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

IB
Number and Algebra

IB Mathematics Analysis and Approaches Number and Algebra Questionbank

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