Where the marks actually go in IB Math AA SL: twelve common mistakes

You got a 4 again and the teacher wrote "silly mistakes" next to half of them. That comment is true, but it does not tell you what to do. Many of these mistakes are not random: the same ones turn up again and again, in the same places, and each has a specific fix. Here are twelve common ones, with the line where each goes wrong.

The algebra ones

1. The last two lines. The method is right, the setup is right, and the question goes wrong while rearranging. A sign flips moving a term across, a bracket gets expanded as (a + b)² = a² + b², a fraction gets "cancelled" by removing a term from a sum, a whole equation gets divided by something that is zero for one of the solutions. Fix: after every rearrangement, substitute your answer back into the original line for five seconds. Few students do this, and the ones who do catch many of these slips themselves.

2. The missing second solution. Solve sin x = 1/2 for 0 ≤ x ≤ 2π and write x = π/6. That is half the marks; 5π/6 is the other half. Same with quadratics where both roots are valid, with x² = 9, with any modulus. Fix: whenever a question gives you a domain, check whether there is more than one answer. Draw the graph or the unit circle every time.

3. Dividing by the variable. Solving x² = 3x by dividing both sides by x gives x = 3 and loses x = 0. Factorise instead: x(x − 3) = 0. Fix: never divide by anything that could be zero; move everything to one side and factorise.

The form-of-the-answer ones

4. Exact value versus decimal. Paper 1 has no calculator for a reason: it wants √2, 2π/3, ln 5, 1/√3. Writing 1.41 where the question said "exact" or where the working produced a surd loses the accuracy mark. On Paper 2 the reverse applies: give the decimal to three significant figures unless the question asks for exact. Fix: read the command term and match the paper.

5. Rounding. Three significant figures unless told otherwise, and never round in the middle. A student who rounds 2.3456 to 2.35 in line two and carries it forward arrives at a final answer that is off in the third figure and loses the mark. Fix: keep full precision on the calculator until the last line, then round once.

6. Radians and degrees. The sector-area formula, arc length, the derivative of sin x and every calculus question involving trig assume radians. A calculator left in degree mode from a triangle question can spoil the next few answers without any sign that something is wrong. Fix: the calculator lives in radian mode. Switch to degrees for the one triangle question and switch back before the next one.

The calculus ones

7. The chain rule that was not applied. The derivative of e^(2x) is 2e^(2x), not e^(2x). The derivative of sin(3x) is 3cos(3x). The derivative of (2x + 1)⁵ has a 2 in it. This omission is one of the most common lost marks in the calculus section at SL. Fix: when the inside of a function is anything other than a plain x, the derivative of the inside multiplies the result. Say it out loud until it is automatic.

8. Integration housekeeping. No "+ c" on an indefinite integral. Limits written on the integral sign but not carried through the substitution. Area below the x-axis reported as negative, or two regions on either side of the axis added instead of taken separately. Fix: a checklist of three items at the end of every integration question: constant, limits, sign.

9. The discriminant condition. "Two distinct real roots" is b² − 4ac > 0. "Real roots" is ≥ 0. "No real roots" is < 0. Students write ≥ where > was needed and lose the final mark on a question they otherwise did perfectly. Fix: underline "distinct" whenever it appears.

The reasoning ones

10. "Show that", written backwards. The answer is in the question, so the marks are entirely for the route. Starting from the printed result and working backwards, or skipping the step where the actual difficulty is, scores nothing. Fix: in a "show that" question, write every step you would want to see if you were marking it, and never write the given answer until your working has produced it.

11. Logarithms and domains. log(a + b) is not log a + log b. ln(x − 2) only exists for x > 2, so a "solution" of x = 1 is not a solution and must be rejected, in writing. e^x = −3 has no solution; writing x = ln(−3) is a lost mark and a wasted minute. Fix: after solving any log or exponential equation, check each answer against the domain of every log in the original question, and write the rejection down.

12. "Hence". When part (c) says "hence", it means use the result of part (b). Students who start (c) from scratch either run out of time or take a route the mark scheme does not reward. And students who could not do (b) often can still do (c) by using the result printed in (b), which the paper allows. Fix: treat "hence" as an instruction, and use a printed result even if you could not derive it.

And one more: time

Time. Ninety minutes for eighty marks is a little over a minute a mark. A 4-mark question deserves five minutes, not fifteen. The long Section B question at the end is worth fourteen to sixteen marks and students at a 4 often leave it untouched or half done. Fix: practise with a clock from the first week, and avoid spending more than double a question's mark value in minutes before moving on and coming back.

Find your own pattern in ten minutes

Take one marked paper. For every lost mark, write one of four letters in the margin: B (blank), M (wrong method), S (slip, right method broken by algebra or arithmetic), P (presentation: form, rounding, missing working, wrong mode). Count the letters.

Mostly S and P: you know most of the maths and are losing marks in the working. These marks usually come back with timed practice, the fixes above, checking your own work, and feedback from someone else, without new teaching. Mostly B: content is missing and the eight-week revision plan tells you the order to fill it in. Mostly M: the ideas are not in place yet, and that is where more explanation helps most.

Show the letters to whoever is helping you, or to a parent. "I lose eleven marks a paper on S and P" tells them exactly what to work on.