IB Mathematics Analysis & Approaches HL Past Papers

How to sit and review official IB papers your school is licensed to use, plus original walkthroughs. Official papers are not hosted here.

Past Papers

Resources for IB Mathematics Analysis & Approaches HL

Using an official IB paper

Where licensed AA HL papers come from, and a 15-minute warm-up that does not copy any paper.

Official papers are IB property. iStudyPlus does not host or reproduce IB examination papers or markschemes. Use a pack your school is licensed to give you, or buy the examination paper and markscheme pack from the Follett IB Store (Diploma Programme). Background on the course and on assessment lives on the IB mathematics curriculum page and the IB assessment and exams page.

Analysis and Approaches HL is examined in three papers. Your coordinator or teacher should give you the session pack the school has purchased. A typical purchase is the IB examination paper and markscheme pack (download or USB) sold through the Follett IB Store. Those files are for people covered by the school licence. Do not upload them to this site, and do not paste question text into a Hub Resource.

What to download from your school, not from a random PDF link

  • The AA HL paper for the session your teacher named (Paper 1, 2, or 3).
  • The matching markscheme, kept closed until you have finished the sitting.
  • The formula booklet your cohort is allowed to use. iStudyPlus does not republish it.

15-minute warm-up before a licensed paper

  1. 3 min. Read the cover: calculator rule, time, and how many questions you must answer. AA HL papers are not multiple choice.
  2. 6 min. Skim every question. Write a one-line plan for the first question you will actually start (diagram, substitution, or distribution). Do not solve yet.
  3. 4 min. On scrap paper, list formulas you expect to need. Close the booklet.
  4. 2 min. Start the clock for a 30-minute first block. Stop at 30 minutes and note which part you were on. That note is more useful than finishing one question slowly and never seeing the rest.

When you want questions you can open immediately, use the iStudyPlus practice sets under Practice Exams. Those are original. They are not a substitute for a licensed past paper, and they are not labelled as one.

Calculator and non-calculator drill

Two original 15-minute blocks with answers, so calculator habits stay on the paper that allows them.

iStudyPlus original. This set was written for iStudyPlus. It is not an official IB examination, it does not use a real session code, and it is not copied from an IB past paper. Official IB examination papers and markschemes remain the property of the International Baccalaureate Organization.

Work Block A with the calculator closed. Then work Block B and write the command or window, not only the output. These items are iStudyPlus drills, not extracts from an IB paper.

Block A — non-calculator (15 minutes)

A1. Find the exact value of $sinfrac{pi}{3}cosfrac{pi}{6} – cosfrac{pi}{3}sinfrac{pi}{6}$. [3]

A2. Solve $e^{2x} = 5$ for $x$, in exact form. [3]

A3. Differentiate $ln(3x^{2}+1)$. [3]

Block B — calculator (15 minutes)

B1. $X sim N(20, 3^{2})$. Find $P(X gt 25)$ to 3 significant figures, and write the calculator command you used. [3]

B2. Find $int_{0}^{2} e^{-x^{2}},dx$ to 3 significant figures. [3]

B3. Solve $x^{3} – 4x – 1 = 0$ for the real root between $2$ and $3$, to 3 significant figures. [3]

Mark scheme

A1. This is $sinleft(frac{pi}{3}-frac{pi}{6}right) = sinfrac{pi}{6} = frac{1}{2}$ [3].

A2. $2x = ln 5$, so $x = frac{1}{2}ln 5$ [3].

A3. $frac{6x}{3x^{2}+1}$ [3].

B1. $z = frac{25-20}{3} = frac{5}{3}$. $P(Z gt 1.67) = 0.0478$ (accept $0.0476$ to $0.0480$ from a calculator normal cdf) [3].

B2. No elementary antiderivative is required. Numerical integral $approx 0.882$ [3].

B3. The root is $2.11$ (the cubic is negative at $2$ and positive at $2.2$) [3].

After-paper review sheet

A debrief table you can copy, with one filled example from the iStudyPlus Paper 1 set.

Official papers are IB property. iStudyPlus does not host or reproduce IB examination papers or markschemes. Use a pack your school is licensed to give you, or buy the examination paper and markscheme pack from the Follett IB Store (Diploma Programme). Background on the course and on assessment lives on the IB mathematics curriculum page and the IB assessment and exams page.

Mark a licensed IB paper from the school markscheme, offline. Mark an iStudyPlus set from the scheme printed on that Hub Resource. Either way, copy this table into your notes. One lost mark gets one row.

Question Topic Error type What I will do next
iStudyPlus Paper 1, Q1(c) Arithmetic series Stopped at $S_{n} = n(n+2)$ and did not test $n = 13$ and $n = 14$ Redo Q1(c) closed-book, then one more “least n” series question from the Question Bank

Error types that are worth naming

  • Setup. The diagram, the distribution, or the substitution never got onto the page.
  • Algebra. The method was right and a sign or a factor died in the middle.
  • Calculator. Degree mode, a missed root, or a rounded intermediate.
  • Incomplete method. The answer appeared without the line a marker can credit.
  • Command term. “Show that” stopped early, or “hence” started a new method.

If the same topic appears twice, open that Key Concepts refresher before you sit another paper. Leave the school’s IB markscheme in the licensed copy. Do not paste it here.

Exam technique walkthrough — a logistic model

A fully worked original multi-part question, written as a marker would read it. Not an IB past paper.

iStudyPlus original. This set was written for iStudyPlus. It is not an official IB examination, it does not use a real session code, and it is not copied from an IB past paper. Official IB examination papers and markschemes remain the property of the International Baccalaureate Organization.

Read the question once, then cover the commentary and try it. The commentary is the walkthrough: what to write, and why a line earns a mark.

Question. A population is modelled by $P(t) = dfrac{1200}{1 + 5e^{-0.3t}}$, where $t ge 0$ is the time in years after the population is first observed and $P$ is the number of individuals. [12]

  1. Find the initial population. [2]
  2. Write down the limiting population as $t$ becomes large, and say what it means. [2]
  3. Find the value of $t$ at which the population reaches $900$. [5]
  4. Show that $P'(t) gt 0$ for all $t ge 0$, and state what that means for the population. [3]

Walkthrough and mark scheme

(a) Substitute before you simplify. $P(0) = frac{1200}{1+5} = 200$. The sentence “the initial population is 200 individuals” is the answer mark; the substitution is the method mark.

(b) $e^{-0.3t} to 0$, so $P(t) to 1200$. In context: the model levels off at 1200 individuals. Do not call 1200 the initial value.

(c) Set $900 = frac{1200}{1+5e^{-0.3t}}$. Invert carefully: $1+5e^{-0.3t} = frac{1200}{900} = frac{4}{3}$. Then $5e^{-0.3t} = frac{1}{3}$, so $e^{-0.3t} = frac{1}{15}$. Hence $t = frac{ln 15}{0.3} = 9.03$ years (3 s.f.). A marker wants the exact line and the rounded line, plus a check that $t ge 0$.

(d) Quotient or chain rule: $P'(t) = frac{1800 e^{-0.3t}}{left(1+5e^{-0.3t}right)^{2}}$. The numerator and the denominator are both positive for every real $t$, so $P'(t) gt 0$. The population is increasing for the whole domain of the model. “The derivative is positive” without that sentence does not finish an “interpret” or “state what this means” demand.