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100+ Free IB Math AI HL Practice Questions

Pass your IB Diploma Mathematics: Applications and Interpretation HL exam on the first try — instant access, no signup required.

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Use laws of logs to simplify log(8) + log(125) - log(10).

A
B
C
D
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Key Facts: IB Math AI HL Exam

110 marks

Paper 1 and Paper 2 each

IB Mathematics AI guide

55 marks

Paper 3 extended response

IB Mathematics AI guide

20%

Internal Assessment weighting

IB Mathematics AI guide

100

Free practice questions here

OpenExamPrep

IB Math AI HL is assessed via Paper 1 (GDC, 110 marks, 2 hours), Paper 2 (GDC, 110 marks, 2 hours), Paper 3 (extended GDC problems, 55 marks, 1 hour) and a 20% Internal Assessment exploration. Coverage spans Number and Algebra, Functions, Geometry and Trigonometry, Statistics and Probability, and Calculus with HL extensions including matrices, graph theory and modelling with differential equations on the current syllabus first examined in 2021.

Sample IB Math AI HL Practice Questions

Try these sample questions to test your IB Math AI HL exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Use laws of logs to simplify log(8) + log(125) - log(10).
A.2
B.log(123)
C.log(143)
D.3
Explanation: log(8) + log(125) = log(8 x 125) = log(1000) = 3. Then 3 - log(10) = 3 - 1 = 2 (assuming base 10).
2$5000 is invested at 4% per year compounded continuously. What is the value after 3 years? Use A = Pe^(rt).
A.$5637.48
B.$5624.32
C.$5600.00
D.$5249.04
Explanation: A = 5000 x e^(0.04 x 3) = 5000 x e^(0.12). e^(0.12) approx 1.127497, so A approx 5637.48.
3A loan of $20,000 is repaid in equal monthly amortisation payments over 5 years at 6% APR (nominal, monthly compounding). What is the monthly payment? Use M = P r / (1 - (1+r)^(-n)) with r = 0.06/12, n = 60.
A.$386.66
B.$333.33
C.$400.00
D.$1060.66
Explanation: r = 0.005, n = 60. (1.005)^(-60) approx 0.74137. 1 - 0.74137 = 0.25863. M = 20000 x 0.005 / 0.25863 approx 386.66.
4An annuity pays $1000 at the end of each year for 10 years with interest 5% per year. What is the present value? Use PV = PMT (1 - (1+r)^(-n))/r.
A.$7721.73
B.$10000.00
C.$8107.82
D.$6139.13
Explanation: (1.05)^(-10) approx 0.61391. 1 - 0.61391 = 0.38609. PV = 1000 x 0.38609 / 0.05 approx 7721.73.
5Given A = [[1,2],[3,4]] and B = [[2,0],[1,3]], find AB.
A.[[4,6],[10,12]]
B.[[2,0],[3,12]]
C.[[3,2],[4,7]]
D.[[4,10],[6,12]]
Explanation: Row 1 of A x columns of B: (1)(2)+(2)(1)=4, (1)(0)+(2)(3)=6. Row 2: (3)(2)+(4)(1)=10, (3)(0)+(4)(3)=12.
6Find the determinant of M = [[3,1],[4,2]].
A.2
B.10
C.6
D.-2
Explanation: det(M) = (3)(2) - (1)(4) = 6 - 4 = 2.
7Find the inverse of A = [[2,1],[5,3]].
A.[[3,-1],[-5,2]]
B.[[3,1],[5,2]]
C.[[1/2,1],[1/5,1/3]]
D.[[-3,1],[5,-2]]
Explanation: det(A) = 6 - 5 = 1. A^(-1) = (1/det) [[d,-b],[-c,a]] = [[3,-1],[-5,2]].
8Solve the system using matrices on a GDC: x + 2y + z = 6, 2x + y + 3z = 14, 3x + y + z = 10. Find z.
A.3
B.2
C.1
D.4
Explanation: Write as A x = b with A = [[1,2,1],[2,1,3],[3,1,1]], b = [6,14,10]. GDC gives x = 1, y = 1, z = 3.
9Find the eigenvalues of M = [[4,1],[2,3]].
A.5 and 2
B.4 and 3
C.6 and 1
D.5 and -2
Explanation: Solve det(M - lambda I) = 0: (4-lambda)(3-lambda) - 2 = 0, lambda^2 - 7 lambda + 10 = 0, (lambda - 5)(lambda - 2) = 0, so lambda = 5, 2.
10Find an eigenvector of M = [[2,1],[0,3]] corresponding to lambda = 3.
A.[1, 1]
B.[1, 0]
C.[0, 1]
D.[3, 1]
Explanation: (M - 3I) v = 0 gives [[-1,1],[0,0]] v = 0, so -v1 + v2 = 0, i.e. v1 = v2. Choose [1,1].

