Annuities and regular withdrawals: VCE General Mathematics Unit 3 Recursion and financial modelling

Syllabus dot point

“Use a first-order linear recurrence relation and an amortisation table to model and analyse an annuity, and use technology to find the amount to invest, the regular payment, the number of payments or the balance”

VCEGeneral MathematicsUnit 3 Recursion and financial modelling18 min readUpdated 23 Sep 2026

Quick answer

An annuity is a lump sum that pays a regular income: $V_0$ is the amount invested and $V_{n+1} = RV_n - d$ , with interest added before each payment. In an amortisation table, interest is on the previous balance, principal reduction is payment minus interest, and the balance falls by the principal reduction. Use the finance solver with $PV$ negative and $PMT$ positive; if the payment equals the interest, it is a perpetuity.

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What this dot point is asking
The answer
Exam-style questions
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What this dot point is asking

An annuity turns a lump sum into a regular income. Someone invests a large amount (often at retirement), the balance earns compound interest, and after the interest is added each period a fixed payment is paid out. VCAA wants you to model this with the first-order recurrence relation $V_{n+1} = RV_n - d$ , to investigate it step by step with an amortisation table, and to use a CAS finance solver to find whatever is unknown: the amount to invest, the payment, the number of payments, the interest rate, a balance part-way through, or the final payment. The study design groups annuities with perpetuities, the special case where the payment exactly equals the interest so the balance never falls.

Annuities appear on both examinations every year. The 2023 and 2025 examinations both included annuity amortisation tables and recurrence relations, and the 2025 examination included two multi-stage annuity problems.

The answer

How an annuity works

Each period two things happen, in this order:

Interest is added to the balance at the rate per period.
The regular payment is subtracted and paid to the investor.

If $V_n$ is the balance after $n$ payments, $R = 1 + \frac{r}{100}$ is the growth factor for the rate $r\%$ per period, and $d$ is the payment, then

V_0 = \text{amount invested}, \qquad V_{n+1} = RV_n - d.

This is the formula sheet recurrence $u_{n+1} = Ru_n + d$ with $R > 1$ and a negative constant. It is exactly the same mathematics as a reducing balance loan: in a loan the bank lends you the lump sum and you make the payments; in an annuity you lend the lump sum to the financial institution and it makes the payments to you.

Three possible behaviours

Compare the payment $d$ with the interest earned in the first period, $\frac{r}{100}V_0$ .

Payment compared with interest	What happens to the balance	Name
$d > \frac{r}{100}V_0$	Falls, slowly at first then faster, until it runs out	Annuity
$d = \frac{r}{100}V_0$	Stays exactly the same forever	Perpetuity
$d < \frac{r}{100}V_0$	Grows, because some interest stays in the account	Neither: the investment is growing

For $650 000 earning $1.6\%$ per quarter, the interest in the first quarter is $0.016 \times 650\,000 = 10\,400$ dollars. A quarterly payment of $10 400 is a perpetuity. A payment of $22 126.27 exhausts the annuity in exactly 10 years. The figure shows both.

The annuity curve bends downward: early payments are mostly interest, so the balance falls slowly; later payments are mostly principal, so it falls quickly. Note that halfway through the time the balance is well over half of the original amount ($376 159.43 out of $650 000). That fact sank most students on the 2025 examination question above.

Key fact

Annuity: $V_0$ is the amount invested and $V_{n+1} = RV_n - d$ with $R = 1 + \frac{r}{100}$ for the rate per period. Each period: interest $=$ previous balance $\times \frac{r}{100}$ ; principal reduction $=$ payment $-$ interest; new balance $=$ previous balance $-$ principal reduction. If $d$ equals the interest, the annuity is a perpetuity.

The amortisation table

An amortisation table records every step of the recurrence in columns. For $400 000 invested at $4.8\%$ per annum compounding monthly ( $0.4\%$ per month) paying $3000 a month:

Payment number	Payment ($)	Interest ($)	Principal reduction ($)	Balance ($)
0	0.00	0.00	0.00	400 000.00
1	3000.00	1600.00	1400.00	398 600.00
2	3000.00	1594.40	1405.60	397 194.40
3	3000.00	1588.78	1411.22	395 783.18

Reading the columns:

Interest is always calculated on the previous balance: $400\,000 \times 0.004 = 1600$ , then $398\,600 \times 0.004 = 1594.40$ .
Principal reduction is the part of the payment not used up by interest: $3000 - 1600 = 1400$ .
Balance falls by the principal reduction, not by the whole payment.
As the balance falls, the interest column decreases and the principal reduction column increases. The sum of the two is always the payment.

