Mathematical Literacy - Data, Functions and Applied/Word Problems
Data, Functions and Applied/Word Problems tests your ability to read quantitative information, choose the right model, and translate a verbal scenario into an equation or rate.
Core rules
- Mean = sum ÷ count; median = middle value when ordered; mode = most frequent. Outliers pull the mean but not the median.
- Percentage change = (new − old) ÷ old × 100. Reverse a percentage change by dividing by the multiplier: a price after 15% off is 0.85 × original.
- Linear functions: y = mx + c, where m is the slope (change in y per unit change in x) and c is the y-intercept.
- Rate problems: distance = speed × time; work rates add as reciprocals of times.
- When setting up equations, define the variable in words, then translate each sentence.
- On graphs, check axis labels, scales and units before reading a value.
Worked example
A jacket is sold for $68 after a 15% discount. What was the original price? The sale price is 85% of the original: 0.85P = 68. P = 68 ÷ 0.85 = 80. The original price was $80. A common wrong answer is 68 × 1.15 = 78.20, which adds 15% to the discounted price instead of reversing the discount from the original.
Traps
- Taking a percentage of the wrong base.
- Averaging two group averages without weighting by group size.
- Reading a graph's height without checking where the axis starts.
- Mixing units such as minutes and hours in a rate.
- Solving for the variable but not answering the question asked (for example, total cost rather than unit price).