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Geometry and Trigonometry

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

Coordinate Geometry in 2D and 3D

Subtopic

Coordinate Geometry in 2D and 3D under Geometry and Trigonometry for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the distance between (1,2,2)(1, 2, 2) and (1,2,3)(1, 2, 3)?

    A.

    0

    B.

    1

    C.

    2

    D.

    3

  2. 2.

    A line has the equation 3x−y=03x - y = 0. What is its gradient?

    A.

    -3

    B.

    3

    C.

    1

    D.

    0

  3. 3.

    What is the gradient of a line that passes through (0,0)(0, 0) and (5,5)(5, 5)?

    A.

    0

    B.

    5

    C.

    1

    D.

    -1

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

The Unit Circle, Radians, and Degrees

Subtopic

The Unit Circle, Radians, and Degrees under Geometry and Trigonometry for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the reference angle for θ=11π6\theta = \frac{11\pi}{6}?

    A.

    π6\frac{\pi}{6}

    B.

    π3\frac{\pi}{3}

    C.

    π4\frac{\pi}{4}

    D.

    5π6\frac{5\pi}{6}

  2. 2.

    What is the value of cos⁡(2π)\cos(2\pi)?

    A.

    00

    B.

    11

    C.

    −1-1

    D.

    undefined

  3. 3.

    Convert 30∘30^\circ to radians.

    A.

    π3\frac{\pi}{3}

    B.

    π4\frac{\pi}{4}

    C.

    π6\frac{\pi}{6}

    D.

    π12\frac{\pi}{12}

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

Trigonometric Ratios and Identities

Subtopic

Trigonometric Ratios and Identities under Geometry and Trigonometry for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Convert 300∘300^\circ to radians.

    A.

    4π3\frac{4\pi}{3}

    B.

    5π3\frac{5\pi}{3}

    C.

    7π4\frac{7\pi}{4}

    D.

    11π6\frac{11\pi}{6}

  2. 2.

    Which trigonometric ratio represents the x-coordinate of a point on the unit circle?

    A.

    sin⁡θ\sin \theta

    B.

    cos⁡θ\cos \theta

    C.

    tan⁡θ\tan \theta

    D.

    csc⁡θ\csc \theta

  3. 3.

    What is the range of the function f(x)=3sin⁡(x)f(x) = 3\sin(x)?

    A.

    [−1,1][-1, 1]

    B.

    [−3,3][-3, 3]

    C.

    [0,3][0, 3]

    D.

    (−∞,∞)(-\infty, \infty)

Download the worksheet for Geometry and Trigonometry - Trigonometric Ratios and Identities 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 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Calculate the period of the function y=sin⁡(34x)y = \sin(\frac{3}{4}x).

    A.

    3π2\frac{3\pi}{2}

    B.

    8π3\frac{8\pi}{3}

    C.

    3π4\frac{3\pi}{4}

    D.

    4π3\frac{4\pi}{3}

  2. 2.

    What is the principal axis (midline) of the function y=1−4cos⁡(x)y = 1 - 4\cos(x)?

    A.

    y=−4y = -4

    B.

    y=1y = 1

    C.

    y=0y = 0

    D.

    y=−3y = -3

  3. 3.

    What is the amplitude of the function y=sin⁡(x)2y = \frac{\sin(x)}{2}?

    A.

    2

    B.

    1

    C.

    0.5

    D.

    0

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

Solving Trigonometric Equations

Subtopic

Solving Trigonometric Equations under Geometry and Trigonometry for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Solve the equation tan⁡(x2)=1\tan(\frac{x}{2}) = 1 for 0∘≤x≤180∘0^\circ \leq x \leq 180^\circ.

    A.

    45∘45^\circ

    B.

    60∘60^\circ

    C.

    90∘90^\circ

    D.

    180∘180^\circ

  2. 2.

    Solve cos⁡(x)=−12\cos(x) = -\frac{1}{2} for 180∘≤x≤360∘180^\circ \leq x \leq 360^\circ.

    A.

    210∘210^\circ

    B.

    240∘240^\circ

    C.

    300∘300^\circ

    D.

    330∘330^\circ

  3. 3.

    Solve the equation 2sin⁡(x)−1=02\sin(x) - 1 = 0 for 0≤x≤π0 \leq x \leq \pi.

    A.

    π6,5π6\frac{\pi}{6}, \frac{5\pi}{6}

    B.

    π3,2π3\frac{\pi}{3}, \frac{2\pi}{3}

    C.

    π6,2π3\frac{\pi}{6}, \frac{2\pi}{3}

    D.

    π4,3π4\frac{\pi}{4}, \frac{3\pi}{4}

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

The Sine Rule, Cosine Rule, and Area of a Triangle

Subtopic

The Sine Rule, Cosine Rule, and Area of a Triangle under Geometry and Trigonometry for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    In triangle ABCABC, a=7a = 7, b=10b = 10, and c=12c = 12. Find the value of cos⁡B\cos B.

    A.

    0.55360.5536

    B.

    0.12500.1250

    C.

    0.44640.4464

    D.

    0.62250.6225

  2. 2.

    In triangle ABCABC, a=6a = 6, ∠A=25∘\angle A = 25^\circ, and ∠B=75∘\angle B = 75^\circ. Find side bb.

    A.

    13.7113.71

    B.

    2.622.62

    C.

    15.4415.44

    D.

    10.2110.21

  3. 3.

    Find the area of a triangle with a=20a = 20, b=25b = 25, and ∠C=37∘\angle C = 37^\circ.

    A.

    150.45150.45

    B.

    250.00250.00

    C.

    200.00200.00

    D.

    300.90300.90

Download the worksheet for Geometry and Trigonometry - The Sine Rule, Cosine Rule, and Area of a Triangle to practice offline. It includes additional chapter-level practice questions.

Introduction to Vectors

Subtopic

Introduction to Vectors under Geometry and Trigonometry for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the result of 10⋅(0.8−0.6)10 \cdot \begin{pmatrix} 0.8 \\ -0.6 \end{pmatrix}?

    A.

    (8−6)\begin{pmatrix} 8 \\ -6 \end{pmatrix}

    B.

    (80−60)\begin{pmatrix} 80 \\ -60 \end{pmatrix}

    C.

    (0.08−0.06)\begin{pmatrix} 0.08 \\ -0.06 \end{pmatrix}

    D.

    (10.89.4)\begin{pmatrix} 10.8 \\ 9.4 \end{pmatrix}

  2. 2.

    Find the distance between points (1,1,1)(1, 1, 1) and (2,2,2)(2, 2, 2).

    A.

    1

    B.

    3

    C.

    3\sqrt{3}

    D.

    1\sqrt{1}

  3. 3.

    The displacement vector BA⃗\vec{BA} is equal to:

    A.

    AB⃗\vec{AB}

    B.

    −AB⃗-\vec{AB}

    C.

    OA⃗+OB⃗\vec{OA} + \vec{OB}

    D.

    0⃗\vec{0}

Download the worksheet for Geometry and Trigonometry - Introduction to Vectors to practice offline. It includes additional chapter-level practice questions.