The examiners stress one habit: round each value to the cent as you write it, and use the rounded values in the next step, exactly as the table shows. In 2023 only $40\%$ of students completed the next line of an annuity table correctly, and the report put this down to rounding and to students writing only the payment.

You can also run the table backwards. Given two consecutive balances you can recover the rate: from the first line above, $\frac{1600}{400\,000} = 0.004$ , so $0.4\%$ per month, $4.8\%$ per annum.

The finance solver

On a CAS finance solver (TVM solver), an annuity needs:

Field	Meaning	Annuity entry
$N$	number of payments	e.g. 240 for 20 years monthly
$I(\%)$	annual interest rate	e.g. 5.4
$PV$	present value	amount invested, negative
$PMT$	payment	payment received, positive
$FV$	future value	balance left, 0 if exhausted, positive if some remains
$PpY$ , $CpY$	payments and compounding periods per year	e.g. 12 and 12

The sign convention follows the cash: money leaving you is negative, money coming to you is positive. You pay $500 000 into the annuity ( $PV$ negative) and receive payments back ( $PMT$ positive). If money is still in the annuity at the end, it is yours, so $FV$ is positive. With the signs right, you can solve for any one field.

Typical uses:

Payment for a fixed term: fill $N$ , $I(\%)$ , $PV$ , $FV = 0$ , solve $PMT$ .
Amount to invest for a target income: fill $N$ , $I(\%)$ , $PMT$ , $FV = 0$ , solve $PV$ .
How long it lasts: fill $I(\%)$ , $PV$ , $PMT$ , $FV = 0$ , solve $N$ . A non-integer answer means the last payment is smaller.
Balance after $n$ payments: fill $N = n$ , $I(\%)$ , $PV$ , $PMT$ , solve $FV$ .
Interest rate: fill $N$ , $PV$ , $PMT$ , $FV$ , solve $I(\%)$ .

The final payment

When $N$ comes out as a decimal, say $138.98$ , the annuity pays 138 full payments and then one smaller final payment. To find it:

Solve for $FV$ with $N = 138$ (the whole number of full payments). This is the balance after the last full payment.
Add one period of interest: final payment $=$ that balance $\times R$ .

For $250 000 at $6\%$ per annum monthly paying $2500, the balance after 138 payments is $2427.32 and the final payment is $2427.32 \times 1.005 = 2439.45$ dollars.

Totals: received and interest earned

Over the life of an annuity:

\text{total received} = \text{sum of all payments}, \qquad \text{interest earned} = \text{total received} - \text{amount invested} \; (+ \text{any balance remaining}).

For $500 000 over 20 years at $5.4\%$ per annum monthly, the payment is $3411.26, the total received is $240 \times 3411.26 = 818\,702.40$ dollars, and $318 702.40 of that is interest. Long annuities pay out far more than was invested, because the balance keeps earning interest while it is being drawn down.

Multi-stage annuities

A favourite VCAA structure changes something part-way through: the payment, the rate, or the remaining term. The rule is always the same:

The balance at the moment of change becomes the new present value (or the new $V_0$ ).

So you solve the first stage for its $FV$ , then start a fresh calculation with that value as $PV$ . Writing a recurrence relation for the second stage means writing that balance as $V_0$ and the (possibly new) payment as $d$ . The 2025 Examination 2 question above asked for exactly this and most students missed it, writing the original $650 000 as the starting value.

How exam questions ask about annuities

"Write a recurrence relation for the balance of the annuity." $V_0 = \ldots$ , $V_{n+1} = RV_n - d$ , with $R$ for the rate per period (for example $1.0042$ for $0.42\%$ per month, not $1.042$ ).
"Complete the next line of the amortisation table." Interest on the previous balance, principal reduction, new balance, each to the cent.
"Showing recursive calculations, find the balance after two payments." Write each step; an answer alone scores nothing (the examiners have repeated this every year).
"What would the annuity be called if the balance stayed constant?" A perpetuity.
"How much must be invested...", "what monthly payment...", "how many years..." Finance solver with correct signs, $PpY$ and $CpY$ .
"What is the value of the final payment?" Balance after the last full payment, times $R$ .
"After $k$ years the payment changes..." Two stages linked by the balance at the change.

