DP Further Mathematics HL Questionbank

• Syllabus

1.8

Sub sections and their related questions

Geometric transformations represented by $2 \times 2$ matrices include general rotation, general reflection in $y = (\tan \alpha )x$ , stretches parallel to axes, shears parallel to axes, and projection onto $y = (\tan \alpha )x$.

• 15M.2.hl.TZ0.5a: By considering the points $(1,{\text{ }}0)$ and $(0,{\text{ }}1)$ determine the...
• 15M.2.hl.TZ0.5b: Determine the matrix $A$ which represents a rotation from the direction...
• 15M.2.hl.TZ0.5c: A triangle whose vertices have coordinates $(0,{\text{ }}0)$, $(3,{\text{ }}1)$ and...
• 15M.2.hl.TZ0.5d: The matrix $B = {A^{ - 1}}XA$ represents a reflection in the line $y = mx$. Find the value of...
• 18M.1.hl.TZ0.4c: Write down the 2 × 2 matrices representing T3, T4 and T5.
• 18M.1.hl.TZ0.4d.i: Find the 2 × 2 matrix representing T.
• 18M.1.hl.TZ0.4d.ii: Give a geometric description of the transformation T.

Compositions of the above transformations.

• 15M.2.hl.TZ0.5c: A triangle whose vertices have coordinates $(0,{\text{ }}0)$, $(3,{\text{ }}1)$ and...
• 15M.2.hl.TZ0.5d: The matrix $B = {A^{ - 1}}XA$ represents a reflection in the line $y = mx$. Find the value of...
• 18M.1.hl.TZ0.4c: Write down the 2 × 2 matrices representing T3, T4 and T5.
• 18M.1.hl.TZ0.4d.i: Find the 2 × 2 matrix representing T.
• 18M.1.hl.TZ0.4d.ii: Give a geometric description of the transformation T.

Geometric interpretation of determinant.

• 18M.1.hl.TZ0.4c: Write down the 2 × 2 matrices representing T3, T4 and T5.
• 18M.1.hl.TZ0.4d.i: Find the 2 × 2 matrix representing T.
• 18M.1.hl.TZ0.4d.ii: Give a geometric description of the transformation T.