Paper 6 (calculator), Higher

In a sale, prices are reduced by 10%. A coat costs £37.80 in the sale. Work out the price before the sale.

A car is bought for £9,600. Its value depreciates by 6% each year. Work out its value after 5 years, to the nearest pound.

In a right-angled triangle the side opposite angle θ is 13 cm and the hypotenuse is 21 cm. Calculate θ to 1 decimal place.

A cuboid measures 9 cm by 9 cm by 4 cm. Calculate the length of the longest diagonal to 1 decimal place.

Triangle ABC has AC = 5.2 cm, BC = 7.9 cm and angle ACB = 99°. (a) Calculate AB to 3 significant figures. (b) Calculate the area of the triangle to 3 significant figures.

A solid cone has radius 6.5 cm and perpendicular height 15 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 : 2. The smaller has surface area 72 cm² and volume 45 cm³. Find the surface area and volume of the larger solid.

Metal A has density 9 g/cm³. A block of metal A has volume 30 cm³ and is melted together with 250 g of metal B to make an alloy of volume 55 cm³ (metal B has density 10 g/cm³). Work out the density of the alloy.

A cyclist accelerates uniformly from rest to 9 m/s in 5 s, travels at 9 m/s until t = 25 s, then decelerates uniformly to rest at t = 33 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 ≤ 5	10
5 < t ≤ 10	25
10 < t ≤ 20	40
20 < t ≤ 40	30
40 < t ≤ 60	15

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

Solve the simultaneous equations x² + y² = 25 y = x − 1

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

y is inversely proportional to x². When x = 2, y = 36. Find y when x = 3.

A sector has radius 14 cm and angle 50°. Work out (a) its area and (b) its perimeter, to 1 decimal place.

A line passes through (-3, 1) and (1, -11). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.

A bag contains 9 red and 3 blue counters. Two counters are taken at random without replacement. Work out the probability that they are the same colour.

Two parallel lines are crossed by a transversal. One of the angles formed is 124°. Work out the size of the co-interior angle and the alternate angle, giving reasons.

A rectangle has length 40 cm to the nearest 1 cm and width 22 cm to the nearest 1 cm. Work out the upper bound and lower bound of the area.

Solve x² − 4x − 21 < 0.

Solve sin x = −√3/2 for 0° ≤ x ≤ 360°.

A regular polygon has 18 sides. Work out the size of each interior angle, and explain why regular polygons with interior angle 100° cannot exist.

250 people took a driving test. 48% passed first time. Of those who failed first time, 60% passed second time. How many people passed on their second attempt?

The probability that a biased coin lands on heads is 0.3. The coin is thrown 220 times. Work out the expected number of heads.

£3,000 is invested at 1.9% compound interest per year. Work out the value of the investment after 8 years. Give your answer to the nearest penny.

In triangle PQR, angle P = 38°, angle Q = 81° and QR = 9.5 cm. Calculate PR to 3 significant figures.

Estimate the value of (6.89² − 21.3) ÷ 0.512. Show your rounding.

A cylindrical tank has radius 25 cm and height 60 cm. Water flows in at 8 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 900 N on the floor. Its base is a rectangle 0.6 m by 0.4 m. Work out the pressure in N/m². (pressure = force ÷ area)

In a survey of 80 people: 30 are under 30. Of these, 18 use social media daily. Of the people aged 30 or over, 20 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, 2, 4 and 6 seconds is 0, 11, 18 and 22. Use three trapeziums of equal width to estimate the distance travelled in the first 6 seconds, and state whether this is an under- or over-estimate for a curve that bends downwards (concave).

The graph of y = f(x) has a turning point at (2, 5). Write down the coordinates of the turning point of (a) y = f(x − 3) (b) y = −f(x).