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🧰 Foundations Toolkit

When a topic feels impossible, the gap is almost never the new stuff. It's one of four older skills hiding underneath. This page is the safety net. No shame in starting here. This is the smart move, not the slow one.

Read this first

Year 12 maths quietly assumes you're rock-solid on four things from earlier years. If finance feels like a foreign language, or a graph makes no sense, 9 times out of 10 it's one of these, not the actual Year 12 topic.

Fix the foundation and the topic on top of it suddenly clicks. Each section below tells you exactly which topics it unlocks, so you can see the payoff.

1
Percentages: the engine behind all finance

If you nail one thing on this page, make it this. Every single finance formula is built out of percentages. Get these and finance stops being scary.

A. Turn a % into a decimal: divide by 100 (move the dot 2 places left):

PercentageAs a decimalHow
6%0.066 ÷ 100
15%0.1515 ÷ 100
4.5%0.0454.5 ÷ 100
100%1the whole thing

B. Find a % "of" an amount: multiply by the decimal:

6% of $20 000 = 0.06 × 20 000 = $1200

C. Increase or decrease by a %: this is the big one:

Increase $20 000 by 6% → 20 000 × 1.06 = $21 200
Decrease $20 000 by 6% → 20 000 × 0.94 = $18 800
🔑 The penny-drop moment: "increase by 6%" means "× 1.06". That 1.06 is exactly the R in every finance formula. R = 1 + the interest rate as a decimal. So 6% per period → R = 1.06. 10% → R = 1.1. That's all R ever is. If percentages click, the whole finance unit clicks.
🔓 This unlocks:
Compound Interest Annuities Loans Depreciation Shares
2
Substituting into a formula

A formula is just a recipe. Each letter is a slot. "Substitute" means swap each letter for its number, then do the arithmetic. That's it. No algebra wizardry needed.

1

Write the recipe

The annuity/loan recipe is Vnext = R × Vnow + d

2

Swap each letter for its number

Say R = 1.06, Vnow = 20 000, and it's a repayment of $400 (so d = −400):

Vnext = 1.06 × 20 000 + (−400)

3

Do × before + (the calculator does this for you)

= 21 200 − 400

= $20 800
🧮 Calculator order matters. Your calculator always does × and ÷ before + and −. So typing 1.06 × 20000 − 400 gives the right answer. But if the maths needs the subtraction first, you must use brackets: 1.06 × (20000 − 400). When in doubt, add the brackets.
The minus-key trap: for a negative number like −400, use the (−) key, not the subtract key. Mixing them up is the #1 cause of "ERROR" on the screen.
🔓 This unlocks:
Recurrence Relations Annuities Loans Sequences
3
Reading scales & axes

Half of data and networks marks are just reading a number off a line correctly. The trick: work out what one square (one gridline gap) is worth first.

1

Find what one gap is worth

If the axis runs 0 to 50 across 10 gaps, each gap = 50 ÷ 10 = 5.

2

Read between the lines

A point sitting halfway between the 30 and 35 marks = 32.5. Two-fifths of the way from 30 to 35 = 32.

0 10 20 30 40 50 32.5
Each small gap = 5. The gold dot sits halfway between 30 and 35 → 32.5
🔓 This unlocks:
Scatterplots Time Series Residuals Networks (weights)
4
Rounding (without losing marks)

Easy marks get dropped here. Two rules cover almost everything.

Asked forMeansExample
2 decimal placeskeep 2 digits after the dot3.14159 → 3.14
Nearest cent2 decimal places of dollars$8.346 → $8.35
Nearest dollarwhole number$127.80 → $128
The rule: look at the next digit along. If it's 5 or more, round up; if it's 4 or less, leave it. ($8.346 → the 6 rounds the 4 up to 5 → $8.35.)
The biggest finance mistake: rounding too early. Keep the full number on your calculator the whole way through, and only round the final answer. If you round $1.0616 down to $1.06 at the start of a 25-year loan, your final answer can be tens of dollars out, and that's a wrong answer in the exam. Round last, not first.
🔓 This unlocks:
Compound Interest Loans Annuities Financial Planning
★
How the foundations connect

If a Year 12 topic is fighting you, here's the foundation to check first:

Finance won't behave?
→ Percentages (R = 1 + r) + Rounding last
Recurrence relations confusing?
→ Substituting into a formula
Scatterplots / time series fuzzy?
→ Reading scales & axes
Money answers marked wrong?
→ Rounding (nearest cent, round last)
5
Quick check (tap to reveal)
1
Write 8% as a decimal. Then write the R value for an account growing at 8% per period.
Tap to reveal ▾
8% = 8 ÷ 100 = 0.08
R = 1 + 0.08 = 1.08
(Growing → add. If it were shrinking by 8%, R would be 1 − 0.08 = 0.92.)
2
A $15 000 car loses 12% of its value in a year. What is it worth after that year?
Tap to reveal ▾
Losing 12% → multiply by (1 − 0.12) = 0.88
15 000 × 0.88 = $13 200
3
Substitute into Vnext = R × Vnow + d when R = 1.05, Vnow = 2000, d = 300.
Tap to reveal ▾
Vnext = 1.05 × 2000 + 300
= 2100 + 300 (× before +)
= $2400
4
A number line runs 0 to 100 across 10 equal gaps. A point sits exactly halfway between the 4th and 5th gridline. What value is it?
Tap to reveal ▾
Each gap = 100 ÷ 10 = 10, so gridlines are at 0, 10, 20, 30, 40, 50...
Halfway between 40 and 50 = 45
5
Round $1463.7268 to the nearest cent. Then to the nearest dollar.
Tap to reveal ▾
Nearest cent (2 dp): next digit is 6 → round up → $1463.73
Nearest dollar: next digit is 7 → round up → $1464

😮‍💨 Still feels hard? That's completely normal.

Foundations are years of skipped lessons stacked up, and nobody fixes them in one sit. Pick ONE section that bit you, do just that section's quick-check questions, and leave the rest for next time. Coming back to a Year 12 topic after patching one foundation is the fastest way to feel it click. You're not behind for being here. This is the smart shortcut.