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Geometry and Trigonometry

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

The Unit Circle and Radian Measure

Subtopic

The Unit Circle and Radian Measure under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the exact value of cos⁡(5π6)\cos\left(\frac{5\pi}{6}\right)?

    A.

    32\frac{\sqrt{3}}{2}

    B.

    −32-\frac{\sqrt{3}}{2}

    C.

    12\frac{1}{2}

    D.

    −12-\frac{1}{2}

  2. 2.

    A sector of a circle with radius 44 cm has an area of 88 cm2^2. What is the central angle in radians?

    A.

    0.50.5

    B.

    11

    C.

    22

    D.

    44

  3. 3.

    What is the exact value of sin⁡(π4)\sin\left(\frac{\pi}{4}\right)?

    A.

    12\frac{1}{2}

    B.

    22\frac{\sqrt{2}}{2}

    C.

    32\frac{\sqrt{3}}{2}

    D.

    11

Download the worksheet for Geometry and Trigonometry - The Unit Circle and Radian Measure to practice offline. It includes additional chapter-level practice questions.

Trigonometric Identities and Equations

Subtopic

Trigonometric Identities and Equations under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Which of the following is equivalent to csc⁡2(x)−cot⁡2(x)\csc^2(x) - \cot^2(x)?

    A.

    0

    B.

    1

    C.

    sin⁡2(x)\sin^2(x)

    D.

    tan⁡2(x)\tan^2(x)

  2. 2.

    What is the value of sin⁡(90∘)\sin(90^\circ)?

    A.

    0

    B.

    0.5

    C.

    1

    D.

    3\sqrt{3}

  3. 3.

    Solve tan⁡(x)=3\tan(x) = \sqrt{3} for 0≤x<π0 \le x < \pi.

    A.

    x=π6x = \frac{\pi}{6}

    B.

    x=π4x = \frac{\pi}{4}

    C.

    x=π3x = \frac{\pi}{3}

    D.

    x=2π3x = \frac{2\pi}{3}

Download the worksheet for Geometry and Trigonometry - Trigonometric Identities and Equations to practice offline. It includes additional chapter-level practice questions.

Graphs of Trigonometric Functions

Subtopic

Graphs of Trigonometric Functions under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the period of the function f(x)=sin⁡(2π5x)f(x) = \sin(\frac{2\pi}{5}x)?

    A.

    5

    B.

    25\frac{2}{5}

    C.

    52\frac{5}{2}

    D.

    2π2\pi

  2. 2.

    What is the midline of the function y=0.2sin⁡(x)−0.2y = 0.2\sin(x) - 0.2?

    A.

    y=0.2y = 0.2

    B.

    y=0y = 0

    C.

    y=−0.2y = -0.2

    D.

    y=−0.4y = -0.4

  3. 3.

    Find the amplitude of the function y=−cos⁡(x)y = -\cos(x).

    A.

    -1

    B.

    1

    C.

    0

    D.

    π\pi

Download the worksheet for Geometry and Trigonometry - Graphs of Trigonometric Functions to practice offline. It includes additional chapter-level practice questions.

Inverse Trigonometric Functions

Subtopic

Inverse Trigonometric Functions under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Evaluate sin⁡(arcsin⁡(0.2))\sin(\arcsin(0.2)).

    A.

    0.20.2

    B.

    −0.2-0.2

    C.

    arcsin⁡(0.2)\arcsin(0.2)

    D.

    0.80.8

  2. 2.

    Evaluate tan⁡(arctan⁡(−5))\tan(\arctan(-5)).

    A.

    55

    B.

    −15-\frac{1}{5}

    C.

    −5-5

    D.

    Undefined

  3. 3.

    Evaluate arccos⁡(cos⁡(−π4))\arccos\left(\cos\left(-\frac{\pi}{4}\right)\right).

    A.

    π4\frac{\pi}{4}

    B.

    −π4-\frac{\pi}{4}

    C.

    7π4\frac{7\pi}{4}

    D.

    3π4\frac{3\pi}{4}

Download the worksheet for Geometry and Trigonometry - Inverse Trigonometric Functions to practice offline. It includes additional chapter-level practice questions.

Applications of Trigonometry (Sine and Cosine Rules)

Subtopic

Applications of Trigonometry (Sine and Cosine Rules) under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the area of an equilateral triangle with side length 55?

    A.

    12.512.5

    B.

    6.2536.25\sqrt{3}

    C.

    12.5312.5\sqrt{3}

    D.

    25325\sqrt{3}

  2. 2.

    In △ABC\triangle ABC, a=20a = 20, ∠A=150∘\angle A = 150^\circ, and ∠B=10∘\angle B = 10^\circ. Which expression represents the length of side bb?

