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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
Elaine invests £150 000 in a savings account for six years.
The account pays compound interest at a rate of 1.2% per annum.
Calculate the total amount of interest Elaine will get at the end of the six years to the nearest pound.
2. | GCSE Higher |
Winky Lash wants to invest £20 000 for 3 years in a bank. She has the following two choices of banks, both offering compound interest but on different terms:
Leftway Bank1% AER |
::-:: | Righton Bank2.1% for the first year |
Which bank will give Winky the most interest at the end of the three years?
Show all of your working.
3. | GCSE Higher |
The value of a boat is £220 000.
Each year the value decreases by 12% of the value at the beginning of that year.
Work out the value of the boat after four years have passed.
Give your answer to the nearest pound.
4. | GCSE Higher |
Davy Browning buys a premium skateboard.
He gets a discount of 15% off the normal price.
Davy pays £170 for the skateboard.
(a) Work out the normal price of the skateboard.
Saj invests £8000 in a savings account.
The savings account pays compound interest at a rate of 1.8% for the first year then 1.2% for each extra year.
(b) Work out the value of Saj’s investment at the end of 4 years.
5. | GCSE Higher |
(a) Davy Browning earns £54000 per year before paying tax.
He pays tax on his earnings at a rate of 18%.
Calculate the amount Davy has after paying tax.
(b) Patty O’Dawes earns £57810 per year after paying tax at a rate of 18%.
Calculate the amount that Patty earns before paying tax.
(c) Davy opens a savings account with £2500.
The account pays 2.4% per year simple interest.
Calculate the amount in Davy’s account at the end of 5 years.
(d) Patty opens a savings account with £500 at the same time ad Davy.
The account pays 2.1% per year compound interest.
Patty pays another £500 into her account on the same day every year.
Find who has the greater amount in their account at the end of 5 years.
6. | GCSE Higher |
The value of a new car is £22 000.
The value of the car decreases by 30% in the first year then 10% in each of the next 5 years.
Work out the value of the car after 6 years.
7. | GCSE Higher |
Using \(x_{n+1}=-5-\frac{6}{x_n^2} \)
with \(x_0 = -1.5 \)
(a) find the values of \(x_1, x_2 \) and \(x_3\)
(b) Explain the relationship between the values of \(x_1, x_2 \) and \(x_3\) and the equation \(x^3+5x^2+6=0 \)
8. | GCSE Higher |
Michael Banks invests £2000 in a savings account for two years. The account pays 2% compound interest per annum.
Michael has to pay 15% tax on the interest earned each year. This tax is taken from the account at the end of each year.
How much money will Michael have in his account at the end of the two years? Give your answer to the nearest penny.
9. | GCSE Higher |
The value of a new house, \(V\), is given by:
$$V = 120000 × 1.1^t$$where t is the age of the house in complete years and V is in pounds.
(a) Write down the value of V when t = 0.
(b) What is the value of V when t = 4?
(c) After how many complete years will the house’s value rise above £200 000?
10. | GCSE Higher |
Here are the details for two bank accounts.
Dayter Bank
2% per year compound interest.
No withdrawals until the end of three years.
Rivver Bank
3% interest for the first year
2% for the second year
1% for the third year.
Withdrawals allowed at any time.
Saviour has £2000 he wants to invest.
(a) Calculate, to the nearest penny, which bank would give him most money if he invests his money for 3 years.
(b) Explain why he might not want to use Dayter Bank.
11. | GCSE Higher |
Montague invests £7000 for six years in a bank offering compound interest at \(x%\) per annum.
The investment is worth £7654.10 at the end of the six years.
Find the value of \(x\).
12. | GCSE Higher |
Consider the following cubic equation:
$$x^3-7x-5=0$$
An approximate solution can be found by using the following iterative process.
$$x_{n+1}=\frac{(x_n)^3-5}{7}$$(a) Find \(x_2\) and \(x_3\) if \(x_1=-1\)
Work out the solution to 6 decimal places.
13. | IB Analysis and Approaches |
Ramin buys a car for £25,000. The value of the car decreases by 20% in the first year.
(a) Find the value of the car at the end of the first year.
After the first year, the value of the car decreases by 15% in each subsequent year.
(b) Find the value of Ramin’s car 12 years after he buys it, giving your answer to the nearest pound.
When Ramin has owned the car for \(n\) complete years, the value of the car is less than 20% of its original value.
(c) Find the least value of \(n\).
14. | IB Analysis and Approaches |
Ruby invests a certain amount of money in a bank account that pays a nominal annual interest rate of 6.7%, compounded quarterly.
The amount of money in Ruby’s account at the end of each year forms a geometric sequence with common ratio, r.
(a) Find the value of the Annual Equivalent Rate (AER) represented by r.
(b) If Ruby invested her money on the 1st January 2022, find the year in which the amount of money in Ruby's account will become three times the amount she invested.
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