Question 1 of 3 · Calculator allowed
A geometric sequence has first term 3 and common ratio 2. Find its sixth term.
u₆ = ar⁵ = 3×2⁵ = 3×32 = 96.
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Question 2 of 3 · Calculator allowed
Simplify i^6.
Powers of i repeat every four. Since i^6=i^4 i^2=1(-1), the result is -1.
Question 3 of 3 · Calculator allowed
How many real solutions does x⁴ + 1 = 3x² have?
Let u = x². Then u² - 3u + 1 = 0 has two positive roots. Each positive value of u gives two real values x = ±√u, so there are four real solutions.
These tiles show your answers to three questions. They are a starting point, not a mastery score or grade prediction.
Sequences
Correct answer: 96
u₆ = ar⁵ = 3×2⁵ = 3×32 = 96.
Complex numbers
Correct answer: -1
Powers of i repeat every four. Since i^6=i^4 i^2=1(-1), the result is -1.
Polynomial functions
Correct answer: 4
Let u = x². Then u² - 3u + 1 = 0 has two positive roots. Each positive value of u gives two real values x = ±√u, so there are four real solutions.
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34 areasFind your starting point.
01Representation of functions
Specification reference: A1 Representation of functions
Representation of functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Representation of functions requires. Keep exact values until the final step and check signs, units and reasonableness.
02Polynomial functions
Specification reference: A2 Polynomial functions
Polynomial functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Polynomial functions requires. Keep exact values until the final step and check signs, units and reasonableness.
03Functions with asymptotes
Specification reference: A3 Functions with asymptotes
Functions with asymptotes requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Functions with asymptotes requires. Keep exact values until the final step and check signs, units and reasonableness.
04Trigonometric functions
Specification reference: A4 Trigonometric functions
Trigonometric functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Trigonometric functions requires. Keep exact values until the final step and check signs, units and reasonableness.
05Piecewise functions
Specification reference: A5 Piecewise functions
Piecewise functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Piecewise functions requires. Keep exact values until the final step and check signs, units and reasonableness.
06Transformations of graphs and functions
Specification reference: A6 Transformations of graphs and functions
Transformations of graphs and functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Transformations of graphs and functions requires. Keep exact values until the final step and check signs, units and reasonableness.
07Complex numbers
Specification reference: AHL 1.12-1.13 Complex numbers
Complex numbers requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Complex numbers requires. Keep exact values until the final step and check signs, units and reasonableness.
08Vector product
Specification reference: AHL 3.13 Vector product
Vector product requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Vector product requires. Keep exact values until the final step and check signs, units and reasonableness.
09Poisson distribution
Specification reference: AHL 4.17 Poisson distribution
Poisson distribution requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Poisson distribution requires. Keep exact values until the final step and check signs, units and reasonableness.
10Hypothesis tests for a correlation coefficient
Specification reference: AHL 4.18 correlation Hypothesis tests for a correlation coefficient
Hypothesis tests for a correlation coefficient requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Hypothesis tests for a correlation coefficient requires. Keep exact values until the final step and check signs, units and reasonableness.
11Hypothesis tests for a normal population mean
Specification reference: AHL 4.18 normal mean Hypothesis tests for a normal population mean
Hypothesis tests for a normal population mean requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Hypothesis tests for a normal population mean requires. Keep exact values until the final step and check signs, units and reasonableness.
12Hypothesis tests for a Poisson population mean
Specification reference: AHL 4.18 Poisson mean Hypothesis tests for a Poisson population mean
Hypothesis tests for a Poisson population mean requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Hypothesis tests for a Poisson population mean requires. Keep exact values until the final step and check signs, units and reasonableness.
13Approximation and error
Specification reference: B1 Approximation and error
Approximation and error requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Approximation and error requires. Keep exact values until the final step and check signs, units and reasonableness.
14Sequences
Specification reference: B2 Sequences
Sequences requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Sequences requires. Keep exact values until the final step and check signs, units and reasonableness.
