Praxis Core Math common mistakes
Praxis Core Math · Understand the traps and how to avoid them.
When a word problem gives a rate (e.g., 'miles per hour' or 'cost per item') and asks for a total, the candidate multiplies or divides by whichever number appears first, without checking that the units cancel to the unit the question asks for.
Rate problems are usually solved by dimensional analysis, but many candidates treat the numbers as a cue to 'do something' and default to multiplication. They skip writing the units, so an answer in the wrong unit (e.g., hours instead of miles) still looks plausible and goes unchecked.
What to do instead
Before computing, write the target unit at the top of your scratch work (e.g., 'answer = miles'). Then set up the expression so the given units cancel: (miles/hour) × hours = miles. If the units left over are not the target, invert the rate. Do this unit check on every rate problem before selecting an answer.
When comparing fractions, decimals, and percents, the candidate converts only some values (e.g., changes 3/8 to 0.375 but leaves 42% as written) and then orders them by the size of the digits rather than by value.
Mixed-format comparisons invite 'digit reading': 0.4 looks bigger than 0.375 because 4 > 3, and 42 looks bigger than 0.5 because 42 > 0.5. Candidates who convert only the awkward fraction feel they have done the work and stop.
What to do instead
Force every value into the same form-decimals are fastest-before comparing. Write each conversion on paper (3/8 = 0.375; 42% = 0.42; 0.4 = 0.400) and line them up with equal decimal places. Then order by place value, not by digit count.
On percent-change problems, the candidate computes the change and then adds or subtracts it from the wrong base-for example, applying a 20% discount to the sale price instead of the original price, or computing a percent increase using the new value as the denominator.
The phrase 'percent of' hides which quantity is the whole. Candidates who have memorized 'part/whole' still need to identify the whole, and under time pressure they grab the most recent number on the page, which is often the new value.
What to do instead
Underline the base before calculating. For a discount, the base is the original price; for a percent increase, the base is the original (smaller) value. Write the formula explicitly: change ÷ original × 100. If a problem chains two changes, apply each to the running total, not to the original, and note that a 20% rise then a 20% fall does not return to the start.
When simplifying an algebraic expression or solving an equation, the candidate distributes a negative sign or a coefficient over only the first term inside parentheses, e.g., writing −3(x − 4) as −3x − 4 or 2(x + 5) as 2x + 5.
The eye reads the sign in front of the parenthesis and the first term as a unit, and the second term sits visually 'outside' the operation. This is a reading habit, not a knowledge gap, so it survives even when the candidate can state the distributive property.
What to do instead
Draw an arrow from the outside factor to each term inside before writing anything. For a negative factor, rewrite subtraction as addition first: −3(x + (−4)). Then multiply term by term and check the sign of each product separately. On multiple-choice items, substitute x = 2 into your simplified expression and the original; if they differ, you dropped a term.
When solving a linear equation, the candidate performs an operation on one side only-adding a constant to the left side but not the right, or dividing only the variable term by a coefficient-and then checks the answer by re-reading the equation rather than substituting.
The 'balance' idea is known but not enacted: candidates work down the page and lose track of which side they last touched. Re-reading feels like checking but only confirms what they wrote, not whether it is correct.
What to do instead
Use a two-column layout with an equals sign down the middle so both sides are visible, and perform each operation on both sides in the same line. Always finish by substituting your value into the original equation and evaluating both sides numerically. If they are not equal, the error is in the operation, not the arithmetic.
When a problem gives two points and asks for the equation of the line, the candidate computes slope correctly but then substitutes the slope and a point into y = mx + b and solves for b using the x-coordinate in place of y, or swaps the coordinates of the point.
Slope is the memorable part of the procedure, so it gets the attention; the intercept step is treated as a formality and done quickly. The point (x, y) is also easy to misread because x comes first, and candidates plug the numbers in that order.
What to do instead
Label the point explicitly as (x₁, y₁) and write the template y₁ = m·x₁ + b with the labels still showing before substituting numbers. Solve for b algebraically, then verify by plugging the other given point into your final equation-both points must satisfy it. Checking with the second point catches coordinate swaps immediately.
On a geometry problem involving a composite figure, the candidate adds all the side lengths to find area, or uses the perimeter formula when the question asks for area (and vice versa), especially with circles and triangles where the formulas look similar.
Both area and perimeter involve the same given numbers, and the question's final word ('area' or 'perimeter') is easy to skim. Composite figures also require deciding which segments are interior and should not be counted, a step candidates skip.
What to do instead
Before computing, write the unit of the answer: square units means area, linear units means perimeter. For composite figures, shade the region whose area (or outline whose perimeter) is wanted, then list the formula for each simple piece. Remember interior dividing segments are not part of the perimeter, and the slant height of a triangle is not its perpendicular height.
When a figure is described in words rather than drawn, the candidate works from the verbal description alone and misassigns which side is the hypotenuse or which angle is the right angle, then applies the Pythagorean theorem to the wrong pair of sides.
The theorem is recalled as a² + b² = c², but c is only the hypotenuse when the triangle is right-angled at the opposite vertex. Without a sketch, candidates label the longest-looking number as c by habit, even when the problem states the right angle is elsewhere.
What to do instead
Sketch the figure from the description and mark the right angle with a square before writing any formula. Label the side opposite the right angle as c and the two legs as a and b. If the problem gives three sides and asks whether the triangle is right, test the longest side as c; if the given sides cannot form a triangle at all, the sum of the two shorter sides must exceed the longest.
When asked for the mean, median, or mode of a data set, the candidate reports the mean when the question says median (or reports the middle value of the list as written without reordering), and does not notice that an outlier has pulled the mean away from the center.
Mean is the most practiced measure, so it becomes the default answer. Median requires the extra step of sorting, which candidates skip when the data already looks ordered, and the distinction between 'typical value' and 'average' is blurred.
What to do instead
Read the measure named in the question and circle it before starting. For median, rewrite the list in ascending order first, then count to the middle; with an even count, average the two middle values. If the data set contains a value far from the rest, note that the mean will be pulled toward it and the median will not-use that to sanity-check which answer the question is really after.
On probability questions, the candidate computes the probability of a single event and reports it as the answer to a question about two events ('probability of A and B' or 'A or B'), without deciding whether the events are independent or whether the outcomes should be added or multiplied.
Single-event probability is the familiar case, and the words 'and'/'or' are small connectives that are easy to read past. Candidates also conflate 'independent' with 'mutually exclusive', so they add probabilities that should be multiplied.
What to do instead
Translate the connective before calculating: 'and' with independent events means multiply; 'or' with mutually exclusive events means add. Write the rule you are using next to the work. Check the result is between 0 and 1-a probability above 1 signals that you added when you should have multiplied. For 'without replacement', adjust the denominator (and numerator) for the second draw.