Worked examples: tables, solver inputs, final payments and two-stage annuities

From a recurrence to a balance by hand

$V_0 = 250\,000$ , $V_{n+1} = 1.005V_n - 2500$ ( $n$ in months). Find the balance after two months.

$V_1 = 1.005 \times 250\,000 - 2500 = 251\,250 - 2500 = 248\,750$ .

$V_2 = 1.005 \times 248\,750 - 2500 = 249\,993.75 - 2500 = 247\,493.75$ .

The balance after two months is $247 493.75.

Marker's note: the phrase "showing recursive calculations" means both lines must appear. The 2023 report noted that "an answer on its own was not sufficient".

Payment, total received and interest

Maria invests $500 000 at $5.4\%$ per annum compounding monthly for 20 years. Find the monthly payment and the interest earned.

Solver inputs: $N = 240$ , $I(\%) = 5.4$ , $PV = -500\,000$ , $PMT = ?$ , $FV = 0$ , $PpY = CpY = 12$ .
Payment: $PMT = 3411.26$ , so $3411.26 per month.
Totals: Received $= 240 \times 3411.26 = 818\,702.40$ ; interest $= 818\,702.40 - 500\,000 = 318\,702.40$ .

Marker's note: write the solver inputs as a list. They earn method marks even if a keying slip spoils the final number.

How long it lasts and the final payment

Ken invests $250 000 at $6\%$ per annum compounding monthly and withdraws $2500 a month.

Solve for $N$: $I(\%) = 6$ , $PV = -250\,000$ , $PMT = 2500$ , $FV = 0$ : $N \approx 138.98$ .
Balance after 138 payments: Set $N = 138$ , solve $FV = 2427.32$ .
Final payment: $2427.32 \times 1.005 = 2439.45$ , the 139th payment. The annuity lasts $139$ months, about $11.6$ years.

Marker's note: the final payment is always a little less than a regular payment. If your final payment is bigger, you have forgotten that the last full payment was already made.

Amount to invest for a target income

A retiree wants $2000 per fortnight for 15 years at $4.68\%$ per annum compounding fortnightly.

Solver inputs. $N = 390$ , $I(\%) = 4.68$ , $PMT = 2000$ , $FV = 0$ , $PpY = CpY = 26$ . Solve $PV = -560\,104.48$ .

Answer. About $560 104 must be invested. The retiree receives $390 \times 2000 = 780\,000$ dollars in total, so the annuity earns about $219 896 of interest along the way.

Marker's note: $N$ counts payments, not years. For fortnightly payments over 15 years that is $15 \times 26 = 390$ .

A two-stage annuity with a new recurrence

Priya invests $600 000 at $4.2\%$ per annum compounding monthly, receiving $4000 per month for 5 years, then changes the payment so the annuity runs out exactly 15 years later.

Stage 1: $N = 60$ , $I(\%) = 4.2$ , $PV = -600\,000$ , $PMT = 4000$ : $FV = 473\,391.70$ .
Stage 2: $N = 180$ , $I(\%) = 4.2$ , $PV = -473\,391.70$ , $FV = 0$ : $PMT = 3549.26$ .
New recurrence: $P_0 = 473\,391.70$ , $P_{n+1} = 1.0035P_n - 3549.26$ .

Marker's note: the second stage starts from the stage 1 balance, not from $600 000. The rate per month is $4.2 \div 12 = 0.35\%$ , so $R = 1.0035$ .

Common traps

Using the annual rate in $R$: $4.8\%$ per annum compounding monthly is $0.4\%$ per month, so $R = 1.004$ . Writing $R = 1.048$ is the most common error in recurrence relations.
Calculating interest on the new balance: Interest in each row is on the balance before that payment.
Subtracting the whole payment from the balance: The balance falls by the principal reduction, which is the payment minus the interest.
Wrong signs in the solver: For an annuity you invest (negative $PV$ ) and receive (positive $PMT$ ). If the solver returns an error or a nonsense value, check the signs first.
Forgetting $PpY$ and $CpY$: They must match the question (12 for monthly, 26 for fortnightly, 52 for weekly, 4 for quarterly).
Starting the second stage from the original amount: In a multi-stage problem the balance at the change is the new starting value.
Rounding the number of payments down and stopping: A decimal $N$ means one extra, smaller payment. The number of payments is the next whole number.