About the IB Math AI HL Exam

IB Diploma Mathematics: Applications and Interpretation Higher Level is one of four IB Diploma mathematics courses, designed for students interested in developing their mathematics for describing the real world, modelling and solving practical problems using technology. Assessment is by three written papers (all GDC required) and an internal assessment exploration.

Questions

100 scored questions

Time Limit

Paper 1: 2 hours, Paper 2: 2 hours, Paper 3: 1 hour, plus Internal Assessment

Passing Score

Grade 4 commonly used as a pass; grades 1-7 awarded (7 highest)

Exam Fee

School-set entry fee (varies by school and country) (International Baccalaureate Organization (IBO))

IB Math AI HL Exam Content Outline

~15%

Number and Algebra HL

Laws of logs, continuous compounding A = Pe^(rt), amortisation and annuities, matrices and matrix multiplication, determinants and inverses (2x2 and 3x3), solving 3x3 systems, eigenvalues and eigenvectors, matrix transformations of the plane, complex numbers in modulus-argument form for AC circuits

~25%

Functions HL

Logarithmic models, logistic growth y = L/(1+e^(-k(x-x0))), piecewise and rational functions with asymptotes, transformations of graphs, sum of two exponentials, sinusoidal models y = a sin(b(x-c)) + d with parameter fitting, model selection from data via GDC regression

~20%

Geometry and Trigonometry HL

3D vectors with scalar and vector (cross) product, equation of a line r = a + lambda b and equation of a plane, graph theory: Eulerian and Hamiltonian paths/circuits, Chinese postman, travelling salesman with nearest-neighbour heuristic, minimum spanning trees via Kruskal's and Prim's algorithms, weighted graphs and adjacency matrices

~25%

Statistics and Probability HL

Non-linear regression and linearisation, goodness of fit, probability density functions, central limit theorem applied, t-distribution confidence intervals, one- and two-sample t-tests (paired and unpaired), chi-squared goodness of fit and independence tests, Poisson distribution (mean = variance = lambda), geometric distribution, Markov chains with transition matrices and steady state

~15%

Calculus HL

Euler's method for dy/dx = f(x,y), additional differentiation and integration, trapezoidal rule, volumes of revolution, introduction to second-order DEs, modelling with differential equations including Newton's law of cooling dy/dx = k(A - y), logistic growth and coupled predator-prey systems

How to Pass the IB Math AI HL Exam

What You Need to Know

  • Passing score: Grade 4 commonly used as a pass; grades 1-7 awarded (7 highest)
  • Exam length: 100 questions
  • Time limit: Paper 1: 2 hours, Paper 2: 2 hours, Paper 3: 1 hour, plus Internal Assessment
  • Exam fee: School-set entry fee (varies by school and country)

Keys to Passing

  • Complete 500+ practice questions
  • Score 80%+ consistently before scheduling
  • Focus on highest-weighted sections
  • Use our AI tutor for tough concepts

IB Math AI HL Study Tips from Top Performers

1Master your GDC for matrix operations, eigenvalues, regression, normal/binomial/Poisson distributions and chi-squared tests — every paper is calculator-active
2Practise Paper 3 extended-response problem-solving questions; they integrate multiple syllabus areas and reward structured working
3Learn to choose the correct regression model from data — AI HL frequently asks 'which model fits best?' and rewards justification
4Memorise graph theory algorithms (Kruskal, Prim, nearest-neighbour); they appear most years and are an easy source of marks

Frequently Asked Questions

What is the difference between IB Math AI HL and AA HL?

Applications and Interpretation (AI) HL emphasises modelling, real-world data analysis, statistics, finance, graph theory and heavy GDC use. Analysis and Approaches (AA) HL is more pure-mathematics focused with proof, abstract calculus and trigonometric identities. AI HL suits students entering social sciences, business, design or applied STEM degrees.

How is IB Math AI HL assessed?

Three external papers (Paper 1: 110 marks, 2 hours, 30%; Paper 2: 110 marks, 2 hours, 30%; Paper 3: 55 marks, 1 hour, 20%) all with a GDC, plus an Internal Assessment mathematical exploration worth 20%. All papers allow a graphic display calculator.

Which calculator is allowed on IB Math AI HL?

All three AI HL papers require an approved graphic display calculator (GDC). Common approved models include the TI-84 Plus CE, TI-Nspire CX (non-CAS), Casio fx-CG50 and Casio fx-9750GIII. CAS calculators are not allowed.

When are IB Math AI HL exams sat?

IB Diploma exams are held in May (Northern Hemisphere schools) and November (Southern Hemisphere schools). Results are released in early July or early January respectively.