Math Analysis & Approaches unit guide
Number and Algebra
Sequences, logs, binomial expansion, proof, complex numbers and systems of equations.
Unit 1 is where Paper 1 is won or lost, because almost none of it can be rescued by a calculator. It is also the unit that most rewards drilling: the techniques are finite, they recur every session, and fluency with them frees up time everywhere else in the paper. Students who are slow at log laws and surd manipulation lose marks in calculus questions that have nothing to do with either.
Topics in this unit
What gets examined
- Arithmetic and geometric sequences, including sums to infinity and the condition for convergence.
- Laws of logarithms and indices, and solving equations that need them applied in exact form.
- Binomial expansion, including finding a specific term without expanding the whole thing.
- Proof by induction at HL: the base case, the assumption, and the inductive step written out properly.
- Complex numbers in Cartesian, modulus-argument and exponential form, and moving between them.
- Solving systems of linear equations, and recognising when a system has no or infinitely many solutions.
How to revise it
Write induction to a fixed template
Prove the base case. State the assumption for n = k. Prove it for n = k + 1 using that assumption. Conclude. Marks are allocated along that structure, so the structure collects them even when the algebra is untidy.
Drill log and index laws until they are reflexive
Ten minutes a day. These appear inside calculus, inside complex numbers and inside sequences, so slowness here costs marks in questions that are not about logs at all.
Use the general term for binomial questions
Questions ask for the coefficient of one term, not the expansion. Setting the power of x equal to what is wanted and solving for r is faster and far less error-prone than expanding.
Pick the right form for complex numbers
Cartesian for adding, modulus-argument for multiplying and powers. Converting first is usually quicker than forcing the wrong form through.
Where marks get lost
- Using the sum to infinity when the common ratio is not between minus one and one.
- Treating log(a + b) as log a + log b.
- Forgetting the base case, or asserting the result for n = k + 1 rather than deriving it.
- Losing the plus or minus when taking a square root, especially with complex roots.
- Giving decimals on Paper 1 where an exact value is required.
Practise this unit
Reading about a unit only goes so far. Work through real IB-style questions on it, with mark schemes.