Exam technique

In Exam 2, always write your finance solver inputs as a labelled list ( $N$ , $I(\%)$ , $PV$ , $PMT$ , $FV$ , $PpY$ , $CpY$ ) before the answer. For an amortisation line, write interest, principal reduction and balance in that order, each rounded to the cent. When a question describes a change part-way through, draw a quick timeline with the balance at the change marked; that balance links the two calculations. In Exam 1, eliminate options by checking the sign and size: an annuity balance must fall, a final payment must be smaller than the regular one, and halfway through the time more than half of the money is still there.

Note

Imagine giving a bank a big pile of money when you retire, and the bank agreeing to send you the same amount every month until the pile is gone. The pile keeps earning interest while it waits, so it lasts longer than you might expect. Each month the bank first adds the interest, then sends you your payment. Early on, most of your payment is just the interest, so the pile shrinks slowly; near the end it shrinks quickly. If the bank only ever sends you the interest, the pile never shrinks at all, and that special case is called a perpetuity.

Exam-style questions

Questions in the style of VCAA exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.

2023 VCAA-style4 marks

Arthur invests $600 000 in an annuity that pays him $3973.00 a month. Interest is calculated monthly at 0.42% per month. The amortisation table begins: payment 0, balance $600 000.00; payment 1, payment $3973.00, interest $2520.00, principal reduction $1453.00, balance $598 547.00; payment 2, payment $3973.00, interest $2513.90, principal reduction $1459.10, balance $597 087.90. (a) Find the interest rate per annum. (b) Complete the line for payment 3, rounding to the nearest cent. (c) Write a recurrence relation for

V_n

, the balance after

n

months. (d) If the balance of an annuity stayed constant from month to month, what would the annuity be called?

Show worked answer →

(a) $0.42\% \times 12 = 5.04\%$ per annum. (1 mark; $70\%$ of students earned it.)

(b) Interest is charged on the previous balance:

597\,087.90 \times 0.0042 = 2507.77.

Principal reduction $= 3973.00 - 2507.77 = 1465.23$ , and the new balance is $597\,087.90 - 1465.23 = 595\,622.67$ . The completed line is: payment $3973.00, interest $2507.77, principal reduction $1465.23, balance $595 622.67. (1 mark for all four values; only $40\%$ of students earned it, and the examiners reported that rounding errors part-way through were common.)

(c) $V_0 = 600\,000$ , $V_{n+1} = 1.0042V_n - 3973$ . (1 mark; $41\%$ correct. The most common error was the multiplying factor: $0.42\%$ per month gives $R = 1.0042$ , not $1.042$ .)

(d) A perpetuity. (1 mark)

Source: VCAA 2023 General Mathematics Examination 2, Question 6, and the 2023 examination report.

2025 VCAA-style1 mark

Dennis invests $800 000 in an annuity earning 4.8% per annum, compounding monthly. After interest is credited each month he receives a payment of $6000. After some years the balance is $521 118.96, and for the remainder of the annuity he receives $4767.66 a month. The total number of years for which Dennis receives payments is closest to: A. 19 B. 20 C. 21 D. 22

Show worked answer →

Treat it as two annuities joined end to end, both at $4.8 \div 12 = 0.4\%$ per month.

Stage 1: Finance solver: $I(\%) = 4.8$ , $PV = -800\,000$ , $PMT = 6000$ , $FV = 521\,118.96$ , $PpY = CpY = 12$ , solve for $N$ : $N = 84$ months.
Stage 2: $I(\%) = 4.8$ , $PV = -521\,118.96$ , $PMT = 4767.66$ , $FV = 0$ , solve for $N$ : $N = 144$ months.
Total: $84 + 144 = 228$ months $= 19$ years. The answer is A. ( $52\%$ of students chose the correct option.)

Notice the signs: the money invested is negative (it leaves Dennis), the payments he receives are positive, and a leftover balance still in the annuity is positive.

Source: VCAA 2025 General Mathematics Examination 1, Question 24, and the 2025 examination report.

