Foundation Mathematics is built around real-world application. This key knowledge area brings together all number skills — operations, percentages, fractions, ratios, rounding — and applies them to financial and measurement situations encountered in everyday life and work.
KEY TAKEAWAY: Number skills are tools. The skill being assessed in VCAA is whether you can choose the right tool and apply it correctly to a realistic scenario.
Example:
Normal rate: \(\$24.50\)/hr. Work \(38\) hrs normal + \(4\) hrs overtime at \(1.5\times\).
\$\(\text{Normal pay} = 38 \times 24.50 = \$931\)\$
\$\(\text{Overtime pay} = 4 \times (24.50 \times 1.5) = 4 \times 36.75 = \$147\)\$
\$\(\text{Total} = \$931 + \$147 = \$1078\)\$
\(20\%\) off \(\$350\): \(350 \times 0.80 = \$280\)
Australia’s GST rate is \(10\%\).
Where \(P\) = principal, \(r\) = annual rate (as decimal), \(t\) = time in years.
\(\$5000\) at \(4\%\) p.a. for \(3\) years:
\$\(I = 5000 \times 0.04 \times 3 = \$600\)\$
A positive balance = surplus; a negative balance = deficit.
EXAM TIP: Show each step of your financial calculation. In multi-step problems, a clear layout earns method marks even if you make an arithmetic error.
| From | To | Operation |
|---|---|---|
| km | m | \(\times 1000\) |
| m | cm | \(\times 100\) |
| cm | mm | \(\times 10\) |
| kg | g | \(\times 1000\) |
| L | mL | \(\times 1000\) |
| hours | minutes | \(\times 60\) |
A car travels \(240\text{ km}\) in \(3\) hours: \(s = \frac{240}{3} = 80\text{ km/h}\)
\(500\text{ g}\) for \(\$3.20\) vs \(750\text{ g}\) for \(\$4.50\):
- \(500\text{ g}\): \(\$3.20 \div 500 = \$0.0064\)/g
- \(750\text{ g}\): \(\$4.50 \div 750 = \$0.0060\)/g → better value
VCAA FOCUS: VCAA exam questions are set in realistic contexts — shopping, building, cooking, travel, wages. Practice reading the scenario carefully and extracting the numbers you need.
