| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 25 | 38 | 52 | 68 |
SL Paper 1
Judged a fair paper in the spirit of the new course; marks were lost to unsimplified answers, ignoring required forms and time wasted on unnecessary Voronoi calculations.
Found difficult
- equation of a straight line
- inverse functions
- domain and range
- trapezoidal rule
- voronoi diagrams
- exact answers
- mean from a frequency table
- differentiation of negative powers
- optimisation
- interpreting results in context
- simultaneous equations
- financial mathematics with the GDC
- loans and amortization
Well prepared
- correlation and linear regression
- using the formula booklet
- surface area and volume of solids
- cumulative frequency graphs
- tree diagrams
- quadratic models
- definite integrals and area
- gradients and perpendicular lines
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | correlation coefficient and regression prediction | Answered well | mixed two and three significant figures along the way; substituted the distance instead of the age into the regression lineTip: Check which variable the regression equation takes as input before substituting a value. |
| 2 | cosine rule and area of a triangle | Mixed | matched the wrong side to the required angle; treated the triangle as right-angled and used half base times height; gave final answers in calculator E notationTip: Use one half ab sin C for non-right triangles and write numbers in proper scientific notation. |
| 3 | exponential model: finding parameters and evaluating | Mixed | could not identify the initial value A from the model at t = 0; used logarithms instead of the GDC and showed no working; read P(t) as a product rather than function notationTip: Write the equation you solve on the GDC so method marks are available if the answer is wrong. |
| 4 | gradient, perpendicular line and line equation in integer form | Answered well | swapped x and y in the gradient formula; left a fraction unsimplified; did not give the line as ax + by + d = 0 with integersTip: When a specific form with integer coefficients is asked for, rearrange fully before moving on. |
| 5 | range of a function, inverse value and its domain | Most struggled | reversed or confused inequality directions for the range; computed h(10) instead of solving h(x) = 10; tried to find an inverse expression algebraically; did not link domain of the inverse to range of the functionTip: To evaluate an inverse at a point, solve f(x) = value on the GDC; remember the domain of the inverse is the range of f. |
| 6 | trapezoidal rule and percentage error | Mixed | substituted the wrong values into the trapezoidal formulaTip: Practise identifying h and the ordinates before substituting into the trapezoidal rule. |
| 7 | Voronoi diagram: comparing distances and adding a cell | Most struggled | compared distances only from one vertex, ignoring the other; rounded a distance incorrectly; wrote the line through two sites instead of the bisector; calculated a perpendicular bisector that could be found by inspectionTip: Horizontal or vertical bisectors can be written by inspection; save calculation time for slanted edges. |
| 8 | arc length and surface area of a cone | Mixed | gave a decimal when an answer in terms of pi was required; confused the two radii; added the base area to a curved surfaceTip: Read whether an exact answer in terms of pi is required and which surfaces actually exist. |
| 9 | median from cumulative frequency and mean from a table with unknowns | Mixed | did not make a the subject when asked to show it; used only frequencies, not values, when finding the mean; divided by the number of classes; did not return to the cumulative frequency graphTip: The mean from a table is the sum of value times frequency divided by the total frequency. |
| 10 | loan repayments with the financial solver | Most struggled | used the wrong number of periods N; used the compound interest formula instead of the solver; did not round money to two decimal places; could not identify which values give total interest paidTip: Write down every TVM solver entry and remember interest paid equals total repayments minus amount borrowed. |
| 11 | probability with a tree diagram | Answered well | Nothing specific reported. |
| 12 | derivative and optimisation of a surface area | Most struggled | did not rewrite 128/x as a negative power; sign errors with the negative index; kept negative solutions that make no sense in context; described volume instead of surface area being minimisedTip: Rewrite terms with x in the denominator as negative powers before differentiating, then interpret the zero derivative. |
| 13 | quadratic model from points and area by integration | Answered well | left coefficients like 8 squared times a unsimplified; substituted the origin incorrectly; integrated over the wrong upper limitTip: Simplify numerical coefficients in equations and check integration limits against the diagram. |
What to practise
- Read every instruction about the required form of an answer, such as integer coefficients or exact values.
