RevisionDojo

Number and Algebra - IB Questionbank | RevisionDojo

Practice Number and Algebra with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SL & HLPaper 1

Find the $7^{th}$ term of the geometric progression $100, 50, 25, \dots$

[3]

Question 2

SL & HLPaper 1

Find the non-zero values of $a$ and $b$ for which $(2x - a)^3 = 8x^3 - bx^2 + \frac{3}{2}bx - a^3$ .

[7]

Question 3

SL & HLPaper 1

The sum of the first $n$ terms of a geometric progression is given by the formula $S_n = 2^{n+1}-2$ , for $n \ge 1$ .

Find the first term of the progression.

[2]

Find the common ratio of the progression.

[3]

Find the $5^{th}$ term of the progression.

[2]

Question 4

SL & HLPaper 1

Simplify the following, leaving your answers in the form $a^k$ :

$27^{\frac{1}{3}} \times 9^{\frac{1}{2}}$

[3]

$\frac{125^{\frac{2}{3}}}{5^{\frac{1}{2}}}$

[3]

Question 5

HLPaper 1

The equation $z^3 - 3z^2 + 7z - 5 = 0$ has one real root and two complex roots.

Verify that $1-2i$ is one of the complex roots.

[3]

Write down the other complex root of the equation.

[1]

Describe how to sketch an Argand diagram showing the point representing the complex number $1-2i$ and the set of points representing the complex numbers $z$ which satisfy $|z-(3+3i)| = |z-i|$ . Your description should include the coordinates of the points and properties of the locus.

[4]

Question 6

SL & HLPaper 1

Find the coefficient of $x^4$ in the expansion of $(1 + 3x)^7$ .

[3]

Question 7

HLPaper 1

Let $f(x) = \frac{5x^2 - 14x + 13}{(x-1)(x-3)^2}$ .

Express $f(x)$ in partial fractions.

[5]

Question 8

HLPaper 1

Solve the following simultaneous equations:

$2x + y = 7 \\ 3x - y = 3$

[5]

Question 9

HLPaper 1

Solve the following simultaneous equations:

$2x + 3y - z = 15 \\ x - 2y + 4z = 80 \\ 3x + y + 2z = 75$

[6]

Question 10

HLPaper 1

Disprove the following statement by providing a counterexample:

"For any integers $a$ , $b$ , and $c$ , if $a$ divides $c$ and $b$ divides $c$ , then $ab$ divides $c$ ."

[3]

Number and Algebra Questionbank