DSST Math for Liberal Arts common mistakes
DSST Math for Liberal Arts · Understand the traps and how to avoid them.
When converting between metric units, the candidate moves the decimal point the wrong number of places - for example writing 4.5 km as 45,000 m or 0.45 m - because they count the prefixes named in the problem rather than the steps between them.
The prefix ladder (kilo, hecto, deca, base, deci, centi, milli) is memorized as a list, not as a set of exponents, so the candidate guesses how many places to shift, especially when the conversion skips prefixes such as kilo to centi.
What to do instead
Convert through the base unit using powers of ten: write each quantity as a number times 10^n of the base unit (4.5 km = 4.5 x 10^3 m; 1 cm = 10^-2 m), then divide or multiply the exponents. Always sanity-check direction: a larger unit means a smaller number.
The candidate computes a probability as (number of favorable outcomes) divided by (number of unfavorable outcomes), or adds probabilities of overlapping events without subtracting the intersection.
Everyday language ('odds' versus 'probability') blurs the distinction, and the addition rule P(A or B) = P(A) + P(B) is learned without the condition that the events must be mutually exclusive.
What to do instead
Write the sample space size explicitly before dividing, and state whether events are mutually exclusive. Use P(A or B) = P(A) + P(B) - P(A and B), and reserve the favorable-to-unfavorable ratio for odds questions only.
When solving a linear inequality, the candidate multiplies or divides both sides by a negative number and keeps the inequality symbol unchanged, producing an answer with the inequality pointing the wrong way.
The procedure is practiced almost entirely on equations, where the direction of the symbol never matters, so the reversal rule is forgotten under time pressure.
What to do instead
Before dividing, note the sign of the coefficient. If it is negative, flip the symbol and then test one value from the resulting interval in the original inequality to confirm the direction.
The candidate treats a compound-interest or exponential-growth problem as simple interest, computing I = Prt and adding it once, or applies the growth factor to the original amount for each year instead of compounding.
The formulas look similar and the word 'interest' triggers the simplest remembered formula; the distinction between linear and exponential growth is not connected to the financial context.
What to do instead
Identify the keyword: 'compounded' or 'each year on the balance' signals A = P(1 + r/n)^(nt). Compute the balance after two periods by hand once to see the difference, and check that the answer exceeds the simple-interest result.
When asked for the mean, median, or effect of an outlier, the candidate reports the mean as the 'typical' value even when the data set is strongly skewed, or confuses median with mode.
Mean is the most familiar average and is computed automatically; the median's resistance to outliers is a conceptual point that is read but not practiced on skewed data.
What to do instead
For any data set, compute all three measures and describe the shape first. If the distribution is skewed, state that the median better represents the center and explain that the mean is pulled toward the tail.
The candidate evaluates a logarithm or exponent expression by multiplying the base and the argument (writing log base 2 of 8 as 16) or by treating log(x + y) as log x + log y.
Logarithm notation is new relative to arithmetic, and the candidate pattern-matches to the nearest familiar operation rather than translating the expression into an exponent question.
What to do instead
Rewrite every log as an exponent sentence: log_2 8 = 3 means 2^3 = 8. For sums inside a log, test with numbers (log 10 + log 10 is not log 20) to see that the product rule applies to multiplication, not addition.
On set and logic questions, the candidate reads 'some A are B' as implying 'some A are not B', or negates a statement by negating the verb instead of the whole quantifier ('not all' becomes 'none').
Natural-language implicature carries conversational assumptions that formal logic does not license, and quantifier negation is rarely drilled outside symbolic notation.
What to do instead
Translate each statement into quantifier form (All, Some, None) and apply the standard negations: not all = some are not; not some = none; not none = some. Test the candidate negation against a concrete counterexample set.
The candidate computes the perimeter of a figure when the area is requested, or uses the diameter in place of the radius in circle formulas, and reports the answer without units or with squared units on a length.
Formula recall is mixed under time pressure, and the words 'perimeter' and 'area' are both associated with 'size of the shape'; the radius-diameter distinction is lost when only the diameter is given.
What to do instead
Before computing, write the quantity requested and its unit (length vs square units). For circles, immediately halve a given diameter and label r. Check that a length answer is not larger than the perimeter unless the shape is unusual.
Given a real-world situation, the candidate identifies slope and intercept correctly in the equation but misinterprets them: calling the y-intercept the starting value when it is the rate, or reading slope as a total rather than a per-unit change.
The algebra is mechanical, and the modeling step - attaching meaning to m and b - is skipped in favor of solving for x.
What to do instead
Write the sentence 'each additional [unit] changes [output] by m' and 'when [input] is zero, [output] is b' before answering. Match each option back to those two sentences and eliminate any that swap them.
The candidate solves a system of two linear equations by substitution or elimination but stops after finding one variable, or accepts a solution pair that satisfies only one of the two original equations.
The final back-substitution step feels redundant, and checking a candidate solution in both equations is not habitual.
What to do instead
Always substitute the pair back into both original equations before selecting an answer, and state the solution as an ordered pair. If one variable drops out entirely, recognize the parallel-line (no solution) or identical-line (infinite solutions) case.