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 triangle ABC, AB = 8 cm, AC = 5 cm and angle BAC = 60°. Work out the value of BC².
(a)49 cm²
(b)129 cm²
(c)69 cm²
(d)89 cm²
2.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.
(a)50 m
(b)201 m
(c)25 m
(d)13 m
3.A locus consists of all the points that are the same perpendicular distance from two parallel lines 6 cm apart. Describe this locus.
(a)a line parallel to both, 3 cm from each
(b)the perpendicular bisector of the gap
(c)a line parallel to both, 6 cm from each
(d)a circle of radius 3 cm, centred midway
4.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?
(a)XP cannot be compared without knowing the line's length
(b)XP equals every other distance from X to the line
(c)XP is the longest distance from X to the line
(d)XP is the shortest distance from X to the line
5.A model of a bridge is built to a scale where every length on the model is 1/240 of the matching length on the real bridge. A support beam on the model measures 3.6 cm. Work out the length of the real support beam, giving your answer in metres.
(a)86.4 m
(b)8.64 m
(c)0.0864 m
(d)864 m
6.PT is a tangent to a circle with centre O, touching the circle at T. C is a point on the circle such that C lies inside angle OTP (the right angle between the radius OT and the tangent PT), and OC is a radius. Angle TOC = 130°. Work out the size of angle PTC, the angle between the tangent PT and the chord TC.
(a)65°
(b)50°
(c)25°
(d)115°
7.In triangle ABC, AB = 5 cm, BC = 3 cm and AC = 7 cm. Work out the size of angle ABC.
(a)120°
(b)150°
(c)90°
(d)60°
8.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°
9.A, B and C are points on a circle with centre O. B is on the major arc AC. Angle AOC = (4x + 20)°. Work out the size of angle ABC in terms of x, in its simplest form.
(a)(4x + 20)°
(b)(2x + 10)°
(c)(8x + 40)°
(d)(4x + 10)°
10.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
11.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.
(a)45 m
(b)4500 m
(c)450 m
(d)0.45 m
12.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.
(a)5 cm
(b)30 cm
(c)7.5 cm
(d)15 cm
13.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.
(a)11.4 cm
(b)4.8 cm
(c)14.7 cm
(d)58.8 cm
14.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.
(a)a rounded rectangle: 5 m by 4 m with semicircular ends
(b)a circle of radius 2 m
(c)a rectangle, 9 m by 4 m
(d)a rectangle, 5 m by 2 m
15.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.
(a)49°
(b)41°
(c)82°
(d)98°

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