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Question
56 students were given a test out of 40 marks. The teacher used the following box and whisker plot to represent the marks of the students.
Write down the median mark.
Write down the 75th percentile mark.
Write down the range of marks.
Estimate the number of students who achieved a mark greater than 32.
Answer/Explanation
Markscheme
30 (A1) (C1)
[1 mark]
32 (A1) (C1)
[1 mark]
38 – 10 = 28 (A1)(A1) (C2)
Note: Award (A1) for 10 and 38 seen, (A1) for correct answer only.
[2 marks]
0.25 × 56 = 14 (M1)(A1) (C2)
Note: Award (M1) for multiplying 0.25 by 56.
[2 marks]
Question
A manufacturer in England makes \(16 000\) garden statues. \(12\% \) are defective and cannot be sold.
Find the number of statues that are non-defective.
The manufacturer sells each non-defective statue for \(5.25\) British pounds (GBP) to an American company. The exchange rate from GBP to US dollars (USD) is \(1{\text{ GBP}} = 1.6407{\text{ USD}}\).
Calculate the amount in USD paid by the American company for all the non-defective statues. Give your answer correct to two decimal places.
The American company sells one of the statues to an Australian customer for \(12{\text{ USD}}\). The exchange rate from Australian dollars (AUD) to USD is \(1{\text{ AUD}} = 0.8739{\text{ USD}}\) .
Calculate the amount that the Australian customer pays, in AUD, for this statue. Give your answer correct to two decimal places.
Answer/Explanation
Markscheme
\(0.88 \times 16000\) OR \(16000 – 0.12 \times 16000\) (M1)
\(14080\) (A1) (C2)
[2 marks]
\(1.6407 \times 5.25 \times 14080\) (M1)
\(121 280.54{\text{ USD}}\) (A1)(ft) (C2)
Note: Follow through from their answer to part (a).
[2 marks]
\(12 \times \frac{1}{{0.8739}}\) (M1)
\(13.73{\text{ AUD}}\) (A1) (C2)
Note: If division used in part (b) and multiplication used in part (c), award (M0)(A0) for part (b) and (M1)(A1)(ft) for part (c).
[2 marks]
Question
In this question give all answers correct to 2 decimal places.
George travelled from the USA to Europe and changed \(1200\) dollars (USD) into Euros (EUR). The exchange rate was \(1{\text{ USD}} = 0.8154{\text{ EUR}}\).
Calculate the number of EUR George received.
On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission charged on the exchange. The exchange rate was \(1\) USD = \(0.8202\) EUR.
Calculate the value, in EUR, of the commission that George paid.
On his return, George had \(160\) EUR to change back into USD. There was \(4.5\% \) commission charged on the exchange. The exchange rate was \(1\) USD = \(0.8202\) EUR.
Calculate the number of dollars George received.
Answer/Explanation
Markscheme
The first time the answer is not given to 2 decimal places the final (A1) in that part is not awarded, incorrect rounding, following correct method, can be ignored in subsequent parts.
\(1200 \times 0.8154\) (M1)
\( = 978.48{\text{ EUR}}\) (A1) (C2)
[2 marks]
The first time the answer is not given to 2 decimal places the final (A1) in that part is not awarded, incorrect rounding, following correct method, can be ignored in subsequent parts.
\(160 \times 0.045\) (M1)
\( = 7.20{\text{ EUR}}\) (A1) (C2)
[2 marks]
The first time the answer is not given to 2 decimal places the final (A1) in that part is not awarded, incorrect rounding, following correct method, can be ignored in subsequent parts.
\(152.80 \times \frac{1}{{0.8202}}\) (M1)
Note: Follow through from their answer to part (b).
\( = 186.30{\text{ USD}}\) (A1)(ft) (C2)
Note: Follow through from part (b).
[2 marks]
Question
Dumisani has received a scholarship of 5000 US dollars (USD) to study in Singapore.
He has to travel from South Africa and must change USD for his air fare of 6600 South African rand (ZAR).
