IB EXAM Review of Number & Algebra (Pt 2)
1a. [2 marks]
The first term of an arithmetic sequence is 3 and the seventh term is 33.
Calculate the common difference;
1b. [2 marks]
Calculate the 95 term of the sequence;
1c. [2 marks]
Calculate the sum of the first 250 terms.
2a. [4 marks]
In a college 450 students were surveyed with the following results
150 have a television
205 have a computer
220 have an iPhone
75 have an iPhone and a computer
60 have a television and a computer
70 have a television and an iPhone
40 have all three.
Draw a Venn diagram to show this information. Use T to represent the set of students who have a television, C the
set of students who have a computer and I the set of students who have an iPhone.
2b. [2 marks]
Write down the number of students that
(i) have a computer only;
(ii) have an iPhone and a computer but no television.
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2c. [1 mark]
Write down
.
2d. [2 marks]
Calculate the number of students who have none of the three.
2e. [6 marks]
Two students are chosen at random from the 450 students. Calculate the probability that
(i) neither student has an iPhone;
(ii) only one of the students has an iPhone.
2f. [3 marks]
The students are asked to collect money for charity. In the first month, the students collect x dollars and the
students collect y dollars in each subsequent month. In the first 6 months, they collect 7650 dollars. This can be
represented by the equation x + 5y = 7650.
In the first 10 months they collect 13 050 dollars.
(i) Write down a second equation in x and y to represent this information.
(ii) Write down the value of x and of y .
2g. [3 marks]
The students are asked to collect money for charity. In the first month, the students collect x dollars and the
students collect y dollars in each subsequent month. In the first 6 months, they collect 7650 dollars. This can be
represented by the equation x + 5y = 7650.
In the first 10 months they collect 13 050 dollars.
Calculate the number of months that it will take the students to collect 49 500 dollars.
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3a. [2 marks]
Sasha travelled from the USA to Mexico and converted 650 US dollars (USD) to Mexican pesos (MXN). Her bank
offered an exchange rate of 1 USD = 12.50 MXN.
Find the number of MXN that Sasha received.
3b. [1 mark]
Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a commission of 1 %.
The exchange rate was still 1 USD = 12.50 MXN.
Write down the commission charged by the bank in MXN.
3c. [3 marks]
Before her return to the USA, Sasha exchanged 2300 MXN back into USD. The bank charged a commission of 1 %.
The exchange rate was still 1 USD = 12.50 MXN.
Calculate the amount of USD that Sasha received after commission. Give your answer correct to the nearest USD.
4a. [1 mark]
Consider the geometric sequence 16, 8, a, 2, b, …
Write down the common ratio.
4b. [1 mark]
Write down the value of a.
4c. [1 mark]
Write down the value of b.
4d. [3 marks]
The sum of the first n terms is 31.9375. Find the value of n.
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5a. [2 marks]
In this question give all answers correct to the nearest whole number.
Fumie is going for a holiday to Great Britain. She changes
Japanese Yen (JPY) into British Pounds (GBP)
with no commission charged.
The exchange rate between GBP and JPY is
1 GBP = 129 JPY.
Calculate the value of
JPY in GBP.
5b. [4 marks]
At the end of Fumie’s holiday in Great Britain she has 239 GBP. She converts this back to JPY at a bank, which does
not charge commission, and receives 30 200 JPY
(i) Find the exchange rate of this second transaction.
(ii) Determine, when changing GBP back to JPY, whether the exchange rate found in part (b)(i) is better value for
Fumie than the exchange rate in part (a). Justify your answer.
6a. [2 marks]
The exchange rates between the British pound (GBP) and the United States dollar (USD) and between the USD and
the Euro (EUR) are given below.
Find the exchange rate between GBP and EUR in the form 1 GBP = k EUR, where k is a constant. Give your answer
correct to two decimal places.
6b. [4 marks]
Isabella changes 400 USD into Euros and is charged 2 % commission.
Calculate how many Euros she receives. Give your answer correct to two decimal places.
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