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IB Mathematics Analysis and Approaches Number and Algebra Questionbank

IB Mathematics Analysis and Approaches Topic Number and Algebra Questionbank (SL/HL) | RevisionDojo

IB Mathematics Analysis and Approaches (AA) Topic Number and Algebra Questionbank

Practice IB Mathematics Analysis and Approaches (AA) Topic Number and Algebra with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for Number and Algebra and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

Paper

Level

Question 1

HLPaper 1

Let $f (x) = \frac{5 x + 2}{( x + 1 ) ( x ^{2} + 4 )}$ .

1.

Express $f (x)$ in the form $\frac{A}{x+1} + \frac{Bx+C}{x^2+4}$ .

[4]

Question 2

HLPaper 1

The complex number $z$ is defined by $z = \frac{4 - 4 i}{1 + i}$ .

1.

Find an expression for $z$ in the form $r e^{i θ}$ , where $r > 0$ and $- π < θ \leq π$ .

[5]

2.

Find the two square roots of $z$ , giving your answers in the form $r e^{i θ}$ , where $r > 0$ and $- π < θ \leq π$ .

[3]

Question 3

SL & HLPaper 1

1.

Prove that for any real number $x$ , $x (x + 2) - (x + 1)^{2} \equiv - 1$ .

[3]

Question 4

HLPaper 1

The complex number $z$ is given in Euler form as $z = 4 e^{i \frac{π}{3}}$ .

1.

Express $z$ in the form $x + i y$ , where $x$ and $y$ are real.

[3]

Question 5

HLPaper 1

1.

Given expression $n^{3} + (n + 1)^{3} + (n + 2)^{3}$ , prove by induction that the expression is divisible by $9$ for all positive integers $n$ .

[5]

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SL 1.1—Using standard form

SL 1.2—Arithmetic sequences and series

SL 1.3—Geometric sequences and series

SL 1.4—Financial apps – compound interest, annual depreciation

SL 1.5—Intro to logs

SL 1.6—Simple proof

SL 1.7—Laws of exponents and logs

SL 1.8—Sum of infinite geo sequence

SL 1.9—Binomial theorem where n is an integer

AHL 1.10—Perms and combs, binomial with negative and fractional indices

AHL 1.11—Partial fractions

AHL 1.12—Complex numbers – Cartesian form and Argand diag

AHL 1.13—Polar and Euler form

AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers

AHL 1.15—Proof by induction, contradiction, counterexamples

AHL 1.16—Solution of systems of linear equations