Work out the exact value of sin 30° × tan 60° + cos 45°.
From Paper 1 (non-calculator), Higher
133 marks
A, B and C are points on a circle with centre O. Angle AOC = 128°. B is on the major arc. (a) Find angle ABC. (b) D is on the minor arc AC. Find angle ADC. Give a reason for each answer.
From Paper 1 (non-calculator), Higher
192 marks
Describe fully the single transformation that maps the triangle with vertices (1, 1), (3, 1), (1, 2) onto the triangle with vertices (−1, 1), (−1, 3), (−2, 1).
From Paper 1 (non-calculator), Higher
234 marks
OABC is a parallelogram with OA = a and OC = c. M is the midpoint of AB and N is the point on OB such that ON : NB = 2 : 1. Find CN and CM in terms of a and c, and hence show that C, N and M lie on a straight line.
From Paper 1 (non-calculator), Higher
263 marks
A regular polygon has 15 sides. Work out the size of each interior angle, and explain why regular polygons with interior angle 100° cannot exist.
From Paper 2 (calculator), Higher
33 marks
In a right-angled triangle the side opposite angle θ is 7 cm and the hypotenuse is 12 cm. Calculate θ to 1 decimal place.
From Paper 2 (calculator), Higher
43 marks
A cuboid measures 8 cm by 6 cm by 5 cm. Calculate the length of the longest diagonal to 1 decimal place.
From Paper 2 (calculator), Higher
55 marks
Triangle ABC has AC = 9 cm, BC = 11 cm and angle ACB = 48°. (a) Calculate AB to 3 significant figures. (b) Calculate the area of the triangle to 3 significant figures.
From Paper 2 (calculator), Higher
63 marks
In triangle PQR, angle P = 52°, angle Q = 71° and QR = 14 cm. Calculate PR to 3 significant figures.
From Paper 2 (calculator), Higher
74 marks
A solid cone has radius 6 cm and perpendicular height 14 cm. Calculate (a) its volume and (b) its total surface area, both to 3 significant figures. (V = ⅓πr²h, curved surface area = πrl)
From Paper 2 (calculator), Higher
124 marks
Two mathematically similar solids have lengths in the ratio 1 : 3. The smaller has surface area 40 cm² and volume 24 cm³. Find the surface area and volume of the larger solid.
From Paper 2 (calculator), Higher
134 marks
A sector has radius 9 cm and angle 140°. Work out (a) its area and (b) its perimeter, to 1 decimal place.
From Paper 2 (calculator), Higher
234 marks
A garden is a trapezium with parallel sides 12 m and 18 m and perpendicular height 8 m. A circular pond of radius 1.5 m is dug in it. Turf costs £4.50 per m². Work out the cost of turfing the rest of the garden.
From Paper 3 (calculator), Higher
33 marks
In a right-angled triangle the side opposite angle θ is 5 cm and the hypotenuse is 13 cm. Calculate θ to 1 decimal place.
From Paper 3 (calculator), Higher
43 marks
A cuboid measures 12 cm by 5 cm by 9 cm. Calculate the length of the longest diagonal to 1 decimal place.
From Paper 3 (calculator), Higher
55 marks
Triangle ABC has AC = 7.5 cm, BC = 10.2 cm and angle ACB = 115°. (a) Calculate AB to 3 significant figures. (b) Calculate the area of the triangle to 3 significant figures.
From Paper 3 (calculator), Higher
64 marks
A solid cone has radius 4.5 cm and perpendicular height 10 cm. Calculate (a) its volume and (b) its total surface area, both to 3 significant figures. (V = ⅓πr²h, curved surface area = πrl)
From Paper 3 (calculator), Higher
74 marks
Two mathematically similar solids have lengths in the ratio 1 : 2. The smaller has surface area 54 cm² and volume 30 cm³. Find the surface area and volume of the larger solid.
From Paper 3 (calculator), Higher
144 marks
A sector has radius 15 cm and angle 72°. Work out (a) its area and (b) its perimeter, to 1 decimal place.
From Paper 3 (calculator), Higher
213 marks
A regular polygon has 12 sides. Work out the size of each interior angle, and explain why regular polygons with interior angle 100° cannot exist.
Score 0 / 71 · 0 of 20 marked
This paper is written by Plasmo in the style of the AQA GCSE Maths exam. It is not a past paper and is not produced or endorsed by the exam board.
Geometry and measures Exam Questions: AQA GCSE Maths | Plasmo