IB Maths AA Number & Algebra questions become much more manageable when you recognize their recurring structures. Most ask you to select a familiar model, translate the information into algebra, show a logically complete method, and check restrictions or accuracy.
The most efficient revision method is to attempt a question before watching it worked through step by step. Comparing your approach with a worked video solution reveals the missing decision or algebraic step far faster than repeatedly reading notes. This guide explains the main question types, reliable methods, and traps that affect both SL and HL students.
How Number and Algebra is examined in IB Maths AA
Number and algebra is one of the five official Mathematics: Analysis and Approaches topics. The IB subject brief assigns 19 recommended teaching hours at SL and 39 at HL, but these figures are curriculum planning recommendations, not fixed percentages of examination marks.
Questions can appear throughout the external assessment because IB papers are based on the syllabus as a whole. The official assessment structure is:
Component
SL
HL
Technology rule
Paper 1
1 hour 30 minutes, 40%
2 hours, 30%
No calculator
Paper 2
1 hour 30 minutes, 40%
2 hours, 30%
GDC required
Paper 3
Not taken
1 hour, 20%
GDC required
Exploration
20%
20%
Internal assessment
Papers 1 and 2 contain compulsory short-response and extended-response questions. HL Paper 3 contains two compulsory extended problem-solving questions, which may combine algebra with functions, trigonometry, probability, or calculus.
A clean copy of the mathematics formula booklet is provided in examinations. This does not remove the need to know when a formula applies, what each symbol means, or whether its conditions are satisfied. The official IB Mathematics: Analysis and Approaches guide and confirm the syllabus and assessment terminology.
Although individual contexts change, the underlying mathematical decisions are predictable.
Question family
What you must recognize
Frequent trap
Arithmetic sequences and series
Constant difference
Confusing a term with a sum
Geometric sequences and series
Constant ratio
Using an infinite sum when $
Financial applications
Repeated percentage multiplication
Using simple rather than compound change
Exponents and logarithms
The unknown appears in an exponent
Ignoring logarithm domain restrictions
Binomial expansion
Required term or coefficient
Misreading the power of x
Proof
A universal claim requiring justification
Verifying examples instead of proving the statement
Accuracy and bounds
Rounded measurements or required precision
Rounding during intermediate steps
HL complex numbers
Cartesian, polar, or exponential form
Losing arguments or roots
HL algebraic methods
Partial fractions, polynomial roots, systems
Dividing by an expression that could equal zero
HL induction and contradiction
A formal logical structure
Omitting the induction hypothesis or conclusion
Students should revise these as question families, not as isolated formulas. The RevisionDojo Number and Algebra topic hub organizes the content by syllabus area for both levels.
A reliable method for answering the questions
1. Identify the structure before calculating
Underline information that determines the model. A constant amount added each period suggests an arithmetic sequence, while a constant percentage change suggests a geometric sequence or exponential model.
Then write the relevant quantities explicitly. For a sequence, identify u1, d or r, the term number n, and whether the question asks for un or Sn. This prevents many substitution errors.
2. Write the governing equation
Do not jump directly from the question to a calculator answer. An equation such as
5000(1.04)n=7000
shows the model and preserves method marks even if the final calculation is wrong. On a calculator paper, technology should execute or solve the mathematics, not replace its communication.
3. Solve with the appropriate method
Paper 1 rewards exact manipulation, factorization, exponent laws, logarithm laws, and clearly structured proof. Paper 2 may require numerical equation solving, financial calculations, or efficient use of lists and graphing features.
Use only a calculator permitted under the current IB calculator policy. Learn the required functions on your own approved model before the examination.
4. Check conditions and answer the question asked
Check that:
a logarithm's argument is positive;
a denominator is non-zero;
an infinite geometric series has ∣r∣<1;
a counting answer is a non-negative integer;
a time or term number makes sense in context;
all required complex roots have been included;
the final accuracy matches the instruction.
IB specimen papers state that, unless otherwise instructed, numerical answers should generally be exact or correct to three significant figures. Read the directions on your own examination paper because a question may demand a different form or accuracy.
Worked examples of common methods
Arithmetic sequence from two known terms
Suppose u3=11 and u8=31. Find S20.
Using un=u1+(n−1)d:
u1+2d=11,u1+7d=31.
Subtracting gives 5d=20, so d=4 and u1=3. Therefore,
S20=220(2(3)+19(4))=820.
The main risk is using u20 when the question asks for the sum of the first 20 terms. Writing the sequence variables first makes that distinction visible.
