Paper 4 (calculator), Higher

£7,500 is invested at 4.2% compound interest per year. Work out the value of the investment after 6 years. Give your answer to the nearest penny.

In a sale, prices are reduced by 30%. A coat costs £73.50 in the sale. Work out the price before the sale.

In a right-angled triangle the side opposite angle θ is 4 cm and the hypotenuse is 9 cm. Calculate θ to 1 decimal place.

A cuboid measures 15 cm by 8 cm by 6 cm. Calculate the length of the longest diagonal to 1 decimal place.

Triangle ABC has AC = 12 cm, BC = 15 cm and angle ACB = 37°. (a) Calculate AB to 3 significant figures. (b) Calculate the area of the triangle to 3 significant figures.

In triangle PQR, angle P = 64°, angle Q = 49° and QR = 18 cm. Calculate PR to 3 significant figures.

A solid cone has radius 7 cm and perpendicular height 18 cm. Calculate (a) its volume and (b) its total surface area, both to 3 significant figures. (V = ⅓πr²h, curved surface area = πrl)

A rectangle has length 8.3 cm to the nearest 0.1 cm and width 5.7 cm to the nearest 0.1 cm. Work out the upper bound and lower bound of the area.

Solve 5x² + 2x − 6 = 0. Give your answers to 2 decimal places.

The table shows the number of goals scored in 40 matches.

Number of goals	0	1	2	3	4	5
Frequency	3	7	11	9	6	4

Work out the mean number of goals per match.

A train travels 234 km in 135 minutes. (a) Work out its average speed in km/h. (b) Convert this speed to metres per second.

Two mathematically similar solids have lengths in the ratio 1 : 5. The smaller has surface area 18 cm² and volume 7 cm³. Find the surface area and volume of the larger solid.

A sector has radius 10 cm and angle 84°. Work out (a) its area and (b) its perimeter, to 1 decimal place.

Using x₀ = 1.5 and the iterative formula xₙ₊₁ = ∛(5 − 2xₙ), find x₁, x₂ and x₃ to 4 decimal places.

f(x) = 2x + 7 and g(x) = x² − 5. (a) Find fg(x). (b) Find f⁻¹(x). (c) Show that f(x) = g(x) can be written as x² − 2x − 12 = 0.

45 fish are caught, tagged and released. Later 60 fish are caught and 9 of them are tagged. Estimate the number of fish in the lake and state one assumption.

Solve 4x + 9 > 3 and −2 < x ≤ 5 together, and list the integers that satisfy both.

From a cumulative frequency graph for 80 students' test marks, the lower quartile is 52, the median 61 and the upper quartile 69. (a) Find the interquartile range. (b) Compare with another class whose median is 64 and IQR is 9.

Two groups sat a test. Group A: minimum 40, lower quartile 55, median 63, upper quartile 71, maximum 90. Group B: minimum 35, lower quartile 49, median 66, upper quartile 70, maximum 82. Compare the distributions of the two groups.

The circle x² + y² = 100 passes through the point P(6, 8). Find the equation of the tangent to the circle at P.

The population of a town fell from 125,400 to 117,900. Work out the percentage decrease to 1 decimal place.

A garden is a trapezium with parallel sides 14 m and 20 m and perpendicular height 6 m. A circular pond of radius 1.2 m is dug in it. Turf costs £5.25 per m². Work out the cost of turfing the rest of the garden.

500 people took a driving test. 62% passed first time. Of those who failed first time, 50% passed second time. How many people passed on their second attempt?

A car is bought for £24,000. Its value depreciates by 15% each year. Work out its value after 3 years, to the nearest pound.

The probability that a biased coin lands on heads is 0.42. The coin is thrown 150 times. Work out the expected number of heads.

Find the highest common factor and the lowest common multiple of 48 and 180.

Pack A has 400 g of cereal for £1.85. Pack B has 650 g for £2.95. Which is better value? Show your working.

A sphere has radius 6 cm. Work out its volume and surface area to 3 significant figures. (V = 4/3πr³, A = 4πr²)

A school has 84 students in the morning shift, 56 students in the evening shift. A stratified sample of 30 students is taken. How many should be from the morning shift?

A spinner is spun 400 times and lands on red 86 times. (a) Work out the relative frequency of red. (b) Estimate how many times it will land on red in 1000 spins. (c) Explain whether the spinner is likely to be fair if it has 4 equal sections.

£1 = €1.17. A bureau charges 1.5% commission on the amount changed. How many euros does someone receive for £800?

The graph of y = f(x) has a turning point at (-1, 4). Write down the coordinates of the turning point of (a) y = f(x − 2) (b) y = −f(x).