IB Maths AI SL starter questions: weeks 1–13
39 short questions to open a lesson for IB Maths Applications and Interpretation SL, 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: Number & Approximation
Write 0.00452 in standard form (a × 10^k).
Question 2: Number & Approximation
A student estimates a length as 50 cm. The exact length is 55 cm. Calculate the percentage error.
Question 3: Number & Approximation
Round 14.568 to 3 significant figures.
Week 2
Question 1: Arithmetic Sequences
For an arithmetic sequence, u_1 = 4 and d = 3. Find the 10th term.
Question 2: Arithmetic Sequences
The 3rd term of an arithmetic sequence is 10 and the 5th term is 16. Find the common difference d.
Question 3: Arithmetic Sequences
Find the sum of the first 10 terms of an arithmetic sequence with u_1 = 2 and d = 5.
Week 3
Question 1: Geometric Sequences
For a geometric sequence, u_1 = 5 and r = 2. Find the 6th term.
Question 2: Geometric Sequences
The 2nd term of a geometric sequence is 12 and the 4th is 48. Find the positive common ratio r.
Question 3: Geometric Sequences
Find the sum of the first 8 terms of a geometric sequence with u_1 = 3 and r = 2.
Week 4
Question 1: Financial Mathematics
€1000 is invested at 4% p.a. compounded annually. Find the value after 3 years.
Question 2: Financial Mathematics
A car depreciates by 15% p.a. Initial value is €20000. Find its value after 2 years.
Question 3: Financial Mathematics
Find the Present Value needed to achieve €5000 in 4 years at 5% p.a. compounded annually.
Week 5
Question 1: Simultaneous Equations
Solve the system of equations: 2x + y = 7 and x - y = 2.
Question 2: Exponents
Evaluate 2³ × 2^4.
Question 3: Linear Equations
Solve 3x - 5 = 10.
Week 6
Question 1: Linear Functions
Find the gradient of the line passing through (1, 2) and (3, 8).
Question 2: Linear Functions
A line has gradient 2 and passes through (0, 5). Write its equation.
Question 3: Linear Functions
A taxi costs €3 plus €2 per km. Find the total cost for 5 km.
Week 7
Question 1: Quadratic Functions
Find the x-coordinate of the vertex for y = x² - 4x + 5.
Question 2: Quadratic Functions
Solve the quadratic equation x² - 5x + 6 = 0.
Question 3: Quadratic Functions
A ball's height is h(t) = 10t - 5t^2. Find the time t it reaches maximum height.
Week 8
Question 1: Exponents & Logarithms
Solve 2^x = 16.
Question 2: Exponents & Logarithms
Evaluate log_10(1000).
Question 3: Exponents & Logarithms
Solve 5(1.2)^x = 10. Give answer to 3 sf.
Week 9
Question 1: Functional Concepts
State the domain of f(x) = 1/(x-2).
Question 2: Functional Concepts
Given f(x) = 2x + 3, find f(4).
Question 3: Functional Concepts
State the horizontal asymptote of y = 3^x + 2.
Week 10
Question 1: Linear Functions
Find the y-intercept of y = 4x - 7.
Question 2: Linear Functions
A line passes through (0,4) and (2,10). Find its equation.
Question 3: Linear Functions
Find the exact distance d where taxi A (C=2.5d+4) and taxi B (C=1.8d+7.5) cost the same.
Week 11
Question 1: Quadratic Functions
Find the axis of symmetry for y = 2x² - 12x + 5.
Question 2: Quadratic Functions
Find the x-intercepts of y = (x-4)(x+1).
Question 3: Quadratic Functions
Does the parabola y = -x² + 2x open upwards or downwards?
Week 12
Question 1: Logarithmic Functions
Write down the vertical asymptote of f(x) = ln(x-3).
Question 2: Logarithmic Functions
Solve ln(x) = 2 exactly.
Question 3: Logarithmic Functions
Find the y-intercept of y = 5(2)^x.
Week 13
Question 1: Modelling Functions
Evaluate the cubic function y = x³ - 2x² + x at x=2.
Question 2: Modelling Functions
Find the period of the sinusoidal function y = 3sin(180t), where 180t is measured in degrees.
Question 3: Modelling Functions
Find the amplitude of y = 4cos(x) + 2.
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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