Number and Algebra - Te Tau me te Taurangi
This domain tests fluency with number operations, proportional reasoning and basic algebra in everyday situations. Questions may be set in shopping, travel, wages or simple patterns, and you must choose the operation and show the reasoning.
Core rules and concepts
- Follow the order of operations: brackets, exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
- Fractions, decimals and percentages are interchangeable: 0.35 = 35% = 7/20. A percentage change is (new − old) ÷ old × 100.
- For percentage increases or decreases, use a multiplier: a 15% increase is ×1.15; a 25% discount is ×0.75.
- A ratio compares parts; a rate compares different units (km/h, $/kg). To compare value, convert to a unit rate.
- In algebra, substitute values carefully, collect like terms, and solve linear equations by doing the same inverse operation to both sides.
- A linear pattern has a constant difference; the nth term rule is start + (n − 1) × common difference.
Worked example
A mobile plan costs $12 per month plus $0.18 per MB. Find the cost for 350 MB, then find how many MB $75 buys. Cost = 12 + 0.18 × 350 = 12 + 63 = $75. For the second part, solve 12 + 0.18m = 75. Subtract 12: 0.18m = 63. Divide by 0.18: m = 350 MB. Checking back in the original context confirms both answers.
Traps
- Rounding too early; keep full values until the final step.
- Confusing percentage points with percent change.
- Adding a 15% increase and a 15% decrease and expecting the original value; multipliers give 1.15 × 0.85 = 0.9775, a 2.25% decrease.
- Using a direct proportion where the relationship is inverse, such as more workers taking less time.