Mathematics: method, number sense and multi-step accuracy
The NSTSE Mathematics section tests method and number sense at your class level, with an emphasis on multi-step accuracy.
What the section rewards
Arithmetic, ratio and proportion, percentage, algebra, geometry, mensuration and data handling all appear. Most items are only one or two steps deep, but each step hides a decision: which base a percentage uses, which unit a ratio needs, or whether a formula wants radius or diameter. Write the intermediate line; do not do it all in your head.
Core rules
- Order of operations: brackets, indices, division and multiplication, then addition and subtraction.
- Successive percentage changes multiply: 1.25 × 0.80, not 25 − 20.
- Ratio: convert both quantities to a common unit before simplifying.
- Scaling: doubling a length quadruples area and multiplies volume by eight.
- Angles: angles on a straight line total 180°, in a triangle 180°, around a point 360°.
Worked example
A trader marks an item 25% above cost and then allows a 20% discount. Find the profit or loss. Let cost = 100. Marked price = 125. Selling price = 125 × 0.80 = 100. The selling price equals cost, so there is no profit and no loss. The discount is 20% of the marked price, not of the cost; subtracting 25 − 20 = 5% profit is the classic error.
Traps that cost marks
- Applying a discount to cost instead of marked price.
- Adding percentages that act on different bases.
- Substituting diameter where a formula needs radius.
- Rounding early in a chain of calculations.
- Solving for x but not answering the quantity actually asked.