8 cm²
14.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.
(a)50
(b)25
(c)13
(d)12
15.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.
(a)4.2 m
(b)2.8 m
(c)1.4 m
(d)7.84 m

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