IB Maths AI SL starter questions: weeks 27–40
42 short questions to open a lesson for IB Maths Applications and Interpretation SL, weeks 27–40 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 27
Question 1: Conditional Probability
Given P(A)=0.6, P(B)=0.5, P(A ∩ B)=0.3. Find P(A ∪ B).
Question 2: Conditional Probability
If P(A ∩ B)=0.2 and P(B)=0.5, find the conditional probability P(A|B).
Question 3: Conditional Probability
In a tree diagram, branch 1 has probability 0.6 and a subsequent branch has 0.3. Find the probability of both occurring.
Week 28
Question 1: Binomial Distribution
A random variable X B(10, 0.2). Find the expected value E(X).
Question 2: Binomial Distribution
For X B(5, 0.5), find P(X=5).
Question 3: Binomial Distribution
In the binomial distribution B(n, p), what does the parameter n represent?
Week 29
Question 1: Normal Distribution
In a normal distribution, approximately what percentage of data lies within one standard deviation of the mean?
Question 2: Normal Distribution
What is the z-score for a data point exactly equal to the mean?
Question 3: Normal Distribution
Given a normal distribution with mean 20, find P(X < 20).
Week 30
Question 1: Chi-Square Test
How many degrees of freedom does a 3 × 3 contingency table have in a Chi-square test?
Question 2: Chi-Square Test
State the standard Null Hypothesis (H_0) for a Chi-square test of independence.
Question 3: Chi-Square Test
If a p-value is 0.02 and the significance level is 5%, do you reject or fail to reject H_0?
Week 31
Question 1: Differentiation Rules
Differentiate y = x³ with respect to x.
Question 2: Differentiation Rules
Find dy/dx if y = 4x² - 5x + 2.
Question 3: Differentiation Rules
Differentiate f(x) = 2/x.
Week 32
Question 1: Tangents and Normals
Find the gradient of y = x² at x=3.
Question 2: Tangents and Normals
If the gradient of a tangent is 2, what is the gradient of the normal?
Question 3: Tangents and Normals
Find the equation of the tangent to y = x² + 1 at x=1.
Week 33
Question 1: Stationary Points
What algebraic condition must be met to find a stationary point?
Question 2: Stationary Points
Find the x-coordinate of the stationary point of y = x² - 6x.
Question 3: Stationary Points
If a curve's gradient changes from positive to negative at a stationary point, what type of point is it?
Week 34
Question 1: Indefinite Integration
Find the indefinite integral ∫ 2x dx.
Question 2: Indefinite Integration
Evaluate ∫ (3x² - 4) dx.
Question 3: Indefinite Integration
Why must you include '+C' when evaluating an indefinite integral?
Week 35
Question 1: Definite Integration
Evaluate the definite integral ∫_0³ 2x dx.
Question 2: Definite Integration
What geometric property does the definite integral of a strictly positive function represent?
Question 3: Definite Integration
Evaluate ∫_0³ x² dx.
Week 36
Question 1: Trapezoidal Rule
What is the primary use of the Trapezoidal Rule in calculus?
Question 2: Trapezoidal Rule
Use the trapezoidal rule with h=2 and y-values 1, 4, 5 to find the area.
Question 3: Trapezoidal Rule
Will the trapezoidal rule overestimate or underestimate the area of a curve that is strictly concave up?
Week 37
Question 1: Review: Linear Equations
Solve the linear equation 2x + 5 = 15.
Question 2: Review: Mensuration
Calculate the exact area of a circle with a diameter of 10 cm.
Question 3: Review: Differentiation
Find the derivative of y = 7x - 2.
Week 38
Question 1: Review: Central Tendency
Find the median of the dataset: 2, 4, 5, 8, 10, 12.
Question 2: Review: Financial Mathematics
What is the compound interest multiplier for a 5% annual increase?
Question 3: Review: Probability
If P(A) = 0.2, find the probability of the complement, P(A').
Week 39
Question 1: Review: Quadratic Equations
Solve the quadratic equation x² = 16.
Question 2: Review: Coordinate Geometry
Find the midpoint of the line segment joining (-2, 4) and (4, -8).
Question 3: Review: Definite Integration
Evaluate the definite integral ∫_0⁵ 1 dx.
Week 40
Question 1: Review: Linear Functions
Write down the equation of the horizontal line passing through (3, 7).
Question 2: Review: Exponents
Evaluate 5^0.
Question 3: Review: Coordinate Geometry
Find the distance between (0, 0) and (3, 4).
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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