Mathematical Reasoning: Structure Before Calculation
What the section tests
Questions reward choosing an efficient method, not just computing. Core content includes fractions, decimals, percentages and ratios; order of operations; area and perimeter; averages; simple algebra; and pattern rules. Many items are word problems, so translating language into an equation is half the work.
Concepts to master
- Ratio and proportion: scale both parts together; find the value of one part first.
- Percentages: a 20% increase then a 20% decrease does not return to the start.
- Averages: total = average × number of items; adding a value changes the total and the count.
- Algebra: substitute known values, then undo operations in reverse order.
- Geometry: keep units consistent; distinguish perimeter (distance around) from area (space inside).
Traps to watch
- Answering the wrong quantity - the question asks for the cost of one item, not the total.
- Mixing units, such as minutes and hours in one rate problem.
- Ignoring the word not or except.
- Rounding too early and losing accuracy.
Rule of thumb
Write down what is asked, list the given values with units, and estimate the answer before calculating. If your result is far from the estimate, recheck the setup rather than the arithmetic.
Worked example
A recipe uses flour and sugar in the ratio 5:2. If 350 g of flour is used, how much sugar? One part = 350 ÷ 5 = 70 g, so sugar = 2 × 70 = 140 g. Checking: 350:140 simplifies to 5:2.