TG POLYCET common mistakes
TG POLYCET · Understand the traps and how to avoid them.
Assuming a quadratic equation always has two real roots and writing both without checking the discriminant, so answers like x = 3, 5 appear even when b² − 4ac is negative.
The formula method is drilled as a mechanical routine; students plug a, b, c into the quadratic formula and forget that a negative discriminant means no real solution, which is common in POLYCET-style items where the equation is deliberately set with no real roots.
What to do instead
Before solving, always compute D = b² − 4ac and classify: D > 0 two distinct real roots, D = 0 equal roots, D < 0 no real roots. Practise 15 equations of each type and write the classification first, then the roots.
Mixing up the trigonometric ratios for complementary angles, writing sin(90° − θ) = cos θ but then using sin(90° − θ) = sin θ in the next step of the same problem.
The complementary-angle identities are memorised as isolated formulas without a unit-circle or right-triangle picture, so under time pressure the wrong identity surfaces.
What to do instead
Derive each identity once from a right triangle with angles θ and 90° − θ, labelling opposite/adjacent sides. Then solve 10 mixed simplification problems and check each substitution against the triangle sketch.
Computing the surface area of a combined solid (cone on cylinder, hemisphere on cylinder) by adding the total surface areas of both solids, counting the shared circular face twice.
Mensuration formulas are learned per solid in isolation; students do not visualise which faces are hidden when solids are joined, and the joined face is invisible in the formula list.
What to do instead
For every combined-solid problem, draw the figure and mark the joined circle, then subtract 2πr² (the hidden face counted twice). Build a one-page table of combined-solid formulas with the subtraction already built in.
Treating probability of 'at least one' as the sum of individual probabilities, e.g. for two dice writing P(at least one 6) = 1/6 + 1/6 = 1/3.
The addition rule is applied without checking whether events are mutually exclusive; 'at least one' events overlap and the double-counted intersection is ignored.
What to do instead
Use the complement: P(at least one) = 1 − P(none). For two dice, 1 − (5/6)(5/6) = 11/36. Practise identifying 'at least one' phrasing and defaulting to the complement method.
Applying the lens/mirror formula with signs chosen by habit, e.g. putting a concave mirror's focal length as positive or using u positive for a real object.
The Cartesian sign convention is a set of rules that is read once and then abandoned; students copy numerical answers from worked examples without re-deriving the sign each time.
What to do instead
Write the sign convention at the top of every optics answer: distances measured against incident light are negative, pole is origin, concave mirror f negative. Substitute signs explicitly in the formula before arithmetic.
Calculating equivalent resistance of a parallel combination as R = R₁ + R₂, or forgetting to invert 1/R at the end of the parallel formula.
Series and parallel formulas look similar and are memorised together; the reciprocal step in 1/R = 1/R₁ + 1/R₂ is the step most often dropped.
What to do instead
Use the product-over-sum shortcut for two resistors, R = R₁R₂/(R₁+R₂), and verify with a sanity check: parallel equivalent must be smaller than the smallest resistor. Do 10 mixed series-parallel networks and check each answer against this rule.
Confusing the mole ratio in a balanced equation with the mass ratio, e.g. saying 2 g of hydrogen reacts with 32 g of oxygen in 2H₂ + O₂ → 2H₂O.
Students balance the equation correctly but then read coefficients as masses; the step of multiplying by molar mass is skipped under exam pressure.
What to do instead
Always convert to moles first, use coefficients only on moles, then convert back to grams. Write 'moles → ratio → moles → mass' as a fixed four-step template for every stoichiometry numerical.
Writing the pH of a strong acid solution as pH = −log[H⁺] without accounting for dilution, so 10⁻³ M HCl is given pH 3 even after 100-fold dilution.
The log formula is applied to the initial concentration; the effect of dilution on concentration is treated as a separate topic and not linked to pH.
What to do instead
For dilution problems, first find the new concentration using M₁V₁ = M₂V₂, then apply pH = −log[H⁺]. Practise a sequence of dilution-then-pH problems so the two steps become one habit.
Labelling the human heart's chambers and blood flow in the wrong direction, stating that oxygenated blood enters the right atrium or that the pulmonary artery carries oxygenated blood.
The diagram is memorised as a picture without tracing the path; the pulmonary circuit is counterintuitive because the artery carries deoxygenated blood, unlike every other artery.
What to do instead
Trace blood flow aloud as a loop: body → right atrium → right ventricle → pulmonary artery (deoxygenated) → lungs → pulmonary vein (oxygenated) → left atrium → left ventricle → aorta → body. Draw it from memory three times.
Describing photosynthesis only as 'plants make food using sunlight' without naming the reactants, products, site, and the light versus dark reaction split.
School-level summaries are retained instead of the detailed process; POLYCET biology items ask for specific terms such as chlorophyll, stroma, grana, and the role of ATP and NADPH.
What to do instead
Write the balanced equation 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ with light and chlorophyll above the arrow, then list the light reaction (thylakoid, water split, O₂ released, ATP/NADPH made) and dark reaction (stroma, Calvin cycle, CO₂ fixed).