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 rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.
(a)18 units
(b)7 units
(c)14 units
(d)12 units
2.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?
(a)Draw equal arcs from X and Y, meeting below line l.
(b)Draw an arc centred at P through only one of X or Y.
(c)Join X and Y with a straight line.
(d)Draw a circle through X, Y and P.
3.A tent has the cross-section of a right-angled triangle. The sloping side of the cross-section is 10 m long, and it makes an angle of 60° with the horizontal ground. Using the exact value of cos 60°, work out the horizontal distance covered by the sloping side.
(a)8.7 m
(b)20 m
(c)5 m
(d)10 m
4.In triangle ABC the angle at C is 90°, AC = 8 cm and the angle at A is 30°. Work out the length of BC. Give your answer to 1 decimal place.
(a)13.9 cm
(b)4.0 cm
(c)6.9 cm
(d)4.6 cm
5.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.
(a)(−35, 55)
(b)(35, −55)
(c)(−35, −55)
(d)(35, 55)
6.A rectangular name card has a perimeter of 30 cm. The card is 9 cm long. Work out the width of the card.
(a)6 cm
(b)21 cm
(c)12 cm
(d)7.5 cm
7.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
(a)7 m
(b)5 m
(c)12 m
(d)25 m
8.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
(a)18
(b)36
(c)13
(d)26
9.Work out the exact value of tan 30° + tan 30°.
(a)2√3/3
(b)√3/3
(c)√3
(d)2√3
10.A circular tabletop has a radius of 15 cm. Work out the area of the tabletop. Use π = 3.14. Give your answer to 1 decimal place.
(a)2826.0 cm²
(b)94.2 cm²
(c)47.1 cm²
(d)706.5 cm²
11.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
12.Which of these statements about the area formula Area = 1/2ab sin C is correct?
(a)AB, BC and angle ABC: Area = 1/2 × AB × BC × sin(BAC)
(b)Three sides, no angle: Area still = 1/2 AB×AC×sin(BAC)
(c)AB, AC and angle BAC: Area = 1/2 × AB × AC × sin(BAC)
(d)AB, AC and angle ABC: Area = 1/2 × AB × AC × sin(ABC)
13.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.
(a)94.2 cm³
(b)90 cm³
(c)282.6 cm³
(d)1130.4 cm³
14.Quadrilateral PQRS has angle P = 92°, angle Q = 84° and angle R = 106°. Work out the size of angle S.
(a)68°
(b)170°
(c)78°
(d)184°
15.Two similar company logos are printed at different sizes. The area of the larger logo is 2.25 times the area of the smaller logo. Work out the length scale factor from the smaller logo to the larger logo.
(a)2.25
(b)5.0625
(c)1.5
(d)1.125

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