Paper 3 (calculator), Higher

A car is bought for £18,500. Its value depreciates by 12% each year. Work out its value after 4 years, to the nearest pound.

In a right-angled triangle the side opposite angle θ is 11 cm and the hypotenuse is 20 cm. Calculate θ to 1 decimal place.

Triangle ABC has AC = 6.4 cm, BC = 9.8 cm and angle ACB = 128°. (a) Calculate AB to 3 significant figures. (b) Calculate the area of the triangle to 3 significant figures.

A solid cone has radius 3.5 cm and perpendicular height 8 cm. Calculate (a) its volume and (b) its total surface area, both to 3 significant figures. (V = ⅓πr²h, curved surface area = πrl)

Two mathematically similar solids have lengths in the ratio 1 : 3. The smaller has surface area 12 cm² and volume 8 cm³. Find the surface area and volume of the larger solid.

Metal A has density 7 g/cm³. A block of metal A has volume 40 cm³ and is melted together with 500 g of metal B to make an alloy of volume 90 cm³ (metal B has density 10 g/cm³). Work out the density of the alloy.

A cyclist accelerates uniformly from rest to 15 m/s in 6 s, travels at 15 m/s until t = 26 s, then decelerates uniformly to rest at t = 36 s. (a) Work out the acceleration. (b) Work out the total distance travelled.

The table shows times taken by commuters.

Time, t (minutes)	Frequency
0 < t ≤ 20	16
20 < t ≤ 30	22
30 < t ≤ 40	28
40 < t ≤ 60	24
60 < t ≤ 100	20

Calculate the frequency density for each class, ready to draw a histogram.

Solve the simultaneous equations x² + y² = 25 y = 2x − 5

Solve 2x² − 9x + 3 = 0. Give your answers to 2 decimal places.

y is inversely proportional to x². When x = 4, y = 20. Find y when x = 10.

A sector has radius 8 cm and angle 230°. Work out (a) its area and (b) its perimeter, to 1 decimal place.

A line passes through (2, -3) and (6, 5). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.

A bag contains 7 red and 5 blue counters. Two counters are taken at random without replacement. Work out the probability that they are the same colour.

The graph of y = x² + 2x − 3 is drawn. Use a tangent to estimate the gradient of the curve at x = 1, and explain why your answer is an estimate.

Solve x² + x − 12 < 0.

Solve cos x = −0.5 for 0° ≤ x ≤ 360°.

400 people took a driving test. 55% passed first time. Of those who failed first time, 40% passed second time. How many people passed on their second attempt?

A garden is a trapezium with parallel sides 9 m and 15 m and perpendicular height 10 m. A circular pond of radius 2 m is dug in it. Turf costs £3.80 per m². Work out the cost of turfing the rest of the garden.

A cylindrical tank has radius 40 cm and height 90 cm. Water flows in at 12 litres per minute. How long does it take to fill the tank? Give your answer in minutes to 1 decimal place. (1 litre = 1000 cm³)

A box exerts a force of 1200 N on the floor. Its base is a rectangle 0.8 m by 0.5 m. Work out the pressure in N/m². (pressure = force ÷ area)

In a survey of 200 people: 90 are under 30. Of these, 72 use social media daily. Of the people aged 30 or over, 44 use social media daily. (a) Complete a two-way table. (b) A daily user is chosen at random. Find the probability they are under 30.

The speed of a car (m/s) at 0, 5, 10 and 15 seconds is 0, 6, 10 and 12. Use three trapeziums of equal width to estimate the distance travelled in the first 15 seconds, and state whether this is an under- or over-estimate for a curve that bends downwards (concave).