Solving an exponential equation
Solve 32x−1=20.
Take logarithms of both sides:
(2x−1)ln3=ln20.
Hence,
x=21(1+ln3ln20).
This exact expression is suitable for Paper 1 unless a decimal is requested. A common error is writing ln(2x−1), but the logarithm power law applies to the exponent: ln(32x−1)=(2x−1)ln3.
Infinite geometric series
For a geometric sequence with first term 12 and ratio 31,
S∞=1−3112=18.
The method is valid because 31<1. Stating this condition is particularly important when the question asks whether a series converges.
A short deductive proof
To prove that the square of an odd integer is odd, begin with the definition. Let n=2k+1, where k∈Z. Then
n2=(2k+1)2=4k2+4k+1=2(2k2+2k)+1.
Since 2k2+2k is an integer, n2 has the form 2m+1 and is therefore odd. Testing 32 and 52 would support the claim but would not prove it for every odd integer.
Additional expectations at Higher Level
HL students retain all SL content and study more advanced algebraic reasoning. Important areas include complex numbers, roots of polynomials, systems of linear equations, partial fractions, counting principles, extended binomial work, and formal proof techniques such as induction and contradiction.
In complex-number questions, select the representation that fits the operation:
Cartesian forma+bi for addition and subtraction;
modulus-argument or exponential form for multiplication, division, powers, and roots;
conjugate pairs when working with real-coefficient polynomials.
For proof by induction, show the base case, state the induction hypothesis, prove the next case from that hypothesis, and write a conclusion. Merely simplifying the statement for k+1 without using the assumption for k does not establish the inductive link.
Why worked video solutions improve performance
Reading a solution can create the impression that a method is obvious because every step is already selected. Real examination skill is the ability to select those steps independently.
Use this practice cycle:
Attempt one question without notes.
Mark the point where you became uncertain.
Watch the question worked through, pausing before each major step.
Compare the mathematical decisions, not only the final answer.
Close the solution and redo the question from a blank page.
Attempt a similar question 24 to 48 hours later.
This attempt-and-review loop is usually faster than rereading a chapter because it exposes the exact gap: recognition, formula selection, manipulation, calculator use, or communication. RevisionDojo's Number and Algebra Questionbank provides targeted practice, while the Number and Algebra worked videos let you inspect methods step by step. Use the per-question solution where available immediately after a serious attempt, not before it.
Common mistakes that lose avoidable marks
Giving only a calculator result: Write the model, equation, or substitution that produced it.
Using rounded intermediate values: Store full calculator values and round once at the end.
Ignoring command terms: “Show that” requires a derivation that reaches the supplied result; “prove” requires a general argument.
Confusing equality with implication: Each line in a proof must follow logically from the previous one.
Forgetting restrictions: Check logarithms, denominators, convergence, and rejected roots.
Using examples as proof: Examples can disprove a universal claim through a counterexample, but cannot normally prove one.
Forcing calculator use: Some Paper 2 questions are faster and clearer algebraically.
Failing to interpret: If n=7.2 represents complete years, determine whether the context requires 7 or 8 years and explain why.
Keep an error log organized by cause rather than question number. Categories such as “wrong model,” “algebra slip,” “restriction missed,” and “insufficient working” produce clearer revision priorities.
A practical revision plan
Begin with the IB Maths AA resource hub and separate SL content from any HL extensions you study. Use Maths AA flashcards for formulas, definitions, and proof structures, but devote most revision time to written problem solving.
Complete short, focused sets before moving to mixed timed practice. Jojo AI can help explain why a step is invalid or where your written method stops earning marks, but you should always produce your own complete solution first.
Conclusion
IB Maths AA Number & Algebra questions use recurring models, even when their wording or context changes. Strong answers identify the structure, state an equation, show a valid method, observe mathematical restrictions, and present the result in the requested form.
The fastest practical route to mastery is repeated retrieval with immediate correction: attempt the problem, watch the worked method, redo it independently, and revisit a similar problem later. RevisionDojo's Number and Algebra Questionbank and worked video solutions are the most relevant tools for building that routine.
Emma holds an MMath from the University of Oxford and has taught IB Mathematics for over 20 years, including every year since Analysis & Approaches replaced the old Higher and Standard Level syllabus in 2019. Her focus is IB Mathematics: Analysis & Approaches at SL and HL, developing genuine mathematical intuition from foundational algebra through to the toughest HL topics.
