IB Mathematics Applications & Interpretation Topic AHL 1.14—introduction to Matrices Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 1.14—introduction to Matrices Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 1.14—introduction to Matrices with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 1.14—introduction to Matrices and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

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 2

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]

Question 3

HLPaper 1

If $A = (2 p - 4 p 3 p)$ and $det (A) = 14$ , find the possible values of $p$ .

[7]

Question 4

HLPaper 1

Determine the condition on $u$ and $v$ such that $T S = S T$ .

[4]

Given the determinant of $T$ is $18$ , calculate the value of $u$ .

[2]

Find the inverse matrix $T^{- 1}$ for the value of u determined above.

[1]

Question 5

HLPaper 1

Given the square matrices $P = (2 - 3 14), Q = (51 - 2 3)$ .

Determine the product $P Q$ .

[2]

Evaluate the determinant $det (P Q)$ .

[2]

Compute the expression $Q (Q^{- 1} P + 4 Q^{- 1}) Q$ .

[3]

IB Mathematics Applications & Interpretation AHL 1.14—introduction to Matrices Questionbank

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IB Mathematics Applications & Interpretation AHL 1.14—introduction to Matrices Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 1.14—introduction to Matrices Questionbank

Unlock all 79 questions with a free account