15Use of technology applications
Specification reference: B3 Use of technology applications
Use of technology applications requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Use of technology applications requires. Keep exact values until the final step and check signs, units and reasonableness.
16Exponentials
Specification reference: B4 Exponentials
Exponentials requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Exponentials requires. Keep exact values until the final step and check signs, units and reasonableness.
17Matrices
Specification reference: B5 Matrices
Matrices requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Matrices requires. Keep exact values until the final step and check signs, units and reasonableness.
18Straight line geometry
Specification reference: C1 Straight line geometry
Straight line geometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Straight line geometry requires. Keep exact values until the final step and check signs, units and reasonableness.
19Surface areas, volumes and measurement in circles
Specification reference: C2 Surface areas, volumes and measurement in circles
Surface areas, volumes and measurement in circles requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Surface areas, volumes and measurement in circles requires. Keep exact values until the final step and check signs, units and reasonableness.
20Trigonometry and its applications
Specification reference: C3 Trigonometry and its applications
Trigonometry and its applications requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Trigonometry and its applications requires. Keep exact values until the final step and check signs, units and reasonableness.
21Vectors
Specification reference: C4 Vectors
Vectors requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Vectors requires. Keep exact values until the final step and check signs, units and reasonableness.
22Graph theory
Specification reference: C5 Graph theory
Graph theory requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Graph theory requires. Keep exact values until the final step and check signs, units and reasonableness.
23Univariate data
Specification reference: D1 Univariate data
Univariate data requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Univariate data requires. Keep exact values until the final step and check signs, units and reasonableness.
24Bivariate data
Specification reference: D2 Bivariate data
Bivariate data requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Bivariate data requires. Keep exact values until the final step and check signs, units and reasonableness.
25Probability
Specification reference: D3 Probability
Probability requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Probability requires. Keep exact values until the final step and check signs, units and reasonableness.
26Probability distributions
Specification reference: D4 Probability distributions
Probability distributions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Probability distributions requires. Keep exact values until the final step and check signs, units and reasonableness.
27Inferential statistics
Specification reference: D5 Inferential statistics
Inferential statistics requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Inferential statistics requires. Keep exact values until the final step and check signs, units and reasonableness.
28Principles of differential calculus
Specification reference: E1 Principles of differential calculus
Principles of differential calculus requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Principles of differential calculus requires. Keep exact values until the final step and check signs, units and reasonableness.
29Techniques of differential calculus
Specification reference: E2 Techniques of differential calculus
Techniques of differential calculus requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Techniques of differential calculus requires. Keep exact values until the final step and check signs, units and reasonableness.
30Techniques of integral calculus
Specification reference: E3 Techniques of integral calculus
Techniques of integral calculus requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Techniques of integral calculus requires. Keep exact values until the final step and check signs, units and reasonableness.
31Problem-solving using calculus
Specification reference: E4 Problem-solving using calculus
Problem-solving using calculus requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Problem-solving using calculus requires. Keep exact values until the final step and check signs, units and reasonableness.
32Differential equations
Specification reference: E5 Differential equations
Differential equations requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Differential equations requires. Keep exact values until the final step and check signs, units and reasonableness.
33Approximation of areas using the trapezoidal rule
Specification reference: SL 5.8 Approximation of areas using the trapezoidal rule
Approximation of areas using the trapezoidal rule requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Approximation of areas using the trapezoidal rule requires. Keep exact values until the final step and check signs, units and reasonableness.
34Logarithms
Specification reference: SL Topic 1 logarithms Logarithms
Logarithms requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Logarithms requires. Keep exact values until the final step and check signs, units and reasonableness.
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IB AI HL · 2021 · IB · Mathematics · first-assessment-2021
Applications and interpretation HL, first assessment May 2021; checked against the 2019 guide and 2029 published reduction list
Source checked: 2026-08-27. The current official specification controls assessment requirements and option choices.
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LearningP currently maps 34 assessed areas for specification first-assessment-2021. The visible topic map below is derived from the verified route; the current official specification remains controlling.
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