Paper 3 (calculator), Higher

In a sale, prices are reduced by 40%. A coat costs £51.00 in the sale. Work out the price before the sale.

A car is bought for £12,000. Its value depreciates by 8% each year. Work out its value after 3 years, to the nearest pound.

In a right-angled triangle the side opposite angle θ is 5 cm and the hypotenuse is 13 cm. Calculate θ to 1 decimal place.

A cuboid measures 12 cm by 5 cm by 9 cm. Calculate the length of the longest diagonal to 1 decimal place.

Triangle ABC has AC = 7.5 cm, BC = 10.2 cm and angle ACB = 115°. (a) Calculate AB to 3 significant figures. (b) Calculate the area of the triangle to 3 significant figures.

A solid cone has radius 4.5 cm and perpendicular height 10 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 54 cm² and volume 30 cm³. Find the surface area and volume of the larger solid.

Metal A has density 8 g/cm³. A block of metal A has volume 25 cm³ and is melted together with 300 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 12 m/s in 8 s, travels at 12 m/s until t = 30 s, then decelerates uniformly to rest at t = 42 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 ≤ 10	18
10 < t ≤ 15	24
15 < t ≤ 20	30
20 < t ≤ 30	26
30 < t ≤ 50	12

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

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

Solve 3x² − 7x − 2 = 0. Give your answers to 2 decimal places.

y is inversely proportional to x². When x = 3, y = 45. Find y when x = 5.

A sector has radius 15 cm and angle 72°. Work out (a) its area and (b) its perimeter, to 1 decimal place.

A line passes through (-2, 5) and (4, -7). (a) Find its equation in the form y = mx + c. (b) Find the gradient of a line perpendicular to it.

A bag contains 6 red and 4 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 − 4x + 1 is drawn. Use a tangent to estimate the gradient of the curve at x = 3, and explain why your answer is an estimate.

A rectangle has length 25 cm to the nearest 1 cm and width 14 cm to the nearest 1 cm. Work out the upper bound and lower bound of the area.

Solve x² − 3x − 10 < 0.

Solve sin x = 0.5 for 0° ≤ x ≤ 360°.

A regular polygon has 12 sides. Work out the size of each interior angle, and explain why regular polygons with interior angle 100° cannot exist.

300 people took a driving test. 35% passed first time. Of those who failed first time, 40% passed second time. How many people passed on their second attempt?

The probability that a biased coin lands on heads is 0.15. The coin is thrown 300 times. Work out the expected number of heads.

Find the highest common factor and the lowest common multiple of 36 and 90.

A length is 6.4 m correct to 1 decimal place. Write down the error interval for the length L.