Skip to the questions

IB Maths AA HL starter questions: weeks 14–26

39 short questions to open a lesson for IB Maths Analysis and Approaches HL, weeks 14–26 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 14

Question 1: Radians & Reciprocal Trig
Write down the exact value of sec((π)/3).
Question 2: Radians & Reciprocal Trig
Express cot θ in terms of sin θ and cos θ.
Question 3: Radians & Reciprocal Trig
Find the exact arc length of a circle sector with radius 5 cm and angle (π)/4 radians.

Week 15

Question 1: Inverse Trig & Identities
State the domain and range of the principal inverse sine function, f(x) = arcsin x.
Question 2: Inverse Trig & Identities
Using a double angle identity, expand cos(2x) entirely in terms of sin x.
Question 3: Inverse Trig & Identities
Simplify the expression sec² θ - 1.

Week 16

Question 1: Trig Functions & Equations
Find the exact period of the function f(x) = tan(3x).
Question 2: Trig Functions & Equations
Solve sin x = 1 for 0 ≤ x ≤ 2π.
Question 3: Trig Functions & Equations
Determine the principal axis of the graph y = -2cos(x) + 5.

Week 17

Question 1: Vectors
Given vectors a and b are non-zero and perpendicular, what is the value of their scalar (dot) product?
Question 2: Vectors
Find the magnitude of the vector v = 2i - j + 2k.
Question 3: Vectors
Write down the definition of a unit vector.

Week 18

Question 1: Lines in Space
Write down the direction vector for the line with vector equation r = 12 + λ 3-4.
Question 2: Lines in Space
Define what is meant by 'skew lines' in 3D geometry.
Question 3: Lines in Space
If a particle's position is given by r = 20 + t 05 meters (t in seconds), find its exact speed.

Week 19

Question 1: The Vector (Cross) Product
Evaluate the vector product i × i.
Question 2: The Vector (Cross) Product
Evaluate the vector product i × j.
Question 3: The Vector (Cross) Product
How can the vector product a × b be used to find the area of the parallelogram formed by vectors a and b?

Week 20

Question 1: Planes in Space
Write down a normal vector to the plane with Cartesian equation 3x - 2y + 4z = 10.
Question 2: Planes in Space
Does the point (1, 2, 1) lie on the plane x + y + z = 4?
Question 3: Planes in Space
State the scalar dot product normal form equation of a plane.

Week 21

Question 1: Intersections & Angles
When finding the angle between two intersecting planes, which vectors do you use in the dot product formula?
Question 2: Intersections & Angles
What geometric object is typically formed by the intersection of two non-parallel planes?
Question 3: Intersections & Angles
If a line is parallel to a plane, what is the value of the dot product between the line's direction vector and the plane's normal vector?

Week 22

Question 1: Descriptive Statistics
State the mathematical relationship between the variance and the standard deviation of a dataset.
Question 2: Descriptive Statistics
If Pearson's correlation coefficient r = 1, how are the data points arranged on a scatter diagram?
Question 3: Descriptive Statistics
Explain the difference between a discrete and a continuous variable.

Week 23

Question 1: Probability Rules
Write down the general addition rule for the union of two events A and B, P(A ∪ B).
Question 2: Probability Rules
If P(A ∩ B) = P(A) × P(B), what term describes the relationship between events A and B?
Question 3: Probability Rules
What is the formula for the conditional probability P(A|B)?

Week 24

Question 1: Bayes' Theorem
According to the law of total probability, if B and B' partition the sample space, write an expression for P(A).
Question 2: Bayes' Theorem
In Bayes' theorem, how is P(A ∩ B) rewritten in the numerator to find P(B|A)?
Question 3: Bayes' Theorem
If drawing without replacement from a deck of cards, are the consecutive draws independent or dependent?

Week 25

Question 1: Discrete Random Variables
Given a random variable X, expand the expression for Expected Value E(3X + 2).
Question 2: Discrete Random Variables
Given a random variable X, expand the expression for Variance Var(3X + 2).
Question 3: Discrete Random Variables
How is the expected value E(X) of a discrete random variable calculated from its probability distribution?

Week 26

Question 1: Probability Distributions
State the formula for the variance of a binomial distribution X B(n, p).
Question 2: Probability Distributions
Write down the formula used to standardise a normal variable X into a Z-score.
Question 3: Probability Distributions
In a binomial distribution, what does the parameter p represent?

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