Errors in IB Maths AA Number & Algebra tend to cluster around sequence notation, logarithm restrictions, financial models, binomial terms, proof, and premature rounding. These are rarely isolated arithmetic slips. They usually reveal a missing step in the student's method, which is why reviewing a complete worked solution is more effective than simply checking the final answer.
This guide explains the main IB Maths AA Number & Algebra common mistakes, shows how to correct each one, and gives you a practical process for learning from worked video solutions. The principles apply to both SL and HL, with additional HL-specific issues identified where necessary.
What Number and Algebra involves in IB Maths AA
Number and algebra is one of the five official syllabus topics in Mathematics: Analysis and Approaches. It includes standard form, arithmetic and geometric sequences, financial applications, logarithms, exponent laws, proof, infinite geometric series, and the binomial theorem. At HL, the topic extends to permutations and combinations, partial fractions, complex numbers, proof by induction and contradiction, and systems of linear equations.
The official IB subject brief assigns 19 recommended teaching hours at SL and 39 at HL to Number and Algebra. These figures are teaching recommendations, not guaranteed examination weightings. Number and Algebra can also appear inside questions involving functions, calculus, probability, or trigonometry.
Paper 1 does not permit technology, while Paper 2 requires access to a graphic display calculator. HL students also take the technology-required Paper 3. A clean formula booklet is provided for the examination papers, but the official guide makes clear that students must still select and apply formulas appropriately.
IB Maths AA Number & Algebra common mistakes and fixes
Common mistake
Why it loses marks
Reliable fix
Using n instead of n - 1 in a sequence formula
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The first term becomes incorrectly shifted
Write out the first three indexed terms before substituting
Applying the infinite-series formula without checking convergence
The formula is invalid when `
r
Combining logarithms incorrectly
Logarithm laws apply to products, quotients, and powers in specific ways
Write the relevant law before using it
Ignoring logarithm domain restrictions
Algebraic solutions may make a logarithm undefined
Check that every logarithm argument is positive
Mixing annual and periodic interest rates
The rate and number of periods no longer match
Convert both rate and time to the same compounding period
Selecting the wrong binomial term
The coefficient or power is taken from the wrong value of r
Write the general term first and solve for the required power
Giving examples instead of a proof
Examples support a claim but do not establish it generally
Begin from a general integer representation
Rounding during intermediate steps
Small errors accumulate and may change the final answer
Store full calculator values and round only at the end
Mistake 1: Confusing sequence type, term number, and sum
Students often use an arithmetic formula for a geometric sequence, confuse u_n with S_n, or write nd instead of (n - 1)d. Remember that u_n is one term, while S_n is the sum of the first n terms.
For an arithmetic sequence, test for a constant difference. For a geometric sequence, test for a constant ratio. Before using a formula, label u_1, d or r, n, and the quantity being requested.
A worked video solution helps because it shows the decision that comes before substitution. Pause the video after the sequence is identified, complete the setup yourself, and then compare your notation with the model.
Mistake 2: Using an infinite geometric sum when it does not exist
The formula S_∞ = u_1/(1-r) is valid only when |r| < 1. Students sometimes check only whether r < 1, overlooking ratios such as r = -2, or apply the formula automatically whenever the word “infinite” appears.
Write the convergence condition before substituting. If |r| ≥ 1, the terms do not approach zero and the series cannot have a finite sum. In a video walkthrough, pay attention to where the condition is checked, rather than skipping directly to the calculation.
Mistake 3: Misusing exponent and logarithm laws
A particularly damaging misconception is treating log(a + b) as log a + log b. There is no logarithm law for splitting a sum. The valid product law is log(ab) = log a + log b, while division produces subtraction and powers become multipliers.
Domain checks are equally important. In a real logarithmic expression, every argument must be positive, so solving an equation is not the final step. Substitute each candidate into the original equation and reject any value that makes an argument zero or negative.
When reviewing a worked solution, copy the line where the logarithm law is stated and identify why it applies. Then cover the next line and reproduce the conversion between logarithmic and exponential form independently.
Mistake 4: Building financial models with inconsistent periods
Compound-interest and depreciation questions require the rate, number of periods, and compounding frequency to agree. If interest is compounded monthly, an annual nominal rate generally needs to be converted to a monthly rate and the number of years converted to months, according to the model stated in the question.
Do not assume every percentage represents growth. Depreciation uses a multiplier below one, such as 1 - r, while appreciation uses 1 + r. A strong worked solution defines the initial amount, periodic multiplier, and number of periods before entering values into a calculator.
