IB Mathematics Applications & Interpretation Topic Number and Algebra Questionbank (SL/HL)

IB Mathematics Applications & Interpretation Topic Number and Algebra Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) 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 $lo g 25 + lo g 4 = lo g c$ . Now consider base- $5$ logarithms: let $lo g_{5} 500 - lo g_{5} 4 = lo g_{5} d$ .

Find the value of $c$ .

[2]

Hence, or otherwise, find the value of $lo g 25 + lo g 4$ .

[2]

Find the value of $d$ .

[3]

Hence, or otherwise, find the value of $lo g_{5} 500 - lo g_{5} 4$ .

[2]

Question 2

HLPaper 1

Let $C = (- 2 1 47)$ and $D = (5 - 1 2 a)$

Find $C D$ .

[3]

Find $D^{- 1}$ .

[3]

Find $D^{2}$ .

[3]

Question 3

HLPaper 2

Let $z = x + y i$ be a complex number.

Given that $w = z + 16$ , write down the conjugate of $w$ .

[1]

Use $w \overline{w}$ to express $∣ w ∣^{2}$ in the form $x^{2} + y^{2} + a x + b$ .

[2]

Express $∣ z + 1 ∣^{2}$ in terms of $x$ and $y$ .

[2]

Given that $∣ z + 16∣ = 4∣ z + 1∣$ , find the value of $∣ z ∣$ .

[5]

Question 4

HLPaper 1

Simplify the following expressions, giving your answers in the form $a x^{n}$ where $a$ and $n$ are rational numbers and any fractions are in lowest terms.

$(\frac{2}{9} x^{\frac{1}{2}} \times \frac{1}{18} x^{\frac{- 3}{4}})^{- \frac{1}{4}}$

[2]

$\frac{( 8 x ^{- \frac{2}{3}} ) ^{\frac{2}{3}}}{( 64 x ^{- \frac{1}{3}} ) ^{\frac{1}{3}}}$

[3]

Question 5

HLPaper 2

A computer graphics program transforms a point $(x, y)$ (measured in cm) to a new point $(u, v)$ using the matrix $(k - 4 - 2 - 3 k + 1)$ , where $k \in R$ . The area scale factor of this transformation is given by the determinant of the matrix.

Calculate the determinant of $(k - 4 - 2 - 3 k + 1)$ in terms of $k$ .

[3]

Solve for the real values of $k$ for which the determinant is equal to zero.

[3]

Interpret what it means for the transformation when the determinant is zero.

[2]

For $k = 2$ , find the image of the point $(3, - 1)$ under the transformation.

[2]

For $k = 2$ , find the area of the image of the triangle with vertices $(0, 0)$ , $(1, 0)$ and $(0, 2)$ .

[2]

IB Mathematics Applications & Interpretation Number and Algebra Questionbank

Unlock all 348 questions with a free account

IB Mathematics Applications & Interpretation Number and Algebra Questionbank

IB Mathematics Applications & Interpretation (AI) Topic Number and Algebra Questionbank

Unlock all 348 questions with a free account