Sit this paper under timed conditions before you look at the marking key. Show your working — method marks are given for it. There is a printable PDF below if you would rather write on paper.

1. Question 14 marks
   At its closest approach, the distance from Earth to Mars is approximately 54 600 000 km.
   1. (a)Write down this distance in the form a × 10^k, where 1 ≤ a < 10 and k. ∈ ℤ1
   2. A radio signal travels through space at a speed of 3.00 × 10⁵ km s⁻¹.
   3. (b)Calculate the time, in seconds, for a radio signal to travel from Earth to Mars.2
   4. (c)Give your answer to part
   5. (b)in minutes.1
2. Question 25 marks
   An engineering student in Tokyo estimates the height of the Tokyo Skytree to be 630 m. The actual height is 634 m.
   1. (a)Calculate the percentage error in the student’s estimate.2
   2. A walkway near the tower is 380 m long, correct to the nearest 10 m.
   3. (b)Write down the lower bound and the upper bound of the length of the walkway.2
   4. (c)Five identical walkways are laid end to end. Write down the minimum possible total length.1
3. Question 35 marks
   The Teatro Colón concert hall in Buenos Aires has 30 rows of seats. The first row has 22 seats, and each successive row has 4 more seats than the row in front of it.
   1. (a)Find the number of seats in row 30.2
   2. (b)Find the total number of seats in the concert hall.2
   3. (c)For a sold-out concert, each ticket costs 150 pesos. Calculate the total ticket revenue.1
4. Question 45 marks
   A music video is posted online in Seoul. On the first day it receives 800 views. The number of views on each following day is 1.35 times the number of views on the previous day.
   1. (a)Find the number of views on day 8.2
   2. (b)Find the total number of views during the first 8 days.2
   3. (c)Find the first day on which the number of views in a single day exceeds 20 000.1
5. Question 56 marks
   Amina invests 12 000 pula (BWP) in a savings account in Gaborone. The account pays a nominal annual interest rate of 4.5 %, compounded monthly. She leaves the money in the account for 6 years.
   1. (a)Calculate the value of Amina’s investment after 6 years.3
   2. During the same period, the average annual rate of inflation is 2.8 %.
   3. (b)Calculate the real value of the investment after 6 years, taking inflation into account.2
   4. (c)State, with a reason, whether the purchasing power of Amina’s money has increased.1
6. Question 65 marks
   The cost, C, in Kenyan shillings (KES), of a taxi journey of d kilometres in Nairobi is modelled by C = 200 + 65 d.
   1. (a)Write down what the value 65 represents in this model.1
   2. (b)Find the cost of a journey of 12 km.2
   3. (c)Wanjiru pays 1500 KES for a journey. Find the distance she travelled.2
7. Question 76 marks
   A water jet at the Dubai Fountain is modelled by h ( x) = − 0.24 x²+ 1.68 x + 1.2, x ≥ 0, where h is the height of the water above the pool surface, in metres, and x is the horizontal distance from the nozzle, in metres.
   1. (a)Write down the height of the nozzle above the pool surface.1
   2. (b)Using your graphic display calculator, find the maximum height reached by the water jet.2
   3. (c)Find the horizontal distance from the nozzle to the point where the water lands on the pool surface.2
   4. (d)Hence write down the domain of h for this model.1
8. Question 85 marks
   A cup of coffee is served in a café in Oslo. Its temperature, T, in °C, after t minutes is modelled by T ( t) = 21 + 69 × ( 0.94)^t.
   1. (a)Write down the temperature of the coffee when it is served.1
   2. (b)Find the temperature of the coffee after 10 minutes.2
   3. (c)Find the time taken for the coffee to cool to 40 °C.2
9. Question 95 marks
   From a point A on level ground, 80 m from the base of the Burj Khalifa, the angle of elevation of the top of the tower is 84.5°.
   1. (a)Find the height of the tower. Give your answer to the nearest metre.2
   2. An observer walks 40 m directly away from the tower, from A to point B.
   3. (b)Find the angle of elevation of the top of the tower from B.3
10. Question 106 marks
    A triangular park in Cape Town has vertices A, B and C, where AB = 140 m, AC = 95 m and angle BAC = 68°.
    1. (a)Find the length of BC.3
    2. (b)Find the area of the park.2
    3. (c)Find the size of angle ABC.1
11. Question 115 marks
    A grain silo in Saskatchewan, Canada, is made of a cylinder of radius 4.5 m and height 11 m, with a hemispherical roof of the same radius on top.
    1. (a)Calculate the total volume of the silo.3
    2. (b)Grain fills 85 % of the total volume. Calculate the volume of grain in the silo.2
12. Question 125 marks
    The monthly rainfall, in mm, recorded in Mumbai during one year was: 2, 1, 3, 14, 92, 485, 617, 340, 264, 64, 13, 3
    1. (a)Write down the median monthly rainfall.1
    2. (b)Find the lower quartile and the upper quartile.2
    3. (c)Determine, using calculations, whether the value 617 is an outlier for this data.2
13. Question 136 marks
    The masses of apples harvested in a Chilean orchard are normally distributed with mean 168 g and standard deviation 12 g. An apple is selected at random.
    1. (a)Find the probability that the apple has a mass greater than 180 g.2
    2. (b)Find the probability that the apple has a mass between 150 g and 180 g.2
    3. The heaviest 5 % of apples are sold as premium fruit.
    4. (c)Find the minimum mass of a premium apple.2
14. Question 146 marks
    A phone factory in Vietnam has two assembly lines. Line A produces 60 % of the phones and Line B produces the remaining 40 %. On average, 3 % of phones from Line A and 8 % of phones from Line B are defective. A phone is chosen at random from a day’s production.
    1. (a)Using a tree diagram or otherwise, find the probability that the phone is defective.3
    2. (b)Given that the phone is defective, find the probability that it was produced by Line A.2
    3. (c)The factory produces 2000 phones in one day. Find the expected number of defective phones.1
15. Question 156 marks
    Consider the curve y = x³− 9 x²+ 24 x − 10.
    1. (a)Find dy dx.2
    2. (b)Find the gradient of the curve at the point where x = 1.1
    3. (c)Find the values of x at the points where the tangent to the curve is horizontal.2
    4. (d)Hence write down the interval of values of x for which the curve is decreasing.1