HiSET Math common mistakes
HiSET Math · Understand the traps and how to avoid them.
When adding or subtracting fractions, the candidate adds the denominators as well as the numerators (e.g., 1/2 + 1/3 = 2/5).
The fraction bar is read as a division instruction applied separately to top and bottom, so the candidate treats numerator and denominator as two independent addition problems instead of parts of one quantity.
What to do instead
Rewrite each fraction with a common denominator before combining, and check the answer by estimation: 1/2 + 1/3 must be close to 1, so 2/5 (less than 1/2) is instantly wrong. Do three estimation checks per practice set until it becomes automatic.
The candidate flips the inequality sign only sometimes when multiplying or dividing by a negative, or never flips it at all.
The rule is memorised as a list of steps without a reason, so under time pressure the step is skipped; the candidate is focused on isolating x and treats the sign flip as optional decoration.
What to do instead
After solving, test one number from the proposed solution set in the original inequality. If it fails, the sign is wrong. Practise by solving five inequalities with negative coefficients and verifying each with a test point.
The candidate computes a percentage increase by taking the percentage of the new value, or reports the change amount as the final answer instead of the new total.
Percent problems are read for keywords ('increase', 'of') rather than modelled, so the candidate grabs whichever number appears last and applies the percent to it.
What to do instead
Write an explicit equation before calculating: new = original x (1 + rate) for increases, new = original x (1 - rate) for decreases. Label original and new in the scratchwork so the wrong base cannot be substituted.
When finding a mean from a frequency table or a list with repeats, the candidate divides by the number of distinct values rather than the total frequency.
The candidate counts rows in the table instead of adding the frequencies, because the table visually presents each value once and the weighting is invisible.
What to do instead
Before dividing, write the total count as a separate labelled number obtained by summing the frequency column. Cross-check that the count is at least as large as the number of rows.
The candidate computes slope as run over rise, or subtracts coordinates in inconsistent order between numerator and denominator, producing a slope with the wrong sign or reciprocal.
The formula is recalled as a jumble of x's and y's without the structure 'change in y per change in x', and the candidate does not track which point was labelled first.
What to do instead
Always label the points (x1, y1) and (x2, y2) in writing, then write the fraction with y's on top before substituting. Sanity-check the sign against a quick sketch of the two points.
The candidate uses the diameter in place of the radius, or forgets to square the radius, when computing area or volume of a circle-based figure.
Formulas are recalled by shape rather than by meaning; the candidate remembers 'pi r squared' as a string and grabs whichever circle measurement the problem supplies.
What to do instead
Circle the given measurement and write 'r = d/2' explicitly whenever a diameter appears. Include units in the substitution (e.g., area in square units) so a missing square is visible.
The candidate adds or compares numbers with different units (minutes and hours, centimetres and metres) without converting, or converts in the wrong direction.
The numbers are treated as pure quantities because the unit labels sit at the end of the sentence and are easy to skim past.
What to do instead
Rewrite every given quantity with its unit on its own line before solving, and convert everything to one unit first. Multiply or divide by the conversion factor and state which direction was used.
When a scale drawing or map problem gives a ratio, the candidate sets up the proportion with the two like quantities in different positions (matching map to actual against actual to map).
The candidate writes the proportion from left-to-right reading order rather than matching corresponding units, so the cross-multiplication is structurally wrong even though the arithmetic is correct.
What to do instead
Label both sides of the proportion with units before cross-multiplying (e.g., cm/map = cm/map). If the units do not match across the equals sign, rewrite the proportion.
The candidate evaluates an expression such as 3 + 4 x 2 left to right, or treats -3^2 as 9.
Reading habits from prose carry over to notation, and the exponent's scope over the negative sign is not visualised, so operation order is applied by position rather than by hierarchy.
What to do instead
Insert parentheses around each operation in the order performed before calculating, and rewrite -3^2 as -(3 x 3). Do a short daily set of mixed-operation expressions with the parenthesising step shown.
The candidate answers a two-step word problem after performing only the first operation, or reports a quantity the question did not ask for.
The candidate stops as soon as a number is produced, treating computation as the goal; the final question sentence is read before the data but not re-read afterwards.
What to do instead
Underline the actual question sentence, then write a one-line answer skeleton ('The answer is ___ [units]') before calculating. After computing, fill the blank and confirm the units match what was asked.