Mathematics Achievement: Curriculum Math Under Time Pressure
What this section tests
Mathematics Achievement is the curriculum-based math section: 47 questions in 40 minutes at the Middle and Upper levels, no calculator. It covers arithmetic, fractions, decimals, percents, ratios, basic algebra, geometry, measurement, statistics, and probability. Unlike Quantitative Reasoning, the setup is usually given; accuracy and fluency decide the score.
Core rules
- Order of operations: parentheses, exponents, multiplication and division left to right, addition and subtraction left to right.
- Fractions: common denominators to add or subtract; multiply straight across; to divide, multiply by the reciprocal.
- Percents: part = percent × whole; percent change = change ÷ original × 100.
- Exponent rules: xᵃ · xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁻ᵃ = 1/xᵃ; x⁰ = 1 for x ≠ 0.
- Geometry: triangle area = ½bh; circle area = πr² and circumference = 2πr; a² + b² = c² for right triangles; triangle angles sum to 180°.
- Statistics: the mean uses every value, the median is the middle of an ordered list, and the mode is most frequent.
Worked example
Solve 3(x − 4) = 18.
Divide both sides by 3: x − 4 = 6. Add 4: x = 10. Check: 3(10 − 4) = 3(6) = 18. Distributing instead gives 3x − 12 = 18, then 3x = 30, x = 10 - same result, but dividing first avoids a sign slip.
Traps
- Distributing a negative incorrectly: −2(x − 5) = −2x + 10, not −2x − 10.
- Confusing radius with diameter, or area with perimeter, when a figure is described in words.
- Mixing units such as minutes with hours before computing.
- Reporting the mean when a skewed data set makes the median the intended answer.