Which courses does AscentIQ cover?

IB Mathematics: Analysis and Approaches SL, Applications and Interpretation SL, and Applications and Interpretation HL — exercises generated for each course's syllabus and marked against the IB mark scheme. Analysis and Approaches HL isn't available yet; it's on our roadmap. We add courses one at a time rather than several superficially.

How does the marking actually work?

Your work is transcribed, then evaluated against the exercise's mark scheme one mark at a time. Each Method, Answer, and Reasoning mark is awarded or withheld with a written reason. Follow-through is applied, so an early error doesn't automatically cost you the marks that depend on it.

Can the AI get the maths wrong?

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What is the asynchronous tutoring?

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← IB Math AI HL

IB Math AI HL · Topic 4

Statistics and probability

SL statistics describes and tests; HL statistics estimates and models. The AHL sections add the Poisson distribution, the distribution of a sample mean, confidence intervals, formal tests with their errors, non-linear regression and Markov chains. It is the topic where the setup — the model, the hypotheses, the conclusion — carries the most marks.

What the syllabus covers

Nineteen assessed sections: SL 4.1 to 4.11, shared with AI SL, and AHL 4.12 to 4.19, which are HL only.

SL 4.1SamplingPopulation versus sample, random sampling techniques and their effectiveness, bias and reliability of sources, and the interpretation of outliers.

SL 4.2Presentation of dataFrequency tables, histograms, box-and-whisker diagrams, and cumulative frequency graphs from which medians, quartiles and percentiles are read.

SL 4.3Central tendency and dispersionMean, median and mode; estimating the mean from grouped data; IQR and standard deviation, including how constant changes to the data move them.

SL 4.4Correlation and regressionScatter diagrams, lines of best fit by eye through the mean point, Pearson's r, and the regression line y = ax + b with its parameters interpreted.

SL 4.5Probability conceptsTrials and equally likely outcomes; P(A) = n(A)/n(U); complementary events; expected number of occurrences.

SL 4.6Combined eventsVenn, tree and sample-space diagrams; the addition rule; mutually exclusive, conditional and independent events.

SL 4.7Discrete random variablesProbability distributions and the expected value E(X) = Σxᵢ·P(X = xᵢ), applied to games and insurance-style contexts.

SL 4.8Binomial distributionNotation X ~ B(n, p) with mean np and variance np(1 − p); individual probabilities via the GDC.

SL 4.9Normal distributionProbabilities and inverse-normal calculations on the GDC, plus judging whether the model is reasonable for the data.

SL 4.10Spearman's rankWhen rank correlation is the better measure than Pearson's r, and how outliers affect each differently.

SL 4.11Hypothesis testingFormulating H₀ and H₁, significance levels and p-values; χ² tests for independence and goodness of fit; the t-test; one- and two-tailed decisions.

AHL 4.12Data collection design, reliability and validityDesigning a collection method, and judging reliability and validity.

AHL 4.13Non-linear regressionFitting quadratic, cubic, exponential, power and sinusoidal models with technology, and the coefficient of determination R².

AHL 4.14Linear combinations and unbiased estimatorsThe mean and variance of combinations of random variables, and unbiased estimates of a population's mean and variance.

AHL 4.15Combinations of normal variables and the central limit theoremThe distribution of a sum, a difference and a sample mean.

AHL 4.16Confidence intervals for the meanConstructing and interpreting an interval for a population mean.

AHL 4.17The Poisson distributionIts conditions, its mean and variance, and probabilities for different interval lengths.

AHL 4.18Hypothesis testing: critical regions and errorsOne- and two-tailed tests, critical regions and p-values, and the probabilities of Type I and Type II errors.

AHL 4.19Transition matrices and Markov chainsThe state after n steps by repeated multiplication, and the steady state of a regular chain.

How it is examined

The calculator does the arithmetic. The marks are for what you asked it, and for the sentence after the number.

State the model before you use it: X ~ Po(λ), or X̄ ~ N(μ, σ²/n), with the numbers. That line carries the method mark, and it is also what stops you using the wrong distribution.
A hypothesis test has a fixed script: H₀ and H₁ in terms of the parameter, the significance level, the p-value or critical region, a comparison, and a conclusion in context. Each stage is marked.
A Type I error is rejecting H₀ when it is true, and its probability is the significance level of the test. A Type II error is not rejecting H₀ when it is false, and is calculated for a stated alternative value.
The unbiased estimate of a population variance divides by n − 1. Use the sample standard deviation s, not the population one, for estimates, intervals and tests.
The Poisson mean scales with the interval: 3 per hour is 1.5 for half an hour. Questions regularly change the interval and expect the mean to change with it.
Non-linear regression is a choice of model, from the context or the scatter diagram, followed by a reading of R². A high R² measures fit; it does not prove the model.
Markov chains use a transition matrix whose columns sum to 1, so the state after n steps is Tⁿ times the starting state; the steady state solves Tπ = π.

A marked question, mark by mark

A Poisson test where the p-value is right and the conclusion is not stated in context — the usual place the last mark goes.

Rehearse the whole procedure, step by step

From SL 4.1 sampling to AHL 4.19 Markov chains, every generated exercise comes back with each mark awarded or withheld and a reason — including the conclusion sentence students habitually leave out.

Start your trial

New to the codes? M1, A1, R1 explained →

Hypothesis test · AHL 4.18

Seed 3R90

Calls to a helpline follow a Poisson distribution with a mean of 4 per hour. After an advert, 8 calls arrive in one hour. A test at the 5% level checks whether the mean has increased. H₀: λ = 4, H₁: λ > 4.

(a)Find the p-value of the test.
(b)State the conclusion, in context.

Your work

X ~ Po(4)

p = P(X ≥ 8) = 1 − P(X ≤ 7) = 0.0511

0.0511 > 0.05, so do not reject H₀.

Marks awarded

M1Mark awarded. Poisson model stated, and the upper tail written as 1 − P(X ≤ 7).
A1Mark awarded. p-value 0.0511, correct to three significant figures.
R1Mark not awarded. The comparison is right, but the conclusion is not in context: no statement that there is insufficient evidence the mean number of calls has increased.

Where marks are actually lost

Here the calculator is rarely the problem. The setup around it, and the sentence after it, are.

Computing P(X ≥ 8) as 1 − P(X ≤ 8), or treating 'more than' as 'at least'.

CostThe probability is for the wrong event. The p-value is off, the accuracy mark goes, and the conclusion can change.

Ending a test with 'reject H₀' or 'do not reject H₀' and nothing else.

CostThe conclusion mark is for the statement in context. The decision alone, without what it means for the situation, earns little.

Using the population standard deviation where an unbiased estimate is needed.

CostThe estimate divides by n instead of n − 1. Every interval and test statistic after it is slightly off, and the accuracy marks are lost.

Using a Poisson mean for one interval length on a question about another.

CostA mean of 4 per hour is not the mean for a half-hour. The model is wrong from its first line.