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.