2025 VCAA-style2 marks

Declan invests $650 000 into a 10-year annuity earning 6.4% per annum, compounding quarterly, and receives a regular quarterly payment. Halfway through the 10 years he writes a recurrence relation for the balance for the rest of the annuity. Let

D_n

be the balance

n

quarters after the halfway point. Complete:

D_0 = \ldots

D_{n+1} = 1.016 \times D_n + \ldots

Show worked answer →

Find the quarterly payment first: $N = 40$ , $I(\%) = 6.4$ , $PV = -650\,000$ , $FV = 0$ , $PpY = CpY = 4$ . Solving gives $PMT = 22\,126.27$ (to the nearest cent).
Find the balance at the halfway point: Keep the same payment and set $N = 20$ , solve for $FV$ : $376\,159.43$ .
Write the recurrence: The halfway balance becomes the new starting value, and the payment is subtracted:

D_0 = 376\,159.43, \qquad D_{n+1} = 1.016 \times D_n - 22\,126.27.

One mark for each blank. This question was answered poorly: $77\%$ of students scored zero (average $0.4$ out of 2), mostly because they did not realise the payment had to be found first, or they wrote $650 000 as $D_0$ .

Source: VCAA 2025 General Mathematics Examination 2, Question 10, and the 2025 examination report.

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation3 marks

$400 000 is invested in an annuity earning 4.8% per annum, compounding monthly, and pays $3000 at the end of each month. (a) Write a recurrence relation for the balance

V_n

after

n

months. (b) Complete the first three lines of the amortisation table.

Show worked solution →

(a) Monthly rate $= 4.8 \div 12 = 0.4\%$ , so $R = 1.004$ :

V_0 = 400\,000, \qquad V_{n+1} = 1.004V_n - 3000.

(1 mark)

(b) Each line: interest $=$ previous balance $\times 0.004$ ; principal reduction $=$ payment $-$ interest; balance $=$ previous balance $-$ principal reduction.

Payment number	Payment	Interest	Principal reduction	Balance
0	0.00	0.00	0.00	400 000.00
1	3000.00	1600.00	1400.00	398 600.00
2	3000.00	1594.40	1405.60	397 194.40
3	3000.00	1588.78	1411.22	395 783.18

(2 marks: 1 for the method, 1 for all values correct to the cent.)

foundation2 marks

An annuity is modelled by

V_0 = 250\,000

V_{n+1} = 1.005V_n - 2500

, where

n

is in months. (a) State the annual interest rate. (b) Find the balance after 2 months, showing the recursive calculations.

Show worked solution →

(a) $R = 1.005$ means $0.5\%$ per month, so $0.5 \times 12 = 6\%$ per annum, compounding monthly. (1 mark)

(b)

V_1 = 1.005 \times 250\,000 - 2500 = 251\,250 - 2500 = 248\,750

V_2 = 1.005 \times 248\,750 - 2500 = 249\,993.75 - 2500 = 247\,493.75

The balance after 2 months is $247 493.75. (1 mark, only with both steps shown)

foundation2 marks

An annuity of $650 000 earns 1.6% per quarter. (a) What quarterly payment would make it a perpetuity? (b) Describe what happens to the balance if the quarterly payment is $9000 instead.

Show worked solution →

(a) A perpetuity pays exactly the interest: $0.016 \times 650\,000 = 10\,400$ . A payment of $10 400 per quarter keeps the balance at $650 000 forever. (1 mark)

(b) $9000 is less than the $10 400 interest earned, so $1400 of interest stays in the account in the first quarter and the balance increases over time (and keeps increasing). (1 mark)

core3 marks

Maria invests $500 000 in an annuity earning 5.4% per annum, compounding monthly. She wants equal monthly payments for 20 years, after which the annuity is exhausted. (a) Find the monthly payment, to the nearest cent. (b) Find the total amount she receives. (c) Find the total interest earned by the annuity.

