EN VIII Mathematics common mistakes
EN VIII Mathematics · Understand the traps and how to avoid them.
When subtracting a negative or subtracting across a minus sign, the sign of the second term is dropped, e.g. writing 7 - (-3) = 4 instead of 10, or -(x - 5) = -x - 5.
The minus sign is read as an operation only, not as part of the following number or bracket, so the sign change is never applied to every term.
What to do instead
Rewrite every subtraction as adding the opposite before computing: 7 - (-3) becomes 7 + 3; distribute a leading minus by writing each term's sign explicitly, then simplify.
Applying the order of operations left to right, e.g. evaluating 2 + 3 x 4 as 20, or 12 / 3 x 2 as 2 instead of 8.
Reading habits from natural language push left-to-right processing, and multiplication/division precedence is not made explicit when the expression is copied.
What to do instead
Before computing, mark the operations that must be done first with brackets, then evaluate one bracket at a time; treat multiplication and division as equal rank, done left to right.
Treating fractions as two separate whole numbers, e.g. adding 1/2 + 1/3 = 2/5, or cancelling a term across a plus sign such as (x + 4)/4 = x.
The fraction bar is not recognised as a grouping symbol and a division by the whole denominator, so numerators and denominators are handled independently.
What to do instead
Always convert to a common denominator before adding or subtracting, and check any cancellation by testing a number: substituting x = 4 into (x + 4)/4 shows it is not x.
Expanding a squared binomial as (a + b)^2 = a^2 + b^2, losing the middle term.
The power is applied to each term visually rather than treating the bracket as a product (a + b)(a + b).
What to do instead
Rewrite every square of a bracket as an explicit product and multiply out all four terms, then collect; verify with a numerical substitution such as a = 3, b = 2.
Solving an equation by doing an operation to one side only, or dividing by a variable without considering that it could be zero.
The equation is treated as a sequence of simplifications rather than a balance that must be preserved, and division by an unknown feels like ordinary cancelling.
What to do instead
Write the operation performed on the left and the identical operation on the right on separate lines; never divide by a variable unless zero has been excluded or checked as a separate case.
Substituting a value into a function or formula but dropping the negative sign or the brackets, e.g. evaluating f(x) = x^2 - 3x at x = -2 as 4 - 6.
The substitution is done mentally and the bracket around the negative input is omitted, so the square and the product are computed with the wrong sign.
What to do instead
Write the substitution with brackets first, f(-2) = (-2)^2 - 3(-2), then evaluate each term on its own line before combining.
Using a length or angle relationship without checking the required condition, e.g. applying Pythagoras to a triangle that has not been shown to be right-angled, or using area scale factor for lengths.
The formula is recalled as a shape-based recipe rather than as a conditional statement, and similar-figure scale factors are confused between length, area and volume.
What to do instead
Before each calculation, state the condition in writing (right angle present, figures similar, units matched) and note whether the scale factor applies to length, area (squared) or volume (cubed).
Confusing perimeter with area, or leaving the answer in the wrong units, e.g. reporting an area in cm or a volume in cm^2.
Both quantities are produced by formulas applied to the same diagram, and units are treated as decoration rather than as part of the answer.
What to do instead
Label every formula with the quantity it gives (P = ..., A = ...) and carry units through the working, squaring or cubing them exactly as the numbers are.
Reading a value from a graph or table at the wrong position, e.g. taking the median from the highest bar of a histogram or reading the cumulative frequency axis as the data value.
The axes and the type of display are not identified before reading, and the difference between raw frequency and cumulative frequency is not tracked.
What to do instead
Before reading any value, state what each axis represents and what kind of chart it is; for cumulative frequency, locate the total first and read the median at half of it.
Treating dependent events as independent, e.g. giving the probability of two cards drawn without replacement as (1/4) x (1/4), or adding probabilities of overlapping events without removing the overlap.
The standard multiplication and addition rules are memorised for the simplest case and applied without checking whether the sample space has changed or the events can occur together.
What to do instead
Redraw the sample space after each stage and adjust the denominator for items already removed; for combined events, decide first whether they are mutually exclusive before choosing to add.