Paper 2 (calculator), Higher

£4,500 is invested at 3.5% compound interest per year. Work out the value of the investment after 4 years. Give your answer to the nearest penny.

In a sale, prices are reduced by 15%. A coat costs £68.85 in the sale. Work out the price before the sale.

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.

A cuboid measures 8 cm by 6 cm by 5 cm. Calculate the length of the longest diagonal to 1 decimal place.

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.

In triangle PQR, angle P = 52°, angle Q = 71° and QR = 14 cm. Calculate PR to 3 significant figures.

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)

A rectangle has length 12.4 cm to the nearest 0.1 cm and width 8.6 cm to the nearest 0.1 cm. Work out the upper bound and lower bound of the area.

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

The table shows the number of goals scored in 25 matches.

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

Work out the mean number of goals per match.

A train travels 126 km in 45 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 : 3. The smaller has surface area 40 cm² and volume 24 cm³. Find the surface area and volume of the larger solid.

A sector has radius 9 cm and angle 140°. Work out (a) its area and (b) its perimeter, to 1 decimal place.

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

f(x) = 3x + 2 and g(x) = x² − 4. (a) Find fg(x). (b) Find f⁻¹(x). (c) Show that f(x) = g(x) can be written as x² − 3x − 6 = 0.

60 fish are caught, tagged and released. Later 50 fish are caught and 12 of them are tagged. Estimate the number of fish in the lake and state one assumption.

Solve 3x + 4 > 7 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 34, the median 47 and the upper quartile 58. (a) Find the interquartile range. (b) Compare with another class whose median is 50 and IQR is 12.

Two groups sat a test. Group A: minimum 21, lower quartile 35, median 48, upper quartile 60, maximum 78. Group B: minimum 30, lower quartile 44, median 52, upper quartile 57, maximum 70. Compare the distributions of the two groups.

The probability that a biased coin lands on heads is 0.35. The coin is thrown 80 times. Work out the expected number of heads.

The circle x² + y² = 25 passes through the point P(3, 4). Find the equation of the tangent to the circle at P.

The population of a town rose from 48,200 to 53,750. Work out the percentage increase to 1 decimal place.

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.

200 people took a driving test. 45% passed first time. Of those who failed first time, 60% passed second time. How many people passed on their second attempt?

Write 0.068 49 correct to 2 significant figures.