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Vectors and Transformations

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Vector Addition, Subtraction, and Scaling

Subtopic

Vector Addition, Subtraction, and Scaling under Vectors and Transformations for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the result of XY⃗+YX⃗\vec{XY} + \vec{YX}.

    A.

    2XY⃗2\vec{XY}

    B.

    0\mathbf{0}

    C.

    11

    D.

    2YX⃗2\vec{YX}

  2. 2.

    Simplify 10i−(2i+j)10\mathbf{i} - (2\mathbf{i} + \mathbf{j}).

    A.

    8i+j8\mathbf{i} + \mathbf{j}

    B.

    12i+j12\mathbf{i} + \mathbf{j}

    C.

    8i−j8\mathbf{i} - \mathbf{j}

    D.

    12i−j12\mathbf{i} - \mathbf{j}

  3. 3.

    Scale the vector (−5−10)\begin{pmatrix} -5 \\ -10 \end{pmatrix} by the factor −15-\frac{1}{5}.

    A.

    (12)\begin{pmatrix} 1 \\ 2 \end{pmatrix}

    B.

    (−1−2)\begin{pmatrix} -1 \\ -2 \end{pmatrix}

    C.

    (2550)\begin{pmatrix} 25 \\ 50 \end{pmatrix}

    D.

    (1−2)\begin{pmatrix} 1 \\ -2 \end{pmatrix}

Download the worksheet for Vectors and Transformations - Vector Addition, Subtraction, and Scaling to practice offline. It includes additional chapter-level practice questions.

Magnitude of a Vector

Subtopic

Magnitude of a Vector under Vectors and Transformations for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Determine the magnitude of the vector z=11i+60j\mathbf{z} = 11\mathbf{i} + 60\mathbf{j}.

    A.

    71

    B.

    61

    C.

    49

    D.

    121

  2. 2.

    Calculate the magnitude of w=(−12−35)\mathbf{w} = \begin{pmatrix} -12 \\ -35 \end{pmatrix}.

    A.

    47

    B.

    37

    C.

    23

    D.

    1369

  3. 3.

    Find the magnitude of the vector MN⃗\vec{MN} where M(−1,−1)M(-1, -1) and N(3,2)N(3, 2).

    A.

    7

    B.

    5

    C.

    7\sqrt{7}

    D.

    25

Download the worksheet for Vectors and Transformations - Magnitude of a Vector to practice offline. It includes additional chapter-level practice questions.

Translations, Rotations, and Reflections

Subtopic

Translations, Rotations, and Reflections under Vectors and Transformations for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Point (4,0)(4, 0) is rotated 90∘90^\circ clockwise about the origin. The image is:

    A.

    (0, 4)

    B.

    (0, -4)

    C.

    (-4, 0)

    D.

    (4, 4)

  2. 2.

    Calculate the magnitude of the vector (13)\binom{1}{\sqrt{3}}.

    A.

    2

    B.

    4

    C.

    1.73

    D.

    1

  3. 3.

    What vector represents the translation from (−2,−2)(-2, -2) to (2,2)(2, 2)?

    A.

    (00)\binom{0}{0}

    B.

    (44)\binom{4}{4}

    C.

    (−4−4)\binom{-4}{-4}

    D.

    (22)\binom{2}{2}

Download the worksheet for Vectors and Transformations - Translations, Rotations, and Reflections to practice offline. It includes additional chapter-level practice questions.

Enlargements and Shear

Subtopic

Enlargements and Shear under Vectors and Transformations for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If a shear transformation is given by the matrix (1−301)\begin{pmatrix} 1 & -3 \\ 0 & 1 \end{pmatrix}, what is the shear factor?

    A.

    33

    B.

    −3-3

    C.

    11

    D.

    00

  2. 2.

    An enlargement with center (0,0)(0,0) and scale factor kk maps (1,0)(1, 0) to:

    A.

    (k,0)(k, 0)

    B.

    (0,k)(0, k)

    C.

    (k,k)(k, k)

    D.

    (1,k)(1, k)

  3. 3.

    A shear with xx-axis invariant maps (2,1)(2, 1) to (5,1)(5, 1). What is the image of (2,2)(2, 2) under the same shear?

    A.

    (5,2)(5, 2)

    B.

    (8,2)(8, 2)

    C.

    (10,2)(10, 2)

    D.

    (4,2)(4, 2)

Download the worksheet for Vectors and Transformations - Enlargements and Shear to practice offline. It includes additional chapter-level practice questions.

Vectors and Transformations - Grade 12 Maths (IGCSE) | Krit.club