VCE General Maths Recursion and Financial Modelling 2023 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 - 2023
A sequence of numbers is generated by the recurrence relation shown below.
\( T_0 = 5, \quad T_{n+1} = -T_n \)
The value of \(T_2\) is
- A. –10
- B. –5
- C. 0
- D. 5
- E. 10
Use the following information to answer Questions 18 and 19.
Gus purchases a coffee machine for $15 000 and depreciates its value using the unit cost method. The rate of depreciation is $0.04 per cup of coffee made. A recurrence relation that models the year-to-year value \(G_n\), in dollars, of the machine is
\( G_0 = 15000, \quad G_{n+1} = G_n - 1314 \)
A rule for \(G_n\), the value of the machine after \(n\) years is
- A. \( G_n = 15000 - 0.04n \)
- B. \( G_n = 15000 + 0.04n \)
- C. \( G_n = 15000 - 1314n \)
- D. \( G_n = 1314 - 0.04n \)
- E. \( G_n = 1314 + 0.04n \)
The number of cups made by the machine per year is
- A. 1314
- B. 13 686
- C. 15 000
- D. 31 536
- E. 32 850
Use the following information to answer Questions 20 and 21.
For taxation purposes, Audrey depreciates the value of her $3000 computer over a four-year period. At the end of the four years, the value of the computer is $600.
If Audrey uses flat rate depreciation, the depreciation rate, per annum is
- A. 10%
- B. 15%
- C. 20%
- D. 25%
- E. 33%
If Audrey uses reducing balance depreciation, the depreciation rate, per annum is closest to
- A. 10%
- B. 15%
- C. 20%
- D. 25%
- E. 33%
Timmy took out a reducing balance loan of $500 000, with interest calculated monthly. The balance of the loan, in dollars, after \(n\) months, \(T_n\), can be modelled by the recurrence relation
\( T_0 = 500\,000, \quad T_{n+1} = 1.00325T_n - 2611.65 \)
A final repayment that will fully repay the loan to the nearest cent is
- A. $2605.65
- B. $2609.18
- C. $2611.65
- D. $2614.12
- E. $2615.81
Tavi took out a loan of $20 000, with interest compounding quarterly. She makes quarterly repayments of $653.65. The graph below represents the balance in dollars of Tavi's loan at the end of each quarter of the first year of the loan.
The effective interest rate for the first year of Tavi's loan is closest to
- A. 3.62%
- B. 3.65%
- C. 3.66%
- D. 3.67%
- E. 3.68%
The following recurrence relation models the value, \(P_n\), of a perpetuity after \(n\) time periods.
\( P_0 = a, \quad P_{n+1} = RP_n - d \)
The value of \(R\) can be found by calculating
- A. \( a + d \)
- B. \( \frac{a+d}{a} \)
- C. \( \frac{a+d}{d} \)
- D. \( 1 + \frac{a+d}{a} \)
- E. \( 1 + \frac{a+d}{d} \)
End of Multiple-Choice Question Book
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