- Build fluency with inverse functions, domains and ranges.
- Practise interpreting numerical results in context using the actual values.
- Keep intermediate values unrounded and simplify final answers.
- Become fluent with the GDC finance application.
SL Paper 2
A fair but demanding, wordy paper where difficulty came from depth and interpretation rather than heavy algebra; some candidates ran short of time.
Found difficult
- reading contextual problems
- percentage change
- mathematical modelling
- trigonometry in 3D solids
- binomial distribution
- command terms
Well prepared
- basic probability
- chi-squared test
- arithmetic and geometric sequences
- sinusoidal functions
- evaluating functions
- surface area and volume of solids
- normal distribution
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | probability from a table, conditional probability and chi-squared test | Mixed | treated single events as compound; did not reduce the sample space for the conditional probability; added P(A) and P(B) without subtracting the overlap; conclusion not stated in contextTip: For P(A or B) subtract the intersection, and always compare p-value with significance level explicitly. |
| 2 | arithmetic and geometric sequences of fees | Mixed | wrong denominator for percentage increase; found the tenth term instead of the sum of ten terms; gave a non-integer n for the crossover; weak justification of long-term growth comparisonTip: Percentage increase divides by the original value; check whether a question wants a term or a sum. |
| 3 | sinusoidal model of a rotating wheel | Mixed | gave a negative amplitude; sketch extended beyond the domain or was not symmetric; rounded prematurely before the final part; no calculation supporting the probability claimTip: Store unrounded values in the GDC and reuse them in later parts. |
| 4 | angles, lengths and volume of a reservoir solid | Most struggled | measured angle of depression from the vertical; worked backwards from the given volume; used 360 days for a year; used the wrong height for the trapezoid faceTip: Sketch the relevant 2D cross-section before finding lengths or angles in a 3D solid. |
| 5 | normal distribution and binomial probability | Mixed | misread the compound event in part (c); used the wrong success probability for the binomial; used the wrong upper bound in the cumulative probabilityTip: State the distribution and its parameters, for example X ~ B(n, p), before computing probabilities. |
What to practise
- Practise long contextual questions and read them fully before calculating.
- Use unrounded GDC values in later parts and include units.
- Learn the command terms so the length of answers matches the demand.
- Sketch diagrams for geometry and graphs, with labelled axes and scales.
- Budget time and look for later parts that can be attempted independently.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. aim unclear, unmeasurable or layered, with title, aim and question not matching
- A. long histories, huge calculation tables and work far over the page limit
- B. unlabelled or illegible graphs, informal calculator notation and inconsistent variable letters
- C. personal interest stated but not shown through questioning and refining the work
- D. generic limitations and reflection lumped in one paragraph at the end
- E. statistics computed by hand instead of with technology, adding no understanding
- E. regression on weak correlation, unchecked chi-squared conditions and unjustified outlier removal
- E. models chosen without describing the data shape; R squared used to justify extrapolation
About this summary
After every session the IB sends schools a subject report: how candidates did on each paper and question, and what teachers should work on. This page is my reading of the Maths AI SL report for November 2021, in my own words. No text from the report or from the exam questions is reproduced, and it is not endorsed by the International Baccalaureate.
Session codes: TZ is the time zone variant of the papers. Corrections: pietro@pietromeloni.com.
Frequently asked questions
Which questions were hardest in Maths AI SL November 2021?
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The questions most candidates struggled with were on range of a function, inverse value and its domain, Voronoi diagram: comparing distances and adding a cell, loan repayments with the financial solver and derivative and optimisation of a surface area. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in November 2021?
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Across the papers the examiners listed equation of a straight line, inverse functions, domain and range, trapezoidal rule, voronoi diagrams, exact answers, mean from a frequency table and differentiation of negative powers, among others.
What were the grade boundaries for Maths AI SL November 2021?
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Maths AI SL: a 7 from 68 out of 100 overall in November 2021. The component boundaries are in the table on this page.
Is this the official IB subject report?
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No. It is my summary of the report the IB issues to schools after each session, rewritten in my own words with a teacher's reading of it. No text from the report or from exam questions is reproduced. Your school's IB coordinator can access the original.