Georgia Unified Math common mistakes
Georgia Unified Math · Understand the traps and how to avoid them.
When simplifying or combining expressions with radicals or rational exponents, the candidate multiplies the radicands or adds the exponents without checking that the index or base matches, e.g. writing √2·√3 as √5 or adding 2^3·2^4 as 2^7 only when bases differ.
The rules for radicals and exponents are memorized as isolated formulas and rehearsed only in single-step drills, so under mixed practice the candidate pattern-matches to whichever rule was seen most recently rather than verifying the precondition (same index, same base) before applying it.
What to do instead
Before each operation, require the candidate to write the precondition in the margin: 'same index?' for radicals, 'same base?' for exponents. Then re-derive one example of each rule from the definition (e.g. √2·√3 = √6 because (√6)² = 6 = 2·3) and practice ten mixed items where some items are deliberately inapplicable so the check is exercised, not assumed.
On unit-conversion and dimensional-analysis items, the candidate sets up the conversion ratio with the units inverted (multiplying by a ratio that should divide) and reports a number with no unit, so the answer is off by a squared factor or by a reciprocal.
The candidate treats conversion as a fraction-reduction exercise and cancels numbers rather than units, and because the arithmetic still 'works out' to a clean number, nothing signals that the orientation is wrong.
What to do instead
Mandate that every conversion be written as a chain of fractions with units carried through, and that the final line show the unit. Require the candidate to check the direction by estimating: 'a larger unit means a smaller number.' Practice five items where the wrong orientation produces a plausible-looking number, so the unit check is the only detector.
When solving linear equations and inequalities with fractions or negative coefficients, the candidate multiplies through by the least common denominator but forgets to distribute to every term, and when dividing an inequality by a negative it retains the original inequality sign.
The candidate performs the operation on the visibly 'main' side of the equation and treats the flip rule as a separate fact to remember rather than as a consequence of multiplying by a negative number, so it is dropped under time pressure.
What to do instead
Require a two-line ritual: write the LCD above the problem and tick each term as it is multiplied, and after any division by a negative, physically rewrite the inequality symbol before continuing. Then have the candidate verify with a test value (e.g. x = 0 or x = -10) substituted into the original inequality, which exposes a wrong sign immediately.
When factoring quadratics or solving by factoring, the candidate finds two numbers that multiply to the constant but ignores the sign requirement of the middle coefficient, or solves (x-3)(x+5)=0 as x=3 and x=5 by dropping the sign when setting each factor to zero.
The candidate has automated the 'product and sum' search but rehearses it mostly on quadratics with positive roots, so negative roots are handled by copying the visible number rather than solving the factor equation.
What to do instead
Force the intermediate step: write each factor set equal to zero as its own line, (x-3)=0 gives x=3, (x+5)=0 gives x=-5, before collecting roots. Have the candidate expand the factored form back and confirm the middle coefficient matches, and drill a set deliberately weighted toward negative and mixed-sign roots.
When working with function notation and composition, the candidate reads f(x+2) as f(x)+2, or computes f(g(x)) by multiplying the two expressions rather than substituting g(x) into every occurrence of x in f.
Function notation looks like multiplication to a candidate who has spent years seeing juxtaposition mean 'times', and composition is introduced with only one worked example, so the substitution structure is never made explicit.
What to do instead
Have the candidate rewrite the outer function with a blank in place of every x, e.g. f(□)=3□-1, then insert the inner expression into the blank. Use numerical checks: compute f(g(1)) both by the composition and by direct substitution and confirm they agree, which catches the multiplication error at once.
When identifying domain and range, the candidate gives the domain of a rational or radical function as all real numbers, missing the value that makes a denominator zero or the restriction that a square root's radicand must be non-negative.
The candidate evaluates the expression at a convenient point, finds it defined, and generalizes; the excluded values are invisible unless explicitly hunted, and the candidate has no routine for hunting them.
What to do instead
Institute a two-question domain scan for every function: 'where could a denominator be zero?' and 'where could a radicand go negative?' Solve those conditions before doing anything else with the function, and state the domain in interval notation as a required line of work. Practice on functions where the excluded value is non-obvious, such as (x+1)/(x²-4).
On exponential and linear modelling items, the candidate confuses the growth factor with the growth rate, using r directly as the multiplier (writing 0.06^x for 6% growth) or treating a percent change as an additive constant.
Percent and multiplier are used interchangeably in everyday speech, and the candidate has not built the habit of translating a rate into a factor of (1+r) before writing the model.
What to do instead
Require the candidate to write the translation explicitly before modelling: 6% growth means multiply by 1.06, 6% decay means multiply by 0.94, and state which quantity is the initial value. Then sanity-check the model at one step: after one period the output must be 6% larger than the start, which immediately exposes the 0.06^x error.
In coordinate geometry and triangle problems, the candidate applies a formula with the coordinates or sides in the wrong order or substitutes a side length where an angle belongs, e.g. using the Law of Sines with two sides and no opposite angle, or computing slope as run over rise.
The candidate recalls the shape of the formula but not the conditions under which it is valid, and works from memory of the visual form rather than from a labelled diagram of the given information.
What to do instead
Require a labelled sketch with every given value placed on it before any formula is chosen, and a one-line statement of which case applies (SSS, SAS, ASA, right triangle). For slope and distance, write the formula with subscripts (y₂-y₁)/(x₂-x₁) and assign point 1 and point 2 explicitly before substituting.
On circle and angle items, the candidate uses the inscribed-angle measure directly as the central angle (or vice versa), or applies the arc-length formula with the diameter in place of the radius.
The two angle relationships look like the same picture, and the radius/diameter substitution is a reading slip that survives because the candidate does not track which quantity the formula expects.
What to do instead
Have the candidate annotate every circle diagram with 'central = arc' and 'inscribed = half arc' before computing, and write the formula with the quantity named (arc length = rθ with r the radius) and circle the given value as radius or diameter. Include items where the diameter is given to force the conversion step.
In statistics items, the candidate reads a two-way table or conditional-probability question using the grand total as the denominator when the condition restricts the sample space, and reports P(A|B) as P(A and B).
The candidate computes a single fraction from the table without restating the condition in words, and the grand total is the most visually prominent number in the table, so it becomes the default denominator.
What to do instead
Require the candidate to write the condition as a sentence first: 'given B, the denominator is the B total.' Then shade or circle the restricted row or column on the table before forming the fraction. Verify by checking that the conditional probabilities across a row sum to 1, which fails if the grand total was used.