AP POLYCET common mistakes
AP POLYCET · Understand the traps and how to avoid them.
Expanding (a−b)² as a²−2ab−b², or dropping the minus sign when substituting a negative number into a formula such as x²−5x+6.
The identity is memorised as a string of symbols rather than as a signed quantity, so the final term is written from habit and negative substitutions are processed piecemeal under time pressure.
What to do instead
Write the identity with brackets first: (a−b)² = a² − 2ab + b². Then substitute negatives inside brackets, e.g. x=−3 gives (−3)²−5(−3)+6. Do five sign-heavy expansions before moving to the next question.
Using 2πr² for the total surface area of a cylinder, or giving a volume in cm³ when the options are in litres.
Mensuration formulas are recalled as visual shapes rather than derived from CSA plus two bases, and unit conversion is skipped because the numerical answer looks plausible.
What to do instead
Derive TSA as CSA + 2 × base area, and write the unit conversion before calculating: 1 litre = 1000 cm³. Check each formula by its dimensions: area must be in square units, volume in cubic units.
Recalling standard trigonometric values incorrectly, for example sin 30° = √3/2, or using tan where the question requires cot.
The standard-value table is learned by rote without a reference triangle, so 30° and 60° values swap easily and co-ratios are confused.
What to do instead
Reconstruct the 30-60-90 and 45-45-90 triangles and read ratios from them. Write SOH-CAH-TOA at the top of rough work, and check that sin 30° is the small value 1/2, not √3/2.
In coordinate geometry, substituting points into the section formula in the wrong order, or computing slope as (y1−y2)/(x1−x2) in one line and (y2−y1)/(x2−x1) in the next.
The formula is recalled as a single blob without labelling which point is point 1 and which is point 2, so coordinate order changes between numerator and denominator.
What to do instead
Label A(x1,y1) and B(x2,y2) explicitly. Write the formula with labels before substituting, and calculate the numerator and denominator on separate lines so the same point order is preserved.
In arithmetic and geometric progressions, using the sum formula Sₙ = n/2[2a+(n−1)d] when the question asks for the nth term, or applying an AP formula to a GP.
The formulas look similar and the final sentence of the question is often read after the first formula is already chosen.
What to do instead
Underline whether the question asks for the nth term, the sum of n terms, or the sum of a finite GP. Write the required formula first, then test it with n=1 or n=2 to see whether it gives a sensible first term.
In kinematics, taking g = +10 m/s² for an upward throw and then adding it to the upward velocity, or mixing km/h and m/s in the same calculation.
The positive direction is not fixed before writing equations, and unit conversion is treated as optional because the numbers look compatible.
What to do instead
At the start of the problem declare the positive direction, e.g. upward positive, so g = −10 m/s². Convert every speed to m/s before substitution: multiply km/h by 5/18.
In electric circuits, applying 1/R = 1/R₁ + 1/R₂ to resistors in series, or using P = V²/R with the total supply voltage across a resistor that has only part of that voltage.
The formula is selected by pattern matching rather than by identifying whether the same current or the same voltage is shared.
What to do instead
First mark the circuit as series if the same current flows through each resistor, parallel if the same voltage is across each. Then choose the formula: series R = R₁+R₂; parallel reciprocal rule; power from the voltage actually across that component.
In ray optics, ignoring the Cartesian sign convention, for example putting u positive for a real object or f positive for a concave mirror.
The mirror/lens formula is memorised without the sign rules, and a correct-looking magnitude is accepted without checking the sign.
What to do instead
Write the sign convention before substituting: distances measured against the incident light are negative; f is negative for a concave mirror and positive for a convex lens. Substitute signs explicitly, then interpret a negative image distance as a virtual image.
In mole calculations, using 22.4 L mol⁻¹ for a solid or for a gas not at STP, or calculating molar mass by adding atomic masses incorrectly.
22.4 L is memorised as a universal molar volume, and molar mass is computed mentally without writing the formula and atomic masses.
What to do instead
Check the state and conditions first: 22.4 L mol⁻¹ applies only to a gas at STP. Write the chemical formula, list each atomic mass, and sum them line by line before using n = m/M or n = V/22.4.
Balancing a chemical equation by changing subscripts, such as turning H₂O into H₂O₂, instead of placing coefficients in front of formulas.
Balancing is treated as making atom counts equal by any visible change, and the rule that formulas are fixed is not applied under time pressure.
What to do instead
Balance only with coefficients, never subscripts. Count each element on both sides, start with the most complex formula, and check polyatomic ions such as SO₄ and NO₃ as whole units.