APS AND GPS PROBLEMS FOR IB STUIES
1. A woman deposits $100 into her son's savings account on his first birthday. On his second birthday she deposits $125, $150 on his third birthday, and so on.
(a) How much money would she deposit into her son's account on his 17th birthday?
(b) How much in total would she have deposited after her son's 17th birthday?
Working:
Answers:
(a) …………………………………………..
(b) …………………………………………..
(Total 4 marks)
2. The population of Bangor is growing each year. At the end of 1996, the population was 40 000. At the end of 1998, the population was 44 100. Assuming that these annual figures follow a geometric progression, calculate
(a) the population of Bangor at the end of 1997;
(b) the population of Bangor at the end of 1992.
Working:
Answers:
(a) …………………………………………..
(b) …………………………………………..
(Total 4 marks)
3. Mr Jones decides to increase the amount of money he spends on food by d GBP every year. In the first year he spends a GBP. In the 8th year he spends twice as much as in the 4th year. In the 20th year he spends 4000 GBP. Find the value of d.
Working:
Answer:
…………………………………………..........
(Total 4 marks)
4. The tuition fees for the first three years of high school are given in the table below.
Year
Tuition fees
(in dollars)
1
2000
2
2500
3
3125 These tuition fees form a geometric sequence.
(a) Find the common ratio, r, for this sequence.
(b) If fees continue to rise at the same rate, calculate (to the nearest dollar) the total cost of tuition fees for the first six years of high school.
Working:
Answers:
(a) …………………………………………..
(b) ..................................................................
(Total 4 marks)
5. The first four terms of an arithmetic sequence are shown below. 1, 5, 9, 13,......
(a) Write down the nth term of the sequence.
(b) Calculate the 100th term of the sequence.
(c) Find the sum of the first 100 terms of the sequence.
Working:
Answers:
(a) …………………………………………..
(b)
(a) How much money would she deposit into her son's account on his 17th birthday?
(b) How much in total would she have deposited after her son's 17th birthday?
Working:
Answers:
(a) …………………………………………..
(b) …………………………………………..
(Total 4 marks)
2. The population of Bangor is growing each year. At the end of 1996, the population was 40 000. At the end of 1998, the population was 44 100. Assuming that these annual figures follow a geometric progression, calculate
(a) the population of Bangor at the end of 1997;
(b) the population of Bangor at the end of 1992.
Working:
Answers:
(a) …………………………………………..
(b) …………………………………………..
(Total 4 marks)
3. Mr Jones decides to increase the amount of money he spends on food by d GBP every year. In the first year he spends a GBP. In the 8th year he spends twice as much as in the 4th year. In the 20th year he spends 4000 GBP. Find the value of d.
Working:
Answer:
…………………………………………..........
(Total 4 marks)
4. The tuition fees for the first three years of high school are given in the table below.
Year
Tuition fees
(in dollars)
1
2000
2
2500
3
3125 These tuition fees form a geometric sequence.
(a) Find the common ratio, r, for this sequence.
(b) If fees continue to rise at the same rate, calculate (to the nearest dollar) the total cost of tuition fees for the first six years of high school.
Working:
Answers:
(a) …………………………………………..
(b) ..................................................................
(Total 4 marks)
5. The first four terms of an arithmetic sequence are shown below. 1, 5, 9, 13,......
(a) Write down the nth term of the sequence.
(b) Calculate the 100th term of the sequence.
(c) Find the sum of the first 100 terms of the sequence.
Working:
Answers:
(a) …………………………………………..
(b)