| Date | November 2007 | Marks available | 3 | Reference code | 07N.2.sl.TZ0.3 |
| Level | SL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
The following graph shows the temperature in degrees Celsius of Robert’s cup of coffee, \(t\) minutes after pouring it out. The equation of the cooling graph is \(f (t) = 16 + 74 \times 2.8^{−0.2t}\) where \(f (t)\) is the temperature and \(t\) is the time in minutes after pouring the coffee out.
Robert, who lives in the UK, travels to Belgium. The exchange rate is 1.37 euros to one British Pound (GBP) with a commission of 3 GBP, which is subtracted before the exchange takes place. Robert gives the bank 120 GBP.
Find the initial temperature of the coffee.
Write down the equation of the horizontal asymptote.
Find the room temperature.
Find the temperature of the coffee after 10 minutes.
Find the temperature of Robert’s coffee after being heated in the microwave for 30 seconds after it has reached the temperature in part (d).
Calculate the length of time it would take a similar cup of coffee, initially at 20°C, to be heated in the microwave to reach 100°C.
Calculate correct to 2 decimal places the amount of euros he receives.
He buys 1 kilogram of Belgian chocolates at 1.35 euros per 100 g.
Calculate the cost of his chocolates in GBP correct to 2 decimal places.
Markscheme
Unit penalty (UP) is applicable in part (i)(a)(c)(d)(e) and (f)
(UP) 90°C (A1)
[1 mark]
y = 16 (A1)
[1 mark]
Unit penalty (UP) is applicable in part (i)(a)(c)(d)(e) and (f)
(UP) 16°C (ft) from answer to part (b) (A1)(ft)
[1 mark]
Unit penalty (UP) is applicable in part (i)(a)(c)(d)(e) and (f)
(UP) 25.4°C (A1)
[1 mark]
Unit penalty (UP) is applicable in part (i)(a)(c)(d)(e) and (f)
for seeing 20.75 or equivalent (A1)
for multiplying their (d) by their 20.75 (M1)
(UP) 42.8°C (A1)(ft)(G2)
[3 marks]
Unit penalty (UP) is applicable in part (i)(a)(c)(d)(e) and (f)
for seeing \(20 \times 2^{1.5t} = 100\) (A1)
for seeing a value of t between 1.54 and 1.56 inclusive (M1)(A1)
(UP) 1.55 minutes or 92.9 seconds (A1)(G3)
[4 marks]
Financial accuracy penalty (FP) is applicable in part (ii) only.
\(120 - 3 = 117\)
(FP) \(117 \times 1.37\) (A1)
= 160.29 euros (correct answer only) (M1)
first (A1) for 117 seen, (M1) for multiplying by 1.37 (A1)(G2)
[3 marks]
Financial accuracy penalty (FP) is applicable in part (ii) only.
(FP) \(\frac{{13.5}}{{1.37}}\) (A1)(M1)
9.85 GBP (answer correct to 2dp only)
first (A1) is for 13.5 seen, (M1) for dividing by 1.37 (A1)(ft)(G3)
[3 marks]
Examiners report
Many candidates who had not lost a UP in question 2 lost one here. Parts (a), (c) and (d) were reasonably well tackled. Almost everybody had difficulty with the equation of the horizontal asymptote, a common answer being y = 20. Most of the candidates realised that 30 seconds was 0.5 minutes and calculated part (e) correctly. Part (f), solving an exponential equation, was a good discriminator. Trial and error was expected but many students did not think of doing this.
Many candidates who had not lost a UP in question 2 lost one here. Parts (a), (c) and (d) were reasonably well tackled. Almost everybody had difficulty with the equation of the horizontal asymptote, a common answer being y = 20. Most of the candidates realised that 30 seconds was 0.5 minutes and calculated part (e) correctly. Part (f), solving an exponential equation, was a good discriminator. Trial and error was expected but many students did not think of doing this.
Many candidates who had not lost a UP in question 2 lost one here. Parts (a), (c) and (d) were reasonably well tackled. Almost everybody had difficulty with the equation of the horizontal asymptote, a common answer being y = 20. Most of the candidates realised that 30 seconds was 0.5 minutes and calculated part (e) correctly. Part (f), solving an exponential equation, was a good discriminator. Trial and error was expected but many students did not think of doing this.
Many candidates who had not lost a UP in question 2 lost one here. Parts (a), (c) and (d) were reasonably well tackled. Almost everybody had difficulty with the equation of the horizontal asymptote, a common answer being y = 20. Most of the candidates realised that 30 seconds was 0.5 minutes and calculated part (e) correctly. Part (f), solving an exponential equation, was a good discriminator. Trial and error was expected but many students did not think of doing this.
Many candidates who had not lost a UP in question 2 lost one here. Parts (a), (c) and (d) were reasonably well tackled. Almost everybody had difficulty with the equation of the horizontal asymptote, a common answer being y = 20. Most of the candidates realised that 30 seconds was 0.5 minutes and calculated part (e) correctly. Part (f), solving an exponential equation, was a good discriminator. Trial and error was expected but many students did not think of doing this.
Many candidates who had not lost a UP in question 2 lost one here. Parts (a), (c) and (d) were reasonably well tackled. Almost everybody had difficulty with the equation of the horizontal asymptote, a common answer being y = 20. Most of the candidates realised that 30 seconds was 0.5 minutes and calculated part (e) correctly. Part (f), solving an exponential equation, was a good discriminator. Trial and error was expected but many students did not think of doing this.
The financial part was the best done question in the paper and a large majority of candidates gained full marks here.
The financial part was the best done question in the paper and a large majority of candidates gained full marks here.
