Common mistakes · Maths AA · 9 min read
IB Maths AA mistakes: 14 that cost marks, with the correct working
The slips that cost AA students marks year after year, each shown wrong and then right, with the maths worked out.
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Most marks lost in IB Maths AA are not lost on hard questions. They go on familiar slips: a calculator in degree mode, a solution divided away, a log of a negative number left in the answer, a "show that" proved backwards. Below are 14 of the most common, each with the losing answer next to the correct working, so you can recognise them in your own work before the exam does.
Everything here applies to the current AA course, examined until November 2028. Paper 1 is the only maths paper without a calculator, so several of these matter most there; our Paper 1 guide covers that paper's technique in more depth.
Calculator and accuracy mistakes
1. Working in degrees when the question is in radians
On Paper 2, a calculator left in degree mode gives confident, wrong numbers. Any domain written with π, and any calculus involving trig, needs radians: the derivative of sin x is cos x only when x is in radians.
Loses marksf(x) = sin 2x, so f′(1) = 2cos 2 = 2 × 0.99939 ≈ 2.00 (degree mode).
Earns marksf′(x) = 2cos 2x, so f′(1) = 2cos 2 = 2 × (−0.41615) ≈ −0.832 (radian mode).
A gradient of almost exactly 2 for sin 2x at x = 1 should look suspicious. Mode settings, stored values and the other calculator traps are covered in our GDC mistakes guide.
2. Rounding in the middle of a calculation
On calculator papers the IB accepts the exact answer or one correct to 3 significant figures, unless a question says otherwise. That applies to the final answer only.
A population of 2000 grows to 3000 in 4 years. Model it with P = 2000ekt and find P after 20 years.
Loses marksk = ln 1.5 / 4 ≈ 0.101, so P(20) = 2000e2.02 ≈ 15 100.
Earns marksk = ln 1.5 / 4 = 0.101366… (kept in the calculator), so P(20) = 2000e20k = 2000 × 1.55 = 15 187.5 ≈ 15 200.
Write a rounded value on the page if you like, but use the stored one. And 3 significant figures is not 3 decimal places: 0.004567 becomes 0.00457.
Algebra mistakes that lose or add solutions
3. Dividing by something that could be zero
Dividing both sides by a variable expression throws away every solution that makes it zero. Factorise instead.
Solve sin 2x = sin x for 0 ≤ x ≤ π.
Loses marks2sin x cos x = sin x, so 2cos x = 1, cos x = 1/2, x = π/3.
Earns marks2sin x cos x − sin x = 0, so sin x(2cos x − 1) = 0. Then sin x = 0, giving x = 0 or π, or cos x = 1/2, giving x = π/3. So x = 0, π/3, π.
The same trap appears in plain algebra: x2 = 3x has two solutions, 0 and 3, not one.
4. Ignoring the domain of a log or a square root
Combining logs or squaring both sides can create solutions that do not satisfy the original equation. Check every answer in the original.
Solve log2 x + log2(x − 2) = 3.
Loses markslog2(x2 − 2x) = 3, so x2 − 2x − 8 = 0, (x − 4)(x + 2) = 0, x = 4 or x = −2.
Earns marksSame working to x = 4 or −2, then: log2(−2) is undefined, so reject −2. x = 4 (check: log2 4 + log2 2 = 2 + 1 = 3).
A related slip is inventing log laws: ln(x + 3) is not ln x + ln 3. Only products, quotients and powers split.
Calculus mistakes
5. Forgetting the chain rule
Differentiating the outside and forgetting the inside is a classic Paper 1 slip.
Loses marksd/dx [(3x2 + 1)5] = 5(3x2 + 1)4
Earns marksd/dx [(3x2 + 1)5] = 5(3x2 + 1)4 × 6x = 30x(3x2 + 1)4
The same applies to e2x (derivative 2e2x), ln(x2 + 4) (derivative 2x/(x2 + 4)) and sin2 x (derivative 2sin x cos x). Ask every time: is there a function inside a function?
6. Dropping the constant of integration
Without + C you cannot use the initial condition, so you lose the marks that follow as well.
Given f′(x) = 6x2 − 4 and f(1) = 5, find f(x).
Loses marksf(x) = 2x3 − 4x
Earns marksf(x) = 2x3 − 4x + C. Then f(1) = 2 − 4 + C = 5, so C = 7 and f(x) = 2x3 − 4x + 7.
7. Treating a definite integral as an area
A definite integral counts area below the x-axis as negative. If the curve crosses the axis, an "area" question needs splitting at the root (Paper 1) or the absolute value of the function (Paper 2).
Find the area enclosed by y = x2 − 3x, the x-axis and the lines x = 0 and x = 4.
Loses marks∫04 (x2 − 3x) dx = [x3/3 − 3x2/2]04 = 64/3 − 24 = −8/3, so the area is 8/3.
Earns marksThe curve crosses the axis at x = 3. ∫03 = 9 − 27/2 = −9/2 and ∫34 = −8/3 − (−9/2) = 11/6. Area = 9/2 + 11/6 = 19/3 ≈ 6.33.
Functions, trigonometry and binomial mistakes
8. Getting the domain and range of an inverse wrong
The domain of f−1 is the range of f, and the restriction on f decides which square root you keep.
Find f−1 for f(x) = (x − 2)2 + 1, x ≥ 2.
Loses marksf−1(x) = 2 ± √(x − 1), x ≥ 2.
