Common SHSAT Math Traps and How to Avoid Them

The SHSAT math section isn't just testing whether you know math—it's testing whether you can avoid clever tricks and traps. Let's identify the most common ones and learn to spot them instantly.

Why the SHSAT Uses Traps

Math traps serve a purpose:

Test whether you read carefully (not just calculate quickly)
Identify students who truly understand concepts vs. those who memorize
Separate students who check their work from those who don't
Reward careful thinking over careless speed

Key Insight:

If your answer matches answer choice (A) or (B) AND you solved it quickly without checking, you probably fell for a trap. The test makers know most students choose early answer choices—they place trap answers there deliberately!

Trap Category 1: The "Not What They Asked" Trap

You solve correctly, but answer the wrong question.

Example:

"If 3 pencils cost $2.40, what is the cost of 2 dozen pencils?"

The Trap:

Students calculate the cost of 1 pencil ($0.80) and select that as their answer

Students calculate the cost of 12 pencils ($9.60) and select that

What They Asked:

2 dozen = 24 pencils

Cost per pencil: $2.40 ÷ 3 = $0.80

Cost of 24: $0.80 × 24 = $19.20

Correct Answer: $19.20

How to Avoid This Trap:

Circle what they're asking for before you start solving
After solving, reread the question and verify you answered it
Check units: dollars vs. cents, feet vs. inches, hours vs. minutes
Before bubbling, ask: "Is this exactly what the question asked?"

Trap Category 2: The "Looks Easy" Trap

A question appears simple, but there's a twist you miss when rushing.

Example:

"What is the value of 3² + 4²?"

The Trap:

Students calculate (3 + 4)² = 7² = 49

Correct Approach:

3² + 4² = 9 + 16 = 25

Correct Answer: 25

The Lesson:

(a + b)² ≠ a² + b²

The order of operations matters!

Common "Looks Easy" Traps:

Trap	Wrong Thinking	Correct Approach
2 + 3 × 4	(2 + 3) × 4 = 20	2 + (3 × 4) = 14
0.5 × 6	5 × 6 = 30	0.5 × 6 = 3
¾ of 12	12 ÷ 4 = 3	(12 ÷ 4) × 3 = 9
-3²	(-3)² = 9	-(3²) = -9

Trap Category 3: The "Incomplete Work" Trap

You solve the first step correctly, but the problem requires multiple steps.

Example:

"A shirt originally costs $40. It goes on sale for 25% off, then an additional 10% is taken off the sale price. What is the final price?"

The Trap:

Students calculate 25% + 10% = 35% off, then: $40 × 0.65 = $26

Correct Approach:

First discount: $40 × 0.75 = $30 (after 25% off)

Second discount: $30 × 0.90 = $27 (after additional 10% off)

Correct Answer: $27

The Lesson:

Successive percent discounts are NOT additive! You can't just add the percents.

How to Avoid This Trap:

Look for words like "then," "additionally," "after that" → signals multiple steps
Write out each step separately
Never skip steps in your head—show your work!
Check if your answer seems too simple for the problem's complexity

Trap Category 4: The "Units Conversion" Trap

The problem gives information in one unit but asks for the answer in another.

Example:

"A car travels at 60 miles per hour. How many feet does it travel in 30 seconds?"

The Trap:

Students calculate 60 ÷ 2 = 30 miles (since 30 seconds = 0.5 minutes)

Correct Approach:

60 miles/hour = 60 × 5280 feet/hour = 316,800 feet/hour

316,800 feet/hour ÷ 3600 seconds/hour = 88 feet/second

88 feet/second × 30 seconds = 2,640 feet

Correct Answer: 2,640 feet

Common Unit Conversions to Memorize:

1 foot = 12 inches
1 yard = 3 feet = 36 inches
1 mile = 5,280 feet
1 hour = 60 minutes = 3,600 seconds
1 kilogram = 1,000 grams
1 meter = 100 centimeters

Trap Category 5: The "Negative Number" Trap

Problems involving negative numbers have special rules that students often forget.

