PERT Math common mistakes
PERT Math · Understand the traps and how to avoid them.
Simplifies 3 − 2(x − 4) as 3 − 2x − 8, distributing the 2 but negating only the first product.
The minus sign in front of the parentheses is read as belonging to the first term only, so the second product keeps its original sign; the student applies 'distribute' mechanically without treating the leading sign as a factor of −1.
What to do instead
Rewrite the expression as addition before distributing: 3 + (−2)(x − 4), then multiply each term inside by −2 to get 3 + (−2x) + 8. Test with a value such as x = 1 in both the original and rewritten forms; the values must match.
Solves −3x > 12 as x > −4, or reverses the inequality symbol when dividing both sides by a positive number.
The rule is stored as the slogan 'flip it when there is a negative' rather than tied to the specific operation performed on both sides, so the flip is triggered by any negative sign on the page or not at all.
What to do instead
Isolate the variable term with addition/subtraction first, then look only at the number you multiply or divide by: reverse the symbol if and only if that number is negative, and write the reason beside the step. Verify by substituting a value from the solution set into the original inequality.
Combines unlike terms, writing 5x + 3 + 2x as 10x, or treating 3x + 5 as 8x.
The student matches on the numerals and ignores the variable part, because arithmetic practice has trained 'numbers next to each other get added' and the variable is seen as decoration.
What to do instead
Label each term's variable part before combining (x-terms versus constants) and merge only terms with identical labels, giving 7x + 3. Check by substituting x = 2 into the original expression and the simplified one.
Evaluates f(4) for f(x) = 2x² − 3 by multiplying 4 by the whole expression, or substitutes 4 into only one of the x's and leaves the other.
The notation f(4) visually resembles multiplication, and because the rule contains more than one occurrence of x, a single substitution appears complete.
What to do instead
Rewrite the rule with an empty slot, f(□) = 2(□)² − 3, then fill every slot with 4 and keep the parentheses until the substitution is finished: f(4) = 2(4)² − 3 = 29.
Solves a system by elimination or substitution, finds x = 2, and reports 'x = 2' as the final answer, or adds the equations when the coefficients require subtracting.
Experience with single equations creates the expectation of a one-number solution, and sign errors during elimination go undetected because no check is performed.
What to do instead
Always finish with back-substitution and write the answer as an ordered pair; substitute the pair into both original equations before moving on. Line up like terms in columns and state explicitly whether you are adding or subtracting and why.
Solves x² = 25 as x = 5 only, or solves (x − 1)² = 9 as x = 4 only.
The square root is treated as an operation that 'undoes' the square and returns a single number, so the negative branch is never generated.
What to do instead
Rewrite as x² − 25 = 0 and factor to (x − 5)(x + 5) = 0, or write x = ±√25 explicitly and carry the ± through both branches. State the number of solutions before finishing so a missing root is visible.
For x² − 5x + 6 = 0, substitutes b = 5 into the quadratic formula, or loses the sign of b entirely when b is negative in the original equation.
The −b in the formula is remembered as a label ('b is the negative one') rather than as an operation applied to whatever b is, so the sign flips or vanishes during substitution.
What to do instead
List a, b, c with their signs first, then substitute −b with parentheses: −(−5). Simplify the entire numerator before dividing by 2a, and check each root by substituting it back into the original equation.
Reads the slope of 3x + 2y = 6 as 3, or gives the slope of a perpendicular line as 1/3 instead of −1/3.
In y = mx + b the slope is the coefficient of x, so the x-coefficient in standard form looks like the slope; the perpendicular rule is recalled as 'reciprocal' with the sign change dropped.
What to do instead
Convert to y = mx + b before naming the slope, and for perpendicular lines apply both transformations - flip the fraction and change the sign - then confirm with a rough sketch of a rising versus a falling line.
Substitutes the diameter for r in A = πr², computing the area of a circle with diameter 10 as 100π.
The diameter is the number printed in the problem or figure, and the formula is recalled as 'the circle formula' without attaching meaning to the variable r.
What to do instead
Write r = d ÷ 2 and compute the radius as a separate step before substituting. State whether the requested quantity is a length or an area, and attach the correct unit (cm versus cm²) to the result.
Averages two group means without weighting by group size, or reports the median when the question asks for the mean of a data set.
Mean and median are both remembered as 'the average', and combined-group problems look like ordinary averaging because the group sizes sit in a separate column that seems irrelevant.
What to do instead
Underline the statistic the question names, then use its definition: mean = total of all values ÷ number of values, so rebuild the total from each group (group mean × group size) before dividing by the combined count. Order the data and check that the median splits the list into two equal halves.