Mathematics: Number, Algebra, Geometry, and Data
The Mathematics domain covers number and operations, algebraic patterns, geometry and measurement, and data analysis and probability. Expect multi-step problems, estimation, and interpretation of tables, graphs, and diagrams.
Core rules and concepts
- Order of operations: parentheses, exponents, multiply and divide left to right, then add and subtract left to right.
- Fractions: add and subtract with common denominators; multiply across; divide by multiplying by the reciprocal.
- Ratios and proportions: set up equivalent ratios and solve by cross multiplication. A unit rate compares a quantity to one unit.
- Geometry: perimeter is distance around; area of a rectangle is length times width; area of a triangle is one-half base times height; volume of a rectangular prism is length times width times height.
- Data: mean is the sum divided by the count; median is the middle value in order; mode is most frequent; range is maximum minus minimum.
- Probability of a single event is favorable outcomes divided by total outcomes.
Worked example
Compute 3/4 divided by 1/2. Reasoning: Dividing by a fraction is multiplying by its reciprocal: 3/4 times 2/1 equals 6/4, which simplifies to 1 1/2. Check: 1 1/2 groups of 1/2 make 3/4.
Traps that cost marks
Adding denominators when adding fractions; forgetting to convert units before computing; choosing mean when an outlier makes median more representative; confusing percent increase with percent of; and dropping negative signs.
Key points
Write the rule, show each step, and check whether the answer is reasonable.