Skip to the questions

IB Maths AA HL starter questions: weeks 1–13

39 short questions to open a lesson for IB Maths Analysis and Approaches HL, weeks 1–13 of the teaching year, three or four a week. Each question is shown as an image with its text underneath; the answers and mark schemes are free on the free weekly starters page, to show or project in class.

Week 1

Question 1: Sequences & Series
Find the exact sum to infinity of a geometric sequence with first term 10 and common ratio 0.2.
Question 2: Sequences & Series
Evaluate Σ_r=1⁴ (2r + 1).
Question 3: Sequences & Series
For an arithmetic sequence, u_1 = 5 and d = 3. Find the 20th term.

Week 2

Question 1: Exponents & Logarithms
Evaluate exactly e^(2ln 5).
Question 2: Exponents & Logarithms
Solve the equation log_2(x) + log_2(3) = 5.
Question 3: Financial Mathematics
State the multiplier used to find the value of an asset after it depreciates by 15% in one year.

Week 3

Question 1: Combinatorics
Calculate the exact value of 62.
Question 2: Combinatorics
In how many ways can 4 students be arranged in a straight line?
$IB Maths AA HL starter question on The Binomial Theorem: Under what condition is the binomial expansion of (1 + x)^n valid for negative or fractional n?$

Question 3: The Binomial Theorem
Under what condition is the binomial expansion of (1 + x)^n valid for negative or fractional n?

Week 4

$IB Maths AA HL starter question on Advanced Algebra: Set up the partial fraction decomposition format for (3x + 1)/((x-2)(x+3)²). Do not solve for the constants.$

Question 1: Advanced Algebra
Set up the partial fraction decomposition format for (3x + 1)/((x-2)(x+3)²). Do not solve for the constants.
Question 2: Advanced Algebra
Solve the system of equations 2x + y = 5 and x - 3y = -1.
Question 3: Advanced Algebra
A system of three linear equations in three unknowns represents three planes that meet at a single point. How many solutions does the system have?

Week 5

Question 1: Complex Numbers I
Find the exact modulus of the complex number z = 3 - 4i.
Question 2: Complex Numbers I
Find the principal argument of the complex number z = -1 + i.
Question 3: Complex Numbers I
Express the complex number with modulus 2 and argument (π)/2 in Euler form.

Week 6

Question 1: Complex Numbers II
Using De Moivre's Theorem, evaluate (cos π + isin π)^4.
Question 2: Complex Numbers II
If z = a + bi, write down an expression for z z^* (where z^* is the complex conjugate).
Question 3: Complex Numbers II
How many distinct complex roots does the equation z⁵ = 1 have?

Week 7

Question 1: Mathematical Proof
When proving by contradiction that √2 is irrational, what is the initial assumption?
Question 2: Mathematical Proof
In a proof by mathematical induction, what is the purpose of the base case?
Question 3: Mathematical Proof
Provide a counterexample to the statement 'If x² > 4, then x > 2'.

Week 8

Question 1: Functions & Absolute Value
Solve the absolute value equation |2x| = 8.
Question 2: Functions & Absolute Value
A quadratic equation ax² + bx + c = 0 has a discriminant Δ < 0. What does this graphically imply about the parabola y = ax² + bx + c?
Question 3: Functions & Absolute Value
If f(x) = x² and g(x) = x - 3, find the composite function (g ∘ f)(x).

Week 9

Question 1: Polynomials
Use the Remainder Theorem to find the remainder when P(x) = x³ - 2x + 4 is divided by (x - 1).
Question 2: Polynomials
Write down the sum of the roots of the cubic equation 2x³ - 6x² + x - 5 = 0.
Question 3: Polynomials
According to the Factor Theorem, if P(a) = 0, what must be a factor of the polynomial P(x)?

Week 10

Question 1: Rational Functions
What condition regarding the degrees of the numerator and denominator is required for a rational function to have an oblique (slant) asymptote?
Question 2: Rational Functions
Find the vertical asymptote of f(x) = (2x+1)/(x-5).
Question 3: Rational Functions
Find the horizontal asymptote of g(x) = (4x² - 1)/(2x² + 3).

Week 11

Question 1: Exponential, Logarithmic & Special Functions
State the defining algebraic condition for a function to be considered 'odd'.
Question 2: Exponential, Logarithmic & Special Functions
Determine if f(x) = x⁴ + 2 is an odd function, an even function, or neither.
Question 3: Exponential, Logarithmic & Special Functions
What geometric property do self-inverse functions possess regarding their graphs?

Week 12

Question 1: Graph Transformations
Describe the effect on the graph of y = f(x) when it is transformed to y = |f(x)|.
Question 2: Graph Transformations
Describe the single transformation mapping y = f(x) to y = f(x) + 4.
Question 3: Graph Transformations
If y = e^x is horizontally stretched by a scale factor of 1/3, what is the new equation?

Week 13

Question 1: 3D Geometry & Basic Trigonometry
Calculate the exact volume of a sphere with radius 3 cm in terms of π.
Question 2: 3D Geometry & Basic Trigonometry
Find the distance from the origin (0,0,0) to the point P(2, -1, 2).
Question 3: 3D Geometry & Basic Trigonometry
State the Cosine Rule for finding side a in triangle ABC.

More starter questions

Other weeks: Weeks 1–13 · Weeks 14–26 · Weeks 27–40. Answers and mark schemes, free for everyone, are on the free weekly starters page.

Keep your streak going

Save your answers and track your progressA free account remembers the questions you have done and brings you back to this page.

Already have an account? Sign in