The exchange rate is 1USD = 8.2421 ZAR.
In this question give all answers correct to two decimal places.
Calculate the number of USD that Dumisani must change to pay for his air fare.
On arrival in Singapore, Dumisani changes 3000 USD to Singapore dollars (SGD) to pay for his school fees. There is a 2.8% commission charged on the exchange.
Calculate the value, in USD, of the commission that Dumisani has to pay.
The exchange rate is \(1{\text{ USD }} = 1.29903{\text{ SGD}}\).
Calculate the number of SGD Dumisani receives.
Answer/Explanation
Markscheme
\(6600 \times \frac{1}{{8.2421}}\) (M1)
\( = 800.77\) (A1) (C2)
[2 marks]
\(3000 \times 0.028\) (M1)
\( = 84.00\) (accept 84) (A1) (C2)
[2 marks]
\((3000 – 84) \times 1.29903\) (M1)
OR
\(3000 \times 1.29903 \times 0.972\) (M1)
\( = 3787.97\) (A1)(ft) (C2)
Notes: Follow through from their answer to part (b).
Note: Do not penalize in part (c) if conversion process has been reversed consistently ie, multiplication by \(8.2421\) in part (a) and division by \(1.29903\) in part (c).
[2 marks]
Question
Albena travels to Bulgaria on a business trip. She is paid 3550 Bulgarian levs (BGN) at the end of her trip. She converts all her BGN into euros (EUR), at an exchange bureau that sells 1 EUR for 1.95 BGN and charges 3 % commission.
Calculate the amount that Albena receives in EUR.
At the airport shop, Albena buys chocolates that cost 34.50 BGN. She uses 20 EUR to pay for the chocolates but receives her change in BGN. The shop’s exchange rate is 1 EUR = 1.90 BGN.
Find how many BGN she receives as change.
Answer/Explanation
Markscheme
\(\frac{{0.97 \times 3550}}{{1.95}}\) (M1)(M1)(M1)
Note: Award (M1) for \(0.97\) seen, (M1) for \(0.97 \times 3550\), (M1) for division by \(1.95\).
OR
\((3550 – 0.03 \times 3550) \times \frac{1}{{1.95}}\) (M1)(M1)(M1)
Note: Award (M1) for \(0.03 \times 3550\) seen, (M1) for subtracting \(0.03 \times 3550\) from \(3550\), (M1) for division by \(1.95\).
\( = 1765.90{\text{ (EUR)}}\) (A1) (C4)
\(20 \times 1.90 – 34.50\) (M1)
Note: Award (M1) for subtraction of \(34.50\) from their product of \(20 \times 1.90\).
\( = 3.50\,\,\,{\text{(BGN)}}\) (A1) (C2)
Notes: Award at most (M1)(A0) for an answer of \(4\), but only if working seen.
Question
A hotel has a rectangular swimming pool. Its length is \(x\) metres, its width is \(y\) metres and its perimeter is \(44\) metres.
Write down an equation for \(x\) and \(y\).
The area of the swimming pool is \({\text{112}}{{\text{m}}^2}\).
Write down a second equation for \(x\) and \(y\).
Use your graphic display calculator to find the value of \(x\) and the value of \(y\).
An Olympic sized swimming pool is \(50\) m long and \(25\) m wide.
Determine the area of the hotel swimming pool as a percentage of the area of an Olympic sized swimming pool.
Answer/Explanation
Markscheme
\(2x + 2y = 44\) (A1) (C1)
Note: Accept equivalent forms.
\(xy = 112\) (A1) (C1)
\(8\), \(14\) (A1)(ft)(A1)(ft) (C2)
Notes: Accept \(x = 8\), \(y = 14\) OR \(x = 14\), \(y = 8\)
Follow through from their answers to parts (a) and (b) only if both values are positive.
\(\frac{{112}}{{1250}} \times 100\) (M1)
Note: Award (M1) for \(112\) divided by \(1250\).
\( = 8.96\) (A1) (C2)
Note: Do not penalize if percentage sign seen.