Mistake 5: Guessing terms in a binomial expansion
In (a + b)^n, students frequently choose the wrong binomial coefficient or reverse the exponents. The powers of the two components must change systematically, and their exponents add to n in every term when n is a non-negative integer.
Write the general term using the convention taught in your course, then solve an equation for the required power. Only after finding the correct term number should you simplify its coefficient. At HL, negative or fractional indices introduce an infinite expansion with a stated range of validity, so finite-expansion habits cannot be transferred without checking the conditions.
Mistake 6: Treating evidence as proof
Checking several values does not prove a statement for every integer. For parity proofs, write an even integer as 2k and an odd integer as 2k + 1, then manipulate the expression into the required form.
For divisibility, aim to factor the result into the divisor multiplied by an integer expression. At HL, induction requires a valid base case, a clearly stated inductive hypothesis, an inductive step, and a conclusion. Contradiction and counterexample also have specific logical purposes, so the proof method must match the command term.
The IB guide's command-term glossary distinguishes commands such as show, verify, find, and hence. In particular, “hence” signals that preceding work should be used rather than restarted without reason.
Mistake 7: Losing exactness or rounding too early
According to the official specimen papers, unless a question states otherwise, numerical answers should be given exactly or correct to three significant figures. An exact answer may contain fractions, radicals, logarithms, or constants such as π.
Do not replace an exact value with a short decimal on Paper 1. On calculator papers, retain full internal precision and round the final answer only. Also distinguish significant figures from decimal places: 0.004567 to three significant figures is 0.00457, not 0.005.
Mistake 8: HL errors with complex numbers and partial fractions
In complex-number questions, common errors include placing a point incorrectly on an Argand diagram, using the wrong quadrant for the argument, and forgetting that an argument is defined up to multiples of 2π. When finding roots, check both the modulus and the complete set of arguments so that no roots are omitted.
For partial fractions, the denominator structure determines the numerator form. A repeated linear factor needs a separate term for every power, while an irreducible quadratic requires a linear numerator. Worked videos are particularly useful here because they expose setup errors that may be hidden by later algebra.
How to review worked video solutions effectively
Watching mathematics passively creates familiarity, not reliable recall. Use the RevisionDojo Number and Algebra videos and available per-question worked solutions as an active correction tool.
Follow this five-step cycle:
Attempt the question without help. Record every line, even if you become stuck.
Classify the error. Decide whether it involved knowledge, setup, algebra, calculator use, communication, or accuracy.
Watch only until your first incorrect decision. Identify what the solver noticed that you missed.
Close the solution and restart. Reproduce the method without copying it.
Complete a related question within 48 hours. This tests whether the method transferred to a new context.
The aim is not to memorize one answer. It is to recognize the cues that determine the method, such as “sum to infinity,” “coefficient of,” “hence,” or “compounded quarterly.”
For targeted practice, use the Number and Algebra Questionbank after reviewing a video. Jojo AI can help explain where your written method departs from the expected reasoning, but you should still write complete working rather than relying on mental calculation.
A practical Number and Algebra revision routine
Start from the Number and Algebra topic hub and divide your errors into subtopics. Do not label a question merely “careless”; name the exact action that failed, such as “used finite sum instead of infinite sum” or “accepted an invalid logarithmic root.”
A productive weekly cycle is:
Day 1: Review one concept and one worked video.
Day 2: Complete four untimed questions with full working.
Day 3: Correct errors and create short rule-based flashcards.
Day 4: Complete a timed Paper 1 set without a calculator.
Day 5: Complete a calculator-based set and check rounding.
Day 7: Reattempt the original errors without notes.
Students needing a structured syllabus check can use the Number and Algebra bootcamp exercises. Once individual skills are secure, move from the IB Maths AA resource hub to mixed-topic questions, since examination problems often connect algebra with other areas.
The broader RevisionDojo Questionbank can be used to alternate targeted drills with unfamiliar mixed practice. Closer to the examination, apply the same error-review process to timed papers, following the principles in RevisionDojo's IB Maths mock-exam guide.
Conclusion
Most Number and Algebra marks are lost through repeatable process errors: incorrect indexing, unchecked conditions, invalid logarithm manipulation, inconsistent financial periods, weak binomial setup, incomplete proof, and premature rounding. The most effective correction is to compare your first wrong line with a complete worked method, reproduce the solution independently, and then test the same idea on a fresh question.
RevisionDojo's Number and Algebra videos, per-question worked solutions where available, Questionbank, and Jojo AI can support this cycle. Begin with one recurring mistake, study the corresponding video method, and complete a short targeted set before moving to full timed papers.
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.
