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IB Maths AI HL starter questions: weeks 1–13

39 short questions to open a lesson for IB Maths Applications and Interpretation 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: Logs & Infinite Geometric Series
Evaluate log_2(8) + log_2(4).
Question 2: Logs & Infinite Geometric Series
Simplify e^(2 ln 5).
Question 3: Logs & Infinite Geometric Series
Find the sum to infinity of the geometric sequence 10, 5, 2.5, …

Week 2

Question 1: Complex Numbers I
Let z_1 = 3 + 4i and z_2 = 1 - 2i. Find z_1 + z_2.
Question 2: Complex Numbers I
Find the modulus of the complex number z = 3 - 4i.
Question 3: Complex Numbers I
Multiply the complex numbers z_1 = 1 + i and z_2 = 1 - i.

Week 3

Question 1: Complex Numbers II
Convert the complex number z = 2e^(iπ/2) to Cartesian form (a+bi).
Question 2: Complex Numbers II
Multiply z_1 = 2 cis(π/6) and z_2 = 3 cis(π/3).
Question 3: Complex Numbers II
Find the principal argument of z = -1 + i.

Week 4

Question 1: Matrices
Multiply the matrix 1 -2; 0 4 by the scalar 3.
Question 2: Matrices
State the dimensions of the matrix resulting from a 2 × 3 matrix multiplied by a 3 × 1 matrix.
Question 3: Matrices
Find the determinant of the matrix A = 5 2; 3 4.

Week 5

Question 1: Composite & Inverse Functions
Given f(x)=2x and g(x)=x+3, find the composite function f(g(x)).
Question 2: Composite & Inverse Functions
Find the inverse function f⁻¹(x) for f(x) = 3x - 1.
Question 3: Composite & Inverse Functions
If f(x) = e^x, write down f⁻¹(x).

Week 6

Question 1: Graph Transformations
Describe the transformation from f(x) to f(x-2).
Question 2: Graph Transformations
What is the effect of 3f(x) on the graph of f(x)?
Question 3: Graph Transformations
The horizontal asymptote of y = e^x is y=0. Give the horizontal asymptote of y = e^x + 4.

Week 7

Question 1: Modelling Functions
A logistic function has a carrying capacity L = 100. What is the horizontal asymptote as t → ∞?
Question 2: Modelling Functions
In the sinusoidal model y = Asin(Bx) + C, what geometrical feature does A represent?
Question 3: Modelling Functions
Convert 180° to radians.

Week 8

Question 1: Regression Models
To linearize the exponential model y = ab^x, what mathematical operation should you apply to both sides?
Question 2: Regression Models
If ln y = 2x + ln 3, express y in the form a e^(kx).
Question 3: Regression Models
What is the general shape of the quadratic regression model y = ax² + bx + c?

Week 9

Question 1: Radians, Arcs & Sectors
Find the length of an arc with a radius of 5 cm and a central angle of 1.2 radians.
Question 2: Radians, Arcs & Sectors
Find the exact area of a sector with radius 4 m and central angle π/2 radians.
Question 3: Radians, Arcs & Sectors
Convert (π)/4 radians to degrees.

Week 10

Question 1: Vectors
Find the magnitude of the vector v = 3i + 4j.
Question 2: Vectors
Calculate the sum of the vectors a = 2; -1 and b = 3; 4.
Question 3: Vectors
Find the scalar product (dot product) of 1; 2 and 3; -1.

Week 11

Question 1: Vector Equations of Lines
A line passes through the point (1,2) with direction vector 3; 1. Write its vector equation.
Question 2: Vector Equations of Lines
In the kinematic equation r = r_0 + vt, what does the vector v represent?
Question 3: Vector Equations of Lines
If two non-zero vectors a and b are perpendicular, what is the value of their scalar product a · b?

Week 12

Question 1: Graph Theory
In a weighted graph, what might the 'weight' of an edge represent in a real-world context?
Question 2: Graph Theory
What does a complete graph K_n signify in graph theory?
Question 3: Graph Theory
What is the primary objective of the Travelling Salesman Problem?

Week 13

Question 1: Hypothesis Testing
If a hypothesis test yields a p-value of 0.02 and the significance level is α = 0.05, what is the conclusion?
Question 2: Hypothesis Testing
Define a Type I error in hypothesis testing.
Question 3: Hypothesis Testing
State the standard null hypothesis (H_0) for a ² test for independence.

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.

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