SAT Maths — Common Traps

Chapter Overview & Weightage

The SAT is engineered with predictable trap answers — the second-most-common wrong answer is usually the answer to the wrong question or the answer before the last step. Recognising these traps is the highest-leverage skill for moving from $700$ to $760+$ .

Typical SAT impact: roughly 30% of medium-difficulty questions have a “trap” answer choice.

Key Concepts You Must Know

Watch for what the question is actually asking (find $x$ vs find $x + 5$ )
Units must match in word problems
“How many more” is a difference, not a ratio
Negative roots in quadratics — both might be valid
Read every word: “least integer”, “positive value”, “smallest”
Check for extraneous solutions in radical/rational equations
Estimating with answer choices saves time on hard questions

Important Formulas

Re-read the question after solving — does my answer match what was asked?
If a quadratic gives two roots, are both valid in the problem context?
Are the units consistent throughout the problem?
Did I simplify too early (e.g., dividing by a variable that could be zero)?
Does the problem say “approximately” or “exactly”?

Solved Previous Year Questions

Trap 1: Asked for $x + 5$ , not $x$

“If $2x + 6 = 14$ , what is the value of $x + 5$ ?”

Trap: solve $2x = 8$ , $x = 4$ , mark answer (A) $4$ . Wrong — question asks for $x + 5 = 9$ .

Always re-read the question stem after solving.

Trap 2: Hidden unit conversion

“A car travels at $60$ miles per hour. How far does it travel in $30$ minutes?”

Trap: $60 \times 30 = 1800$ miles. Wrong — $30$ minutes is $0.5$ hours, so distance is $30$ miles.

Trap 3: Both roots needed

“If $x^2 = 25$ , what are the possible values of $x$ ?”

Trap answer: $5$ . Correct: $\pm 5$ . SAT explicitly tests this.

Trap 4: Extraneous solution

“Solve $\sqrt{x + 5} = x - 1$ .”

Squaring: $x + 5 = x^2 - 2x + 1$ , so $x^2 - 3x - 4 = 0$ , $(x-4)(x+1) = 0$ , $x = 4$ or $x = -1$ .

Check: $x = -1$ gives $\sqrt{4} = -2$ , which is false. Only $x = 4$ is valid.

Difficulty Distribution

Trap type	Frequency	Hardest level
Misreading the question	High	Medium
Unit conversion	High	Easy/Medium
Both roots	Medium	Medium
Extraneous solutions	Medium	Hard
Off-by-one in counting	Low	Hard

Expert Strategy

Underline what the question asks before solving. “Value of $x + 5$ ”, “least positive integer”, “in inches” — all easy to miss when in flow.

For quadratics, ALWAYS check both roots in the original equation, especially if the problem involves square roots, denominators, or geometric constraints.

If you finish a Math question quickly with a clean integer answer, double-check. SAT trap answers are usually clean integers too — they look right.

Common Traps

Plugging in early, reading later. Always read the entire question first, including “what is the value of [expression]” — the expression isn’t always $x$ .

Missing the negative root. $x^2 = c$ has two solutions: $\pm\sqrt{c}$ . Square roots in absolute value contexts have only the positive.

Confusing percentages. ” $20\%$ more” means multiply by $1.2$ , not add $0.2$ and divide. ” $20\%$ less” is $\times 0.8$ .

Treating “average” carelessly. Average = sum / count. Don’t average two averages directly without weighting by count.

Forgetting to convert minutes to hours, or feet to inches. Always check the units of the final answer.