ACCUPLACER AAF common mistakes
ACCUPLACER AAF · Understand the traps and how to avoid them.
When solving an equation like 5 - 2(x - 3) = 11, the candidate distributes only the 2 and writes 5 - 2x - 3 = 11, or drops the leading minus entirely and writes 5 - 2x + 6 = 11.
The subtraction sign in front of the parentheses is treated as separating terms rather than as a factor of -1 applied to every term inside; students visually attach the minus only to the first term they see.
What to do instead
Rewrite every subtraction-of-a-parenthetical as adding the negative before distributing: 5 + (-2)(x - 3). Then multiply both terms by -2. Do a one-line check by substituting a simple value (e.g., x = 0) into the original and the rewritten form to confirm they agree.
When solving an inequality such as -3x + 4 > 19, the candidate divides by -3 and leaves the symbol as >, giving x > -5.
The reversal rule is memorized as a phrase without a mental model, so it is applied inconsistently or forgotten under time pressure; the arithmetic steps feel identical to equation-solving.
What to do instead
Tie the rule to a number line: multiplying/dividing by a negative reflects the order. Practice by testing a point from the resulting interval back in the original inequality; if x > -5 were correct, x = 0 would satisfy -3(0)+4 > 19, which it does not, exposing the error immediately.
Given a word problem, the candidate produces a correct-looking equation but with the variable bound to the wrong quantity (e.g., lets x be the total instead of the unknown part), then reports a plausible but wrong numeric answer without units.
Candidates jump to algebra before writing down what the variable represents; the translation step is skipped because it feels like extra work.
What to do instead
Force a written 'Let x = ____' line with units before any equation, and finish with a sentence stating the answer with units. Verify by re-reading the question and confirming the answer matches the quantity actually asked for, not an intermediate one.
When finding the equation of a line through two points, the candidate computes slope as (y2 - y1)/(x2 - x1) but then substitutes the wrong point or drops the negative sign, or confuses slope with y-intercept in y = mx + b.
The slope formula and slope-intercept form are recalled as separate procedures, and the roles of m and b are not anchored to the graph.
What to do instead
Always write the template y = mx + b, compute m first and label it, then substitute one point's coordinates explicitly with parentheses: y - y1 = m(x - x1). Check the final equation by plugging in both original points.
When factoring x^2 + bx + c, the candidate finds two numbers that multiply to c but ignores the sign of b, producing factors whose sum is the negative of b (e.g., factoring x^2 - 5x + 6 as (x - 2)(x - 3) is correct, but x^2 + 5x + 6 as (x - 2)(x - 3)).
Only one condition (product) is checked; the sum condition is treated as secondary rather than equally binding.
What to do instead
Write both target conditions side by side before choosing factors: product = c AND sum = b. After writing factors, expand them mentally or on paper to confirm the middle term matches b exactly. Do this expansion check on every factoring problem.
When solving a quadratic by the quadratic formula, the candidate substitutes -b as b or mishandles the discriminant under the radical, e.g., writing x = (b +/- sqrt(b^2 - 4ac))/2a.
The formula is memorized as a string of symbols without attention to the leading negative and the grouping of the denominator over the entire numerator.
What to do instead
Write the formula from a reference each time until automatic, then explicitly identify a, b, c with their signs before substituting. Put the whole numerator in brackets and the whole denominator in brackets: x = [-(b) +/- sqrt((b)^2 - 4(a)(c))] / [2(a)]. Check the discriminant's sign first to predict the number of real solutions.
When simplifying a rational expression like (x^2 - 9)/(x^2 - x - 6), the candidate cancels the x^2 terms or individual terms across the fraction bar, e.g., reducing to (1 - 9)/(1 - x - 6).
Cancellation is treated as deleting matching symbols rather than as dividing common factors of the entire numerator and denominator.
What to do instead
Factor numerator and denominator completely first, then cancel only whole factors that appear as multiplication in both. State the rule explicitly: terms add, factors cancel. After simplifying, test with a numeric value of x (not a restricted value) to confirm the simplified form equals the original.
When solving a rational equation such as 1/(x-2) + 3 = x/(x-2), the candidate multiplies through by the LCD but forgets to multiply the standalone 3, or fails to check for extraneous solutions that make a denominator zero.
The LCD multiplication is applied only to terms that visibly contain fractions; the domain restriction is treated as an optional afterthought.
What to do instead
Before solving, list excluded values (denominators = 0). Then multiply every term, including whole-number terms, by the LCD and show that multiplication explicitly. After finding solutions, compare against the excluded list and discard any match.
When solving sqrt(x + 5) = x - 1, the candidate squares both sides, solves the resulting quadratic, and reports both roots without checking either in the original equation.
Squaring is treated as an invertible operation; the fact that it can introduce solutions is not connected to the act of squaring itself.
What to do instead
Treat every radical equation as requiring a verification step: after squaring and solving, substitute each candidate back into the ORIGINAL radical equation (not the squared one) and discard any that fail. Also state the domain restriction (radicand >= 0) up front to anticipate which roots are impossible.
When working with exponential and logarithmic expressions, the candidate applies log rules incorrectly, e.g., writing log(a + b) = log a + log b, or solving 2^x = 10 by dividing both sides by 2 instead of taking a logarithm.
Log properties are memorized as a list without the underlying exponent relationship, so the sum rule is confused with the product rule and logarithms are not recognized as the tool for isolating an exponent.
What to do instead
Anchor each rule to exponents: log(ab) = log a + log b because a^m * a^n = a^(m+n); there is no rule for log(a + b). For equations with the variable in the exponent, the standard move is to take the log of both sides and use log(a^x) = x log a. Practice by testing rules with numbers (log(2*8) vs. log 2 + log 8).