Show worked solution →

(a) Finance solver: $N = 240$ , $I(\%) = 5.4$ , $PV = -500\,000$ , $FV = 0$ , $PpY = CpY = 12$ . Solve for $PMT$ : $3411.26. (1 mark)

(b) $240 \times 3411.26 = 818\,702.40$ , so $818 702.40. (1 mark)

(c) Interest $=$ total received $-$ amount invested $= 818\,702.40 - 500\,000 = 318\,702.40$ , so $318 702.40. (1 mark)

Using the rounded payment in (b) is the standard approach; the tiny rounding difference is absorbed in the final payment.

core3 marks

Ken invests $250 000 in an annuity earning 6% per annum, compounding monthly, and withdraws $2500 at the end of each month. (a) How many full payments of $2500 does he receive? (b) Find the final, smaller payment that exhausts the annuity. (c) For how many years, to one decimal place, does the annuity last?

Show worked solution →

(a) Finance solver: $I(\%) = 6$ , $PV = -250\,000$ , $PMT = 2500$ , $FV = 0$ , $PpY = CpY = 12$ . Solving for $N$ gives $N \approx 138.98$ . So there are 138 full payments of $2500 and one smaller final payment. (1 mark)

(b) Set $N = 138$ and solve for $FV$ : the balance after 138 payments is $2427.32. One more month of interest is added before the final payment:

2427.32 \times 1.005 \approx 2439.45.

The final payment is $2439.45. (1 mark)

(c) There are $139$ payments in total, $139 \div 12 \approx 11.6$ years. (1 mark)

core2 marks

A retiree wants $2000 every fortnight for 15 years from an annuity earning 4.68% per annum, compounding fortnightly (26 fortnights per year). How much must be invested, to the nearest dollar?

Show worked solution →

Finance solver: $N = 15 \times 26 = 390$ , $I(\%) = 4.68$ , $PMT = 2000$ , $FV = 0$ , $PpY = CpY = 26$ . Solve for $PV$ : $PV \approx -560\,104.48$ . (1 mark for correct inputs, especially $N = 390$ and $PpY = CpY = 26$ .)

The retiree must invest about $560 104. (1 mark) The negative sign on $PV$ shows money leaving the retiree to buy the annuity.

exam3 marks

Priya invests $600 000 in an annuity earning 4.2% per annum, compounding monthly. For the first 5 years she receives $4000 per month. She then changes the payment so that the annuity runs out exactly 15 years later. (a) Find the balance after 5 years, to the nearest cent. (b) Find the new monthly payment. (c) Write a recurrence relation for the balance

P_n

n

months after the change.

Show worked solution →

(a) $N = 60$ , $I(\%) = 4.2$ , $PV = -600\,000$ , $PMT = 4000$ , $PpY = CpY = 12$ . Solve for $FV$ : $473 391.70. (1 mark)

(b) Start a new annuity from that balance: $N = 180$ , $I(\%) = 4.2$ , $PV = -473\,391.70$ , $FV = 0$ . Solve for $PMT$ : $3549.26. (1 mark)

(c) Monthly rate $= 4.2 \div 12 = 0.35\%$ , so $R = 1.0035$ :

P_0 = 473\,391.70, \qquad P_{n+1} = 1.0035P_n - 3549.26.

(1 mark) The key idea, tested in 2025, is that the balance at the change becomes the new starting value.

exam3 marks

An annuity is modelled by

V_0 = 300\,000

V_{n+1} = RV_n - d

, with

n

in months. After one month the balance is $298 850 and after two months it is $297 694.25. (a) Find

R

and

d

. (b) State the annual interest rate. (c) What value of

d

would make this a perpetuity?

Show worked solution →

(a) Write two equations: $298\,850 = 300\,000R - d$ and $297\,694.25 = 298\,850R - d$ . Subtracting eliminates $d$ :

1155.75 = 1150R \quad\Rightarrow\quad R = 1.005.

Then $d = 300\,000 \times 1.005 - 298\,850 = 301\,500 - 298\,850 = 2650$ . (2 marks)

(b) $0.5\%$ per month, so $6\%$ per annum, compounding monthly. (1 mark, combined with (c) for the full 3 marks.)

(c) A perpetuity pays only the interest: $0.005 \times 300\,000 = 1500$ , so $d = 1500$ .

Practise this

Sources & how we know this

VCE General Mathematics Examination 2 (2023) and examination report — VCAA (2023)
VCE General Mathematics Examinations 1 and 2 (2025) — VCAA (2025)
VCE Mathematics Study Design: General Mathematics (from 2023) — VCAA
VCE General Mathematics: examination specifications, past examinations and reports — VCAA