Paper 2 (calculator), Higher

£6,200 is invested at 2.8% compound interest per year. Work out the value of the investment after 5 years. Give your answer to the nearest penny.

In a sale, prices are reduced by 15%. A coat costs £102.00 in the sale. Work out the price before the sale.

In a right-angled triangle the side opposite angle θ is 9 cm and the hypotenuse is 15 cm. Calculate θ to 1 decimal place.

A cuboid measures 10 cm by 7 cm by 6 cm. Calculate the length of the longest diagonal to 1 decimal place.

Triangle ABC has AC = 8 cm, BC = 13 cm and angle ACB = 62°. (a) Calculate AB to 3 significant figures. (b) Calculate the area of the triangle to 3 significant figures.

In triangle PQR, angle P = 47°, angle Q = 68° and QR = 11 cm. Calculate PR to 3 significant figures.

A solid cone has radius 5 cm and perpendicular height 12 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 18.6 cm to the nearest 0.1 cm and width 9.2 cm to the nearest 0.1 cm. Work out the upper bound and lower bound of the area.

Solve 3x² + 4x − 5 = 0. Give your answers to 2 decimal places.

The table shows the number of goals scored in 30 matches.

Number of goals	1	2	3	4	5
Frequency	4	10	8	6	2

Work out the mean number of goals per match.

A train travels 171 km in 54 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 : 4. The smaller has surface area 25 cm² and volume 15 cm³. Find the surface area and volume of the larger solid.

A sector has radius 12 cm and angle 105°. Work out (a) its area and (b) its perimeter, to 1 decimal place.

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

f(x) = 4x − 1 and g(x) = x² − 3. (a) Find fg(x). (b) Find f⁻¹(x). (c) Show that f(x) = g(x) can be written as x² − 4x − 2 = 0.

80 fish are caught, tagged and released. Later 75 fish are caught and 15 of them are tagged. Estimate the number of fish in the lake and state one assumption.

Solve 5x − 3 > 12 and −2 < x ≤ 5 together, and list the integers that satisfy both.

Two groups sat a test. Group A: minimum 12, lower quartile 20, median 31, upper quartile 38, maximum 50. Group B: minimum 8, lower quartile 24, median 27, upper quartile 36, maximum 44. Compare the distributions of the two groups.

The circle x² + y² = 169 passes through the point P(5, 12). Find the equation of the tangent to the circle at P.

The population of a town rose from 36,400 to 41,950. Work out the percentage increase to 1 decimal place.

Pack A has 750 g of cereal for £3.15. Pack B has 500 g for £2.20. Which is better value? Show your working.

A sphere has radius 4.5 cm. Work out its volume and surface area to 3 significant figures. (V = 4/3πr³, A = 4πr²)

A school has 180 students in Year 10, 220 students in Year 11. A stratified sample of 40 students is taken. How many should be from Year 10?

A spinner is spun 200 times and lands on red 64 times. (a) Work out the relative frequency of red. (b) Estimate how many times it will land on red in 500 spins. (c) Explain whether the spinner is likely to be fair if it has 4 equal sections.

The probability that a biased coin lands on heads is 0.18. The coin is thrown 350 times. Work out the expected number of heads.