Download clean, printable lists of the most common mistakes students make — so you can fix them before they cost marks.
Each sheet is aligned to its exam board and built from recurring student errors highlighted in examiner reports and mark schemes.
What you get
A topic-by-topic mistakes list with a “do this instead” fix and a quick self-check.
How to use it
Review before past papers, then use the quick checks to catch errors under timed conditions.
Why it works
Many marks are lost on predictable slips: rounding, sign errors, units, and misreading commands.
Coverage by topic
Preview (up to 5 per topic)
18 total rows in download
| Topic | Common mistake / misconception | Do this instead | Quick check |
|---|---|---|---|
| Algebra | Cancelling incorrectly in fractions: (x+2)/(x+3) = 2/3. | You can only cancel FACTORS, not terms. (x+2)/(x+3) cannot be simplified. Factorise first if possible. | Can you write numerator and denominator as products? If not, nothing cancels. |
| Algebra | Squaring both sides of an equation without checking for extraneous solutions. | Squaring can introduce false solutions. Always substitute solutions back into the original equation to verify. | After squaring, substitute ALL solutions back into the original. |
| Algebra | Incorrect use of the discriminant: saying b²-4ac > 0 means 'two solutions' without context. | b²-4ac > 0: two distinct real roots. = 0: one repeated root. < 0: no real roots. State which case and why. | State the value, state the condition, and state the conclusion. |
| Functions | Finding f(g(x)) by computing g(f(x)). | fg(x) means apply g FIRST, then f. fg(x) = f(g(x)). Order matters: gf ≠ fg in general. | fg: right to left — apply g first, then f. |
| Functions | Finding the inverse by just swapping x and y without rearranging. | Write y = f(x), swap x and y, then rearrange to make y the subject. The result is f⁻¹(x). | After swapping x and y, did you fully rearrange for y? |
| Calculus | Differentiating a product by multiplying derivatives: d/dx[uv] = u'v'. | Product rule: d/dx[uv] = u'v + uv'. Must use product rule for products of two functions. | Is it a product? → Apply u'v + uv'. Not a product? → Differentiate normally. |
| Calculus | Integrating and forgetting the constant of integration. | Indefinite integrals always need '+c'. Only definite integrals have limits and no constant needed. | Indefinite integral? → Add +c every time. |
| Calculus | Evaluating a definite integral without subtracting F(a) from F(b). | Definite integral = F(b) − F(a). Upper limit minus lower limit. Do not just substitute one value. | Did you compute F(b) − F(a)? Upper first, lower second. |
| Calculus | Finding area between two curves by integrating the wrong way: ∫(lower − upper). | Area between curves = ∫(upper − lower)dx. If curves cross, split into sub-intervals and take absolute values. | Which curve is on top in the interval? Integrate (top − bottom). |
| Trigonometry | Using degrees when the question requires radians (or vice versa). | Read the question. If it says 'radians' or uses π, work in radians throughout. Check calculator mode. | Check: question in radians or degrees? Set calculator accordingly. |
| Trigonometry | Forgetting extra solutions when solving trig equations. | sin θ = k gives solutions in two quadrants per period. Always find all solutions in the given range using symmetry and periodicity. | Used the CAST diagram or sin/cos/tan symmetry to find ALL solutions in range? |
| Trigonometry | Using sin²θ + cos²θ = 1 incorrectly when the identity is needed in a different form. | Rearrange as needed: sin²θ = 1 − cos²θ or cos²θ = 1 − sin²θ. Also: 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ. | Which trig function do you want to eliminate? Rearrange the identity accordingly. |
| Vectors | Finding the angle between vectors using scalar product but forgetting to divide by both magnitudes. | cos θ = (a·b) / (|a||b|). Must divide by the product of BOTH magnitudes. Calculate each magnitude separately. | Did you divide the dot product by |a| × |b|? |
| Vectors | Confusing direction vector and position vector of a line. | r = a + td. a = position vector of a known point ON the line. d = direction vector of the line. t is a parameter. | Point on line? Position vector. Which way it goes? Direction vector. |
| Statistics | Using P(A and B) = P(A) × P(B) for dependent events. | P(A and B) = P(A) × P(B) only when A and B are INDEPENDENT. For dependent: P(A and B) = P(A) × P(B|A). | Are the events independent? If drawing without replacement → dependent. |
| Statistics | Confusing the normal distribution Z-score formula. | Z = (X − μ) / σ. Standardise correctly: subtract the mean, divide by standard deviation (not variance). | Divide by σ (standard deviation), NOT σ² (variance). |
| Mechanics | Taking moments without checking that forces are perpendicular to the distance. | Moment = F × d where d is the PERPENDICULAR distance from the pivot to the line of action. Resolve forces if needed. | Is the distance perpendicular to the force? If not, resolve the force or the distance. |
| Mechanics | Forgetting to apply Newton's 2nd law as F_net = ma, not F = ma. | Use the RESULTANT (net) force on the left: F_net = sum of all forces = ma. Don't use just one force. | Have you found the resultant of ALL forces, not just one? |