Mathematics
What the Mathematics subtest asks
TACHS Mathematics covers arithmetic with whole numbers, fractions, decimals, and percents; ratios and proportions; introductory algebra (expressions and one-variable equations); geometry (perimeter, area, volume, angle relationships); measurement and unit conversion; and data (mean, median, mode, reading tables). Calculators are not permitted, so estimation and clean arithmetic matter.
Core rules
- Order of operations: parentheses, exponents, multiply and divide left to right, then add and subtract left to right.
- Percent problems translate directly: "of" means multiply, "is" means equals, and a percent is divided by 100.
- Set up ratios with matching units in the same position, then cross-multiply.
- Isolate a variable by undoing operations in reverse order.
- Know the formulas: A = lw, A = 1/2 bh, A = pi r^2, V = lwh. Perimeter adds edge lengths; area is measured in square units.
- When the arithmetic looks messy, estimate first and eliminate choices.
Worked example
A jacket priced at $80 is marked down 25%, then an extra 10% is taken off the sale price. What is the final cost? First discount: $80 times 0.75 = $60. Second discount applies to $60, not $80: $60 times 0.90 = $54. Final cost: $54. The trap is adding the discounts (35% off $80 = $52). Successive percents multiply, so the second discount is smaller in dollars than the first.
Traps that cost marks
- Adding percents that apply in sequence.
- Mixing units, such as minutes with hours, before computing.
- Confusing area with perimeter, or radius with diameter.
- Solving for x and stopping without answering the question asked.
- Forgetting that the median is the middle value only after the data are ordered.