Example:

"If x < 0, which of the following is ALWAYS true?"

x² > x
x³ > x
x + 1 > 0
|x| < 0

Analysis:

Test with x = -2:

A: (-2)² = 4 > -2 ✓ (This is ALWAYS true for negative x!)
B: (-2)³ = -8 < -2 ✗
C: -2 + 1 = -1 < 0 ✗
D: |-2| = 2 > 0 (absolute value is never negative!) ✗

Correct Answer: A

Negative Number Rules to Remember:

Negative × Negative = Positive
Negative × Positive = Negative
Even exponent makes negative numbers positive: (-2)² = 4
Odd exponent keeps negative numbers negative: (-2)³ = -8
Absolute value is ALWAYS positive or zero: |-5| = 5

Trap Category 6: The "Diagram Not to Scale" Trap

The test explicitly says "Figure not drawn to scale" but students trust their eyes anyway.

Critical Rule:

NEVER estimate angles, lengths, or areas from a diagram. Only use the given numerical information. If it says "Figure not drawn to scale," the diagram is intentionally misleading!

Example:

Triangle ABC has angles of 89°, 89°, and 2°. (Figure not drawn to scale)

What type of triangle is it?

The Trap:

The diagram shows what looks like an equilateral triangle, so students choose "equilateral"

Correct Approach:

Two angles are equal (89° = 89°), so it's isosceles

Correct Answer: Isosceles

Trap Category 7: The "Assume a Value" Trap

The problem doesn't give you a specific number, but students assume one anyway.

Example:

"If 40% of a number is 20, what is 60% of that number?"

The Right Way:

Let the number = x

0.40x = 20

x = 50

60% of 50 = 30

The Shortcut Way:

If 40% = 20, then 10% = 5

60% = 6 × 5 = 30

Both methods work! Correct Answer: 30

Trap Category 8: The "Overlooked Zero" Trap

Zero has special properties that students forget.

Example:

"How many integers are there between -3 and 3?"

The Trap:

Students count: -3, -2, -1, 1, 2, 3 = 6 numbers (forgetting zero!)

Correct Count:

-3, -2, -1, 0, 1, 2, 3 = 7 numbers

Correct Answer: 7

Zero Rules to Remember:

0 is EVEN (not odd!)
0 is an INTEGER
0 is NEITHER positive nor negative
Anything multiplied by 0 equals 0
You CANNOT divide by 0
0⁰ is undefined (special case)

Trap Category 9: The "Word Problem Misdirection" Trap

Extra information is included to confuse you.

Example:

"John has 15 red marbles, 12 blue marbles, and 8 green marbles in a bag. If he randomly selects one marble, what is the probability it is blue?"

What You Need:

Blue marbles: 12
Total marbles: 15 + 12 + 8 = 35
Probability = 12/35

What You DON'T Need:

The specific counts of red and green don't matter separately—only the total!

How to Filter Information:

Read the question first (last sentence)
Underline what they're asking for
Cross out obviously irrelevant information
Extract only the numbers and relationships you need

Trap Category 10: The "Pattern Recognition" Trap

A pattern appears to work, but breaks on the specific case they ask about.

Example:

"In a sequence, each term after the first is found by multiplying the previous term by 2 and subtracting 1."

If the first term is 5, what is the 4th term?

Work it out:

Term 1: 5
Term 2: (5 × 2) - 1 = 9
Term 3: (9 × 2) - 1 = 17
Term 4: (17 × 2) - 1 = 33

Correct Answer: 33

The Trap:

Students notice a pattern (differences of 4, 8...) and try to use it as a shortcut, but get the wrong answer!

The Ultimate Trap-Avoidance Checklist

Before selecting your answer, ask yourself:

✓ Did I answer exactly what they asked?
✓ Did I check my units?
✓ Did I complete all steps?
✓ Did I fall for an "easy" answer in choices A or B?
✓ Can I plug my answer back into the problem to verify?
✓ Does my answer make logical sense?
✓ Did I consider special cases (negative numbers, zero, fractions)?

Success Strategy:

"I used to get 5-7 questions wrong from careless mistakes. Once I started circling what they asked and checking my answer against it, those errors dropped to 0-1. It's not about being smarter—it's about being more careful!"

— David L., Stuyvesant Class of 2025

Remember: The SHSAT math section rewards careful, systematic thinking over speed. Slow down, read twice, check once—and watch your score soar!

Common SHSAT Math Traps and How to Avoid Them