| Component | Max | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Overall | 100 | 34 | 48 | 64 | 78 |
| Internal assessment | 20 | 9 | 12 | 15 | 18 |
| Paper 1 | 80 | 26 | 36 | 49 | 60 |
| Paper 2 | 80 | 27 | 39 | 52 | 62 |
SL Paper 1
Students were more successful at choosing the right mathematics in context, but many lost marks on inverse functions, bounds and probability models, and some gave up too early on later questions.
Found difficult
- reasoning and justification
- upper and lower bounds
- surface area and volume of solids
- increasing and decreasing functions
- gradients and perpendicular lines
- voronoi diagrams
- inverse functions
- derivatives with the GDC
- box plots and outliers
- hypothesis testing
- conditional probability
- binomial distribution
- efficient GDC use
Well prepared
- correlation and linear regression
- differentiation
- gradients and perpendicular lines
- sine and cosine rules
- simultaneous equations
- interpreting results in context
- t-test
- tree diagrams
- independent events
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | linear regression, correlation and validity of extrapolation | Mixed | used x and y instead of the defined variables; rounded or truncated r to 2 significant figures; weak explanation of why the regression line should not be usedTip: Explain unreliable predictions by referring to extrapolation outside the data range, using the actual values. |
| 2 | upper and lower bounds and volume of a pyramid | Most struggled | gave 0.524 rather than 0.525 as the upper bound; used the rounded measurement instead of the lower bound; used a side length or perimeter as the base areaTip: The bounds of a rounded value lie half a unit of the last digit either side. |
| 3 | vertical asymptote, derivative and increasing interval | Most struggled | could not identify the vertical asymptote; partially wrong derivative; gave the minimum point instead of an interval where the function increasesTip: A function is increasing where its derivative is positive; answer with an interval, not a point. |
| 4 | Voronoi diagram: vertex, perpendicular gradient and distances | Mixed | did not write the vertex as a coordinate pair; could not get the perpendicular gradient from the gradient; calculated distances to only one vertex or between the wrong points; answered by inspection when calculation was requiredTip: When a question says distances must be calculated, show each distance and compare them explicitly. |
| 5 | angles in triangles and the sine rule | Answered well | gave the 60 degree angle instead of adding it to 38 degreesTip: Re-check which angle the question names before writing the final value. |
| 6 | value of an inverse function and its domain | Most struggled | tried to find the inverse expression algebraically; substituted 1 into h(x) instead of solving h(x) = 1; could not state the domain of the inverseTip: Find an inverse value by solving f(x) = value graphically; the inverse's domain is the function's range. |
| 7 | quadratic model through given points | Answered well | simplified a correct equation incorrectly; gave a coefficient to 2 significant figures or truncatedTip: Keep model coefficients to at least 3 significant figures. |
| 8 | derivative value on the GDC, normal line and distance | Most struggled | differentiated by hand instead of using the GDC as instructed; evaluated r(2) instead of the derivative; did not take the negative reciprocal for the normal; rounded to 2 significant figures without workingTip: The normal's gradient is the negative reciprocal of the tangent's gradient found from the derivative. |
| 9 | box plot statements and t-test | Mixed | picked box plot statements almost at random; worded hypotheses without referring to population means; gave a p-value above 1; drew a wrong conclusion after a correct comparisonTip: Write hypotheses symbolically with mu and know what each part of a box plot represents. |
| 10 | tree diagram, independent events and conditional probability | Mixed | added branch probabilities instead of multiplying; did not recognise a conditional probabilityTip: Any probability above 1 means the method is wrong; multiply along branches. |
| 11 | binomial probabilities over a week | Most struggled | did not recognise a binomial situation; used a cumulative probability for an exact one; forgot the number of arrangements; found one day's probability but not the week'sTip: If you multiply probabilities by hand, remember to count the orderings with nCr; better, use the binomial GDC function. |
| 12 | Spearman rank correlation and hypothesis test | Mixed | reversed the hypotheses; computed an irrelevant p-value or chi-squared value; compared with the wrong significance levelTip: The alternative hypothesis states the claim; compare r_s with the critical value given. |
What to practise
- Practise significant figures with zeros and show the unrounded value before rounding.
