Subtest II: Mathematics - Number Sense, Algebra, Geometry, Data and Probability
Subtest II Mathematics tests the content and reasoning a multiple-subject teacher needs: number sense and operations on rational and irrational numbers, proportional reasoning, algebraic expressions and functions, geometry and measurement, and statistics and probability. Items often embed the mathematics in a classroom or real-world context, so interpretation counts as much as computation.
Core rules to have automatic
- Order of operations; integer rules for signed numbers; the distributive property and its role in factoring.
- Fractions: common denominators for addition, invert-and-multiply for division. Percent change = (new − old) ÷ old; the base always matters.
- Exponent rules: a^m · a^n = a^(m+n); a^0 = 1; a^(−n) = 1/a^n. Rational numbers terminate or repeat; irrationals such as √2 and π do neither.
- Linear functions: slope m = (y₂ − y₁)/(x₂ − x₁); y = mx + b; parallel lines share slope, perpendicular slopes are negative reciprocals.
- Geometry: triangle angle sum 180°; area of triangle ½bh, circle A = πr², circumference C = 2πr; volume of prism/cylinder = area of base × height; Pythagorean theorem a² + b² = c²; similar figures scale lengths by k and areas by k².
- Statistics: mean is sensitive to outliers, median is not; probability of independent events multiplies; mutually exclusive events add.
Worked example. A tank drains at a constant rate: 62 liters remain at 4 minutes, 44 liters at 10 minutes. Slope = (44 − 62) ÷ (10 − 4) = −18 ÷ 6 = −3 liters per minute. Working backward to time zero: 62 + 3(4) = 74 liters initially, so L(t) = 74 − 3t. Setting L = 0 gives t = 74 ÷ 3 ≈ 24.7 minutes. Each step maps to a tested idea: slope as rate of change, y-intercept as initial value, and solving a linear equation as prediction.
Traps. Distributing a negative only to the first term; mixing up area and perimeter formulas; forgetting to convert units before computing (cm vs. m); confusing percent of with percent increase; assuming independent events are mutually exclusive; using the mean for skewed data where the median is intended; treating a scale factor as applying to area.