VCE General Maths Recursion and Financial Modelling 2024 Exam 1 Mini Test
VCAA General Maths Exam 1
This is the full VCE General Maths Exam with worked solutions. You can also try Mini-Tests, which are official VCAA exams split into short tests you can do anytime.
Number of marks: 8
Reading time: 3 minutes
Writing time: 18 minutes
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Recursion and financial modelling - 2024
A first-order linear recurrence relation of the form
\( u_0 = a, \quad u_{n+1} = Ru_n + d \)
generates the terms of a sequence. A geometric sequence will be generated if
- A. \(R=1\) and \(d=-1\)
- B. \(R=1\) and \(d=1\)
- C. \(R=4\) and \(d=-1\)
- D. \(R=2\) and \(d=0\)
Trevor took out a reducing balance loan of $400 000, with interest calculated weekly.
The balance of the loan, in dollars, after \(n\) weeks, \(T_n\), can be modelled by the recurrence relation
\( T_0 = 400\,000, \quad T_{n+1} = 1.00075T_n - 677.55 \)
Assume that there are exactly 52 weeks in a year.
The interest rate, per annum, for this loan is
- A. 0.75%
- B. 3.9%
- C. 4.5%
- D. 7.5%
Liv bought a new car for $35 000. The value of the car will be depreciated by 18% per annum using the reducing balance method.
A recurrence relation that models the year-to-year value of her car is of the form
\( L_0 = 35\,000, \quad L_{n+1} = k \times L_n \)
The value of \(k\) is
- A. 0.0082
- B. 0.18
- C. 0.82
- D. 1.18
Dainika invested $2000 for three years at 4.4% per annum, compounding quarterly.
To earn the same amount of interest in three years in a simple interest account, the annual simple interest rate would need to be closest to
- A. 4.60%
- B. 4.68%
- C. 4.84%
- D. 4.98%
Lee took out a loan of $121 000, with interest compounding monthly. He makes monthly repayments of $2228.40 for five years until the loan is repaid in full.
The total interest paid by Lee is closest to
- A. $4434
- B. $5465
- C. $10 539
- D. $12 704
Use the following information to answer Questions 22 and 23.
Stewart takes out a reducing balance loan of $240 000, with interest calculated monthly.
Stewart makes regular monthly repayments.
Three lines of the amortisation table are shown below.
| Payment number | Payment ($) | Interest ($) | Principal reduction ($) | Balance ($) |
|---|---|---|---|---|
| 0 | 0.00 | 0.00 | 0.00 | 240 000.00 |
| 1 | 2741.05 | 960.00 | 1781.05 | 238 218.95 |
| 2 | 2741.05 |
The principal reduction associated with Payment number 2 is closest to
- A. $1773.93
- B. $1781.05
- C. $1788.17
- D. $2741.05
The number of years that it will take Stewart to repay the loan in full is closest to
- A. 9
- B. 10
- C. 11
- D. 12
André invested $18 000 in an account for five years, with interest compounding monthly.
He adds an extra payment into the account each month immediately after the interest is calculated.
For the first two years, the balance of the account, in dollars, after \(n\) months, \(A_n\), can be modelled by the recurrence relation
\( A_0 = 18\,000, \quad A_{n+1} = 1.002A_n + 100 \)
After two years, André decides he would like the account to reach a balance of $30 000 at the end of the five years.
He must increase the value of the monthly extra payment to achieve this.
The minimum value of the new payment for the last three years is closest to
- A. $189.55
- B. $195.45
- C. $202.35
- D. $246.55
End of Multiple-Choice Question Book
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