    A.

    20sin⁡10∘20 \sin 10^\circ

    B.

    20sin⁡10∘sin⁡150∘\frac{20 \sin 10^\circ}{\sin 150^\circ}

    C.

    20sin⁡150∘sin⁡10∘20 \sin 150^\circ \sin 10^\circ

    D.

    sin⁡150∘20sin⁡10∘\frac{\sin 150^\circ}{20 \sin 10^\circ}

  3. 3.

    In △ABC\triangle ABC, a=7,b=5,c=3a = 7, b = 5, c = 3. Find the value of cos⁡A\cos A.

    A.

    0.50.5

    B.

    −0.5-0.5

    C.

    0.250.25

    D.

    −0.25-0.25

Download the worksheet for Geometry and Trigonometry - Applications of Trigonometry (Sine and Cosine Rules) to practice offline. It includes additional chapter-level practice questions.

Vectors in 2D and 3D

Subtopic

Vectors in 2D and 3D under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The scalar product of two vectors is positive. What can be said about the angle θ\theta between them?

    A.

    θ\theta is obtuse

    B.

    θ\theta is acute

    C.

    θ=90∘\theta = 90^\circ

    D.

    θ=180∘\theta = 180^\circ

  2. 2.

    Identify the point that lies on the line r⃗=(111)+t(20−1)\vec{r} = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} + t\begin{pmatrix} 2 \\ 0 \\ -1 \end{pmatrix} when t=2t=2.

    A.

    (3,1,0)(3, 1, 0)

    B.

    (5,1,−1)(5, 1, -1)

    C.

    (5,1,1)(5, 1, 1)

    D.

    (2,0,−1)(2, 0, -1)

  3. 3.

    If v⃗=(122)\vec{v} = \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}, what is the unit vector in the direction of v⃗\vec{v}?

    A.

    13(122)\frac{1}{3}\begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}

    B.

    19(122)\frac{1}{9}\begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}

    C.

    (111)\begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}

    D.

    15(122)\frac{1}{5}\begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}

Download the worksheet for Geometry and Trigonometry - Vectors in 2D and 3D to practice offline. It includes additional chapter-level practice questions.

Scalar (Dot) and Vector (Cross) Products

Subtopic

Scalar (Dot) and Vector (Cross) Products under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Calculate the vector product (3i)×(2j)(3\mathbf{i}) \times (2\mathbf{j}).

    A.

    6k6\mathbf{k}

    B.

    −6k-6\mathbf{k}

    C.

    6

    D.

    0\mathbf{0}

  2. 2.

    If a\mathbf{a} and b\mathbf{b} are unit vectors and the angle between them is 60∘60^\circ, find a⋅b\mathbf{a} \cdot \mathbf{b}.

    A.

    0.5

    B.

    1

    C.

    32\frac{\sqrt{3}}{2}

    D.

    0

  3. 3.

    Evaluate (i+j)⋅k(\mathbf{i} + \mathbf{j}) \cdot \mathbf{k}.

    A.

    1

    B.

    2

    C.

    0

    D.

    -1

Download the worksheet for Geometry and Trigonometry - Scalar (Dot) and Vector (Cross) Products to practice offline. It includes additional chapter-level practice questions.

Vector Equations of Lines and Planes

Subtopic

Vector Equations of Lines and Planes under Geometry and Trigonometry for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the result of the dot product (123)⋅(−210)\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} \cdot \begin{pmatrix} -2 \\ 1 \\ 0 \end{pmatrix}?

    A.

    0

    B.

    1

    C.

    -2

    D.

    4

  2. 2.

    Which of these describes a plane containing the yy-axis?

    A.

    x+z=0x + z = 0

    B.

    y=0y = 0

    C.

    y=5y = 5

    D.

    x+y+z=0x + y + z = 0

  3. 3.

    The midpoint of the segment between (0,0,0)(0,0,0) and (4,8,12)(4,8,12) is a point on which line?

    A.

    r=t(123)\mathbf{r} = t \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}

    B.

    r=t(4812)\mathbf{r} = t \begin{pmatrix} 4 \\ 8 \\ 12 \end{pmatrix}

    C.

    r=(246)+t(010)\mathbf{r} = \begin{pmatrix} 2 \\ 4 \\ 6 \end{pmatrix} + t \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}

    D.

    All of the above

Download the worksheet for Geometry and Trigonometry - Vector Equations of Lines and Planes to practice offline. It includes additional chapter-level practice questions.

Geometry and Trigonometry - Grade 12 Maths (IB) | Krit.club