10 Common Mistakes in DSE M2 and How to Avoid Them
Most M2 marks are lost to a short list of repeatable slips, not to hard ideas: a missing + C, limits not changed after a substitution, the sign of the j term in a cross product, multiplying matrices on the wrong side, and induction proofs with a line of wording left out. Each one has a ten-second check.
A Two-Minute Checklist Before You Hand In
- Every indefinite integral has
+ C; every definite integral has limits in the right variable. - Every cross product has been checked with two dot products.
- Every induction proof has its base case, assumption, and concluding sentence.
- Every "hence" part visibly uses the earlier result.
- Angles in calculus are in radians; exact values are left exact unless a decimal is asked for.
💡 Exam Traps & Secrets
1. Missing + CEvery indefinite integral ends with
+ C. Check: is there an integral sign with no limits? Then the answer needs a constant.2. Limits not changed after substitutionAfter
u = g(x), the limits become g(a) and g(b). Check: are the variable inside the integral and the limits about the same letter?3. Area treated as a plain integralWhere the curve dips below the x-axis the integral is negative. For an area, split at the intercepts and add the absolute values. See the graph below.
4. Chain rule factor left out
d/dx e³ˣ = 3e³ˣ. Check: after differentiating the outside, did you multiply by the derivative of the inside?5. The j sign in a cross productThe signs are
+ − +. Check: dot your answer with both original vectors; both must give 0.6. AB written as OA − OB
AB = OB − OA: end minus start. Check: does your vector point from A towards B on the sketch?7. Matrix multiplied on the wrong sideFrom
AX = B, X = A⁻¹B. Check: did you apply A⁻¹ on the same side of both sides of the equation?8. Δ = 0 read as "no solution"
Δ = 0 means no unique solution. Reduce the augmented matrix to decide between none and infinitely many.9. Induction with a line missingState
P(1) is true, write "assume P(k) is true for some positive integer k", mark where the assumption is used, and end with the concluding sentence.10. Ignoring "hence""Hence" requires the previous result. A correct answer by another route can score zero for that part. Check: which earlier line does this part use?
Frequently Asked Questions
Forgetting the constant of integration, not changing limits after a substitution, sign errors in cross products and determinants, multiplying matrices in the wrong order, and incomplete wording in induction proofs.
Attach one specific check to each kind of step, such as the two dot products after a cross product, and do it every time. Having your full working checked line by line also shows which slip you repeat.
A definite integral counts regions below the x-axis as negative. The area is the sum of the sizes of the regions, so you split the interval where the curve crosses the axis and take each part as positive.