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.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°
2.In triangle ABC, AB = x cm, AC = (x + 3) cm, BC = 7 cm and angle BAC = 60°. Work out the value of x.
(a)5
(b)37
(c)−8
(d)8
3.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.
(a)4
(b)45
(c)8
(d)315
4.A tent frame forms a triangle ABC, where AB = 3.5 m is a sloping pole, BC = 2.8 m is the base and AC = 4.2 m is the guy rope. Work out the size of angle ABC, between the pole and the base. Give your answer to 1 decimal place.
(a)75.5°
(b)97.2°
(c)41.4°
(d)82.8°
5.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?
(a)24
(b)6
(c)12
(d)9
6.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
7.Work out the exact value of tan 30° + tan 30°.
(a)2√3/3
(b)√3/3
(c)√3
(d)2√3
8.Two similar triangles have lengths in the ratio 3 : 4. The perimeter of the smaller triangle is 24 cm. Work out the perimeter of the larger triangle.
(a)18 cm
(b)25 cm
(c)32 cm
(d)8 cm
9.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.
(a)18 cm
(b)28 cm
(c)8 cm
(d)4 cm
10.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.
(a)10.0 cm
(b)5.0 cm
(c)7.1 cm
(d)14.1 cm
11.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
12.A garden is made of two triangular flower beds, ABC and ACD, joined along the edge AC. In triangle ABC, angle ABC = 90°, AB = 5 m and BC = 12 m. In triangle ACD, AD = 9 m and angle CAD = 40°, the angle between AC and AD. Work out the area of flower bed ACD. Give your answer to 1 decimal place.
(a)49.2 m²
(b)44.8 m²
(c)37.6 m²
(d)14.5 m²
13.Two similar shapes have lengths in the ratio 1 : 3. A side of the smaller shape is 4 cm long. Work out the length of the corresponding side of the larger shape.
(a)36 cm
(b)12 cm
(c)7 cm
(d)4 cm
14.In geometry, which of the following best describes a 'plane'?
(a)A flat surface extending infinitely in two directions
(b)A straight line extending in one direction
(c)A single, fixed position with no size
(d)A flat, bounded face on a 3D shape
15.A line passes through the points (1, 2) and (3, 6). The line is reflected in the x-axis, and the image is then translated by the vector (2, 0). Work out the gradient of the image line after both transformations.
(a)1/2
(b)−2
(c)2
(d)−1/2

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