- Avoid rounding intermediate values.
- Use graphical GDC methods for inverse values and know the derivative versus inverse notation.
- Write hypotheses symbolically, understanding what mu means.
- If a needed earlier answer is missing, write a reasonable value so follow-through marks are possible.
SL Paper 2
A stern but fair paper with a slope of difficulty in each question; many respected accuracy instructions, but premature rounding still cost marks.
Found difficult
- trapezoidal rule
- unit conversion
- hypothesis testing
- chi-squared test
- loans and amortization
- cost, revenue and profit
- analytic methods
- mathematical modelling
Well prepared
- evaluating functions
- definite integrals and area
- right-angled trigonometry
- percentage error
- arcs and sectors
- mean from a frequency table
- box plots and outliers
- loans and amortization
| Q | Topic | How it went | Where marks were lost |
|---|---|---|---|
| 1 | fitting a curve, trapezoidal rule, integral and percentage error | Mixed | wrong strip width h; missed the brackets around the middle terms; swapped integral and trapezoidal methods between parts; changed the lower limit or omitted dxTip: Compute h as interval width divided by number of strips, or add individual trapezoids if unsure. |
| 2 | lengths, angles, arc length, sector area and volume | Mixed | rounded an angle prematurely; forgot to double the half-angle for the arc; subtracted the wrong region from the sector; multiplied lengths in different units for a volumeTip: Convert all lengths to the same unit before computing a volume, and reuse unrounded angles. |
| 3 | grouped data, quartiles, outliers and chi-squared goodness of fit for a normal distribution | Most struggled | treated data as discrete; GDC not set to use frequencies; reversed or poorly worded hypotheses, omitting parameters; could not compute expected frequencies from normal probabilitiesTip: In a goodness of fit test, name the distribution with its parameters, state df, p-value and the comparison. |
| 4 | car loan with the TVM solver and final payment | Most struggled | gave the down payment as the loan; used the compound interest formula for a payment problem; gave a non-integer number of periods; multiplied the payment by the decimal part of nTip: Problems with regular payments need the TVM solver; the number of payments must be a whole number. |
| 5 | income and profit functions and optimal selling price | Most struggled | included n in the income expression; used the given result in its own justification; insufficient justification that a point was not a maximum; could not build the new cost functionTip: Never use the answer you are asked to show; and use show-that results to re-enter later parts. |
What to practise
- Allow about one minute per mark and move on when stuck.
- Use unrounded values in later steps and give final answers to 3 significant figures.
- Check units and the reasonableness of answers against the constraints.
- For goodness of fit, always state the distribution type and parameters.
- Strengthen analytic skills alongside GDC use.
Internal assessment
What moderators raised about the exploration this session, criterion by criterion.
- A. lengthy introductions, repeated basic calculations and plans that hurt conciseness
- A. processes irrelevant to the aim, such as extra tests in a correlation study
- B. inconsistent case, accuracy and notation; uncited internet diagrams and GDC screenshots
- C. primary data followed only by routine processes, or functions chosen mechanically
- D. reflection limited to obvious description and a final list of generic limitations
- E. assumptions of statistical tests not checked against the data
- E. models chosen by trial with R squared, often very high degree polynomials, ignoring data trends
- E. correlation interpreted as causation
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 2023 TZ1, 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. Other variants of the same session:
Frequently asked questions
Which questions were hardest in Maths AI SL November 2023 TZ1?
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The questions most candidates struggled with were on upper and lower bounds and volume of a pyramid, vertical asymptote, derivative and increasing interval, value of an inverse function and its domain and derivative value on the GDC, normal line and distance. The tables above list every question discussed in the report, paper by paper.
What did candidates find difficult in November 2023 TZ1?
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Across the papers the examiners listed reasoning and justification, upper and lower bounds, surface area and volume of solids, increasing and decreasing functions, gradients and perpendicular lines, voronoi diagrams, inverse functions and derivatives with the GDC, among others.
What were the grade boundaries for Maths AI SL November 2023 TZ1?
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Maths AI SL: a 7 from 78 out of 100 overall in November 2023 TZ1. 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.