Earns marksy − 1 = (x − 2)2 and x ≥ 2, so x = 2 + √(y − 1). f−1(x) = 2 + √(x − 1), with domain x ≥ 1 (the range of f).
9. Misusing double-angle formulas, or the wrong sign of cos
sin 2θ is 2sin θ cos θ, not 2sin θ, and the quadrant decides the sign of the value you work out.
Given sin θ = 3/5 and θ is obtuse, find sin 2θ and cos 2θ.
Loses markscos θ = 4/5, so sin 2θ = 2 × 3/5 × 4/5 = 24/25.
Earns marksθ is obtuse, so cos θ = −4/5. sin 2θ = 2 × 3/5 × (−4/5) = −24/25, and cos 2θ = 1 − 2sin2 θ = 1 − 18/25 = 7/25.
Also, sin(A + B) is not sin A + sin B. Use the compound angle formula from the booklet.
10. Losing the sign in a binomial expansion
With a negative or coefficient-carrying term, bracket the whole term before raising it to a power.
Find the coefficient of x3 in the expansion of (3 − 2x)4.
Loses marks4C3 × 3 × (−2)x3 = 4 × 3 × (−2) = −24.
Earns marks4C3 × 31 × (−2x)3 = 4 × 3 × (−8x3) = −96x3, so the coefficient is −96.
Probability mistakes
11. Confusing P(A | B) with P(B | A)
"Given that" tells you which event you already know happened. That event goes in the denominator.
P(rain) = 0.3. If it rains, a student is late with probability 0.4; if not, with probability 0.1. Given the student is late, find the probability it rained.
Loses marksP(rain | late) = 0.4.
Earns marksP(late) = 0.3 × 0.4 + 0.7 × 0.1 = 0.19. P(rain | late) = 0.12 / 0.19 = 12/19 ≈ 0.632.
A tree diagram makes the two conditional probabilities visibly different. On Paper 1, leave the answer as 12/19.
Exam technique mistakes
12. Proving a "show that" backwards
The marks in a "show that" are for a logical path from the information to the printed result. Starting from the result and working back proves nothing.
Show that 2sin2 x − cos x = 1 can be written as 2cos2 x + cos x − 1 = 0.
Loses marks2cos2 x + cos x − 1 = 0, so 2(1 − sin2 x) + cos x − 1 = 0 … which matches the original.
Earns marks2(1 − cos2 x) − cos x = 1, so 2 − 2cos2 x − cos x − 1 = 0, so −2cos2 x − cos x + 1 = 0, and multiplying by −1 gives 2cos2 x + cos x − 1 = 0.
For a numerical "show that", write the unrounded value before the given one: "area = 12.48… ≈ 12.5", not just "12.5". Our Paper 1 guide covers "show that" and "hence" chains in more detail.
13. Giving a decimal when the question asks for an exact value
Find the exact solution of 3x + 1 = 7.
Loses marksx = 0.771
Earns marks(x + 1) ln 3 = ln 7, so x = ln 7 / ln 3 − 1 (or log3 7 − 1).
The same goes for a sector of radius 6 and angle π/3: the exact area is 6π, not 18.8.
14. Not showing working on Paper 1
A wrong answer with no working scores nothing; a wrong answer with the right method can keep the method marks. Our guide to how IB mark schemes award marks explains M, A and R marks.
Find the gradient of the normal to y = x3 − 2x at x = 1.
Loses marks1 (mental arithmetic, no working, and the negative reciprocal forgotten).
Earns marksdy/dx = 3x2 − 2, which is 1 at x = 1. Gradient of the normal = −1/1 = −1.
How do you stop making the same AA mistakes?
- Keep a mistake log. Every time you lose a mark in practice, write down the mistake type, not just the question: "divided by sin x", "forgot chain rule". After a month, the top three types tell you what to drill.
- Check answers in the original equation. It catches lost solutions, invalid log solutions and sign errors in one step.
- Read the last line of the question twice. "Exact", "show that", "hence" and "area" each change what earns the marks; the command terms guide covers the rest.
- Practise without a calculator. Paper 1 rewards fluent algebra and exact values, which only come from regular work by hand. See how the AA papers differ.
Questions students ask
How many significant figures should I give in IB Maths AA?
On calculator papers, give the exact value or the answer to 3 significant figures unless the question asks for something else. Keep the full calculator value for later steps and round only at the end.
Do I get marks for a correct answer with no working?
Sometimes, but not reliably. A correct answer with no working may not earn every mark, and a wrong answer with no working earns nothing. Showing method protects you whenever the final answer slips.
Should my calculator be in radians or degrees for AA?
Use radians unless the question works in degrees. Any question with π in the domain, or any calculus with trig functions, needs radians. Check the mode at the start of every calculator paper.
What does 'exact value' mean in IB maths?
It means no rounding: leave answers as fractions, surds, logarithms or multiples of π, such as (ln 5)/2 or 6π. A decimal like 0.805 is an approximation and will not earn the final mark.
Try one: Maths AA
Solve the equation 2cos2 x = cos x for 0 ≤ x ≤ 2π. Give your answers as exact values.
[5 marks]Show the answer and why
- Rearranges to 2cos2 x − cos x = 0 (does not divide by cos x)
- Factorises: cos x(2cos x − 1) = 0
- cos x = 0 or cos x = 1/2
- x = π/2, 3π/2
- x = π/3, 5π/3
Dividing both sides by cos x gives cos x = 1/2 and loses π/2 and 3π/2, where cos x = 0. Check: at x = π/2 both sides are 0. Four solutions in total.