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Geometry and Trigonometry

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

Properties of 2D and 3D shapes

Subtopic

Properties of 2D and 3D shapes under Geometry and Trigonometry for Grade 9 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    In a scalene triangle, how many sides are equal in length?

    A.

    00

    B.

    11

    C.

    22

    D.

    33

  2. 2.

    What is the length of the arc of a semi-circle with a radius of 7 cm7\text{ cm}? (Use π≈227\pi \approx \frac{22}{7})

    A.

    11 cm11\text{ cm}

    B.

    22 cm22\text{ cm}

    C.

    44 cm44\text{ cm}

    D.

    154 cm154\text{ cm}

  3. 3.

    Find the volume of a square-based pyramid where the base side is 3 cm3\text{ cm} and the height is 4 cm4\text{ cm}. (Use V=13BhV = \frac{1}{3}Bh)

    A.

    36 cm336\text{ cm}^3

    B.

    12 cm312\text{ cm}^3

    C.

    9 cm39\text{ cm}^3

    D.

    4 cm34\text{ cm}^3

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

Pythagorean theorem and its applications

Subtopic

Pythagorean theorem and its applications under Geometry and Trigonometry for Grade 9 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    In a right-angled triangle, the legs are 60 mm60\text{ mm} and 80 mm80\text{ mm}. What is the length of the hypotenuse?

    A.

    140 mm140\text{ mm}

    B.

    100 mm100\text{ mm}

    C.

    120 mm120\text{ mm}

    D.

    90 mm90\text{ mm}

  2. 2.

    A rhombus has diagonals of 12 cm12\text{ cm} and 16 cm16\text{ cm}. What is the length of its side?

    A.

    10 cm10\text{ cm}

    B.

    20 cm20\text{ cm}

    C.

    14 cm14\text{ cm}

    D.

    28 cm28\text{ cm}

  3. 3.

    The hypotenuse of a right-angled triangle is 1.7 m1.7\text{ m} and one leg is 0.8 m0.8\text{ m}. Find the other leg.

    A.

    1.5 m1.5\text{ m}

    B.

    0.9 m0.9\text{ m}

    C.

    2.5 m2.5\text{ m}

    D.

    1.2 m1.2\text{ m}

Download the worksheet for Geometry and Trigonometry - Pythagorean theorem and its applications to practice offline. It includes additional chapter-level practice questions.

Coordinate geometry: distance, midpoint, and gradient of a line

Subtopic

Coordinate geometry: distance, midpoint, and gradient of a line under Geometry and Trigonometry for Grade 9 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the distance between the origin (0,0)(0, 0) and the point Z(1,1)Z(1, 1)?

    A.

    11

    B.

    22

    C.

    sqrt2\\sqrt{2}

    D.

    sqrt1\\sqrt{1}

  2. 2.

    Calculate the gradient of the line passing through P(1,4)P(1, 4) and Q(3,0)Q(3, 0).

    A.

    22

    B.

    −2-2

    C.

    0.50.5

    D.

    −0.5-0.5

  3. 3.

    Find the midpoint of the segment with endpoints K(1,7)K(1, 7) and L(5,7)L(5, 7).

    A.

    (3,14)(3, 14)

    B.

    (3,7)(3, 7)

    C.

    (6,7)(6, 7)

    D.

    (3,0)(3, 0)

Download the worksheet for Geometry and Trigonometry - Coordinate geometry: distance, midpoint, and gradient of a line to practice offline. It includes additional chapter-level practice questions.

Right-angled triangle trigonometry (SOH CAH TOA)

Subtopic

Right-angled triangle trigonometry (SOH CAH TOA) under Geometry and Trigonometry for Grade 9 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    In ΔXYZ\Delta XYZ where ∠X=90∘\angle X = 90^\circ, XY=12XY = 12 and YZ=13YZ = 13. Find the value of sin⁡(Z)\sin(Z).

    A.

    1213\frac{12}{13}

    B.

    513\frac{5}{13}

    C.

    125\frac{12}{5}

    D.

    512\frac{5}{12}

  2. 2.

    Find the length of the adjacent side if the hypotenuse is 10 units10 \text{ units} and the angle is 60∘60^\circ.

    A.

    5 units5 \text{ units}

    B.

    8.66 units8.66 \text{ units}

    C.

    5.77 units5.77 \text{ units}

    D.

    7.07 units7.07 \text{ units}

  3. 3.

    In a right-angled triangle, if the opposite side is exactly twice the length of the adjacent side, what is the value of tan⁡(θ)\tan(\theta)?

    A.

    2

    B.

    0.5

    C.

    2\sqrt{2}

    D.

    Undefined

Download the worksheet for Geometry and Trigonometry - Right-angled triangle trigonometry (SOH CAH TOA) to practice offline. It includes additional chapter-level practice questions.

Surface area and volume of prisms, cylinders, pyramids, cones, and spheres

Subtopic

Surface area and volume of prisms, cylinders, pyramids, cones, and spheres under Geometry and Trigonometry for Grade 9 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the total surface area of a rectangular prism with length 4 cm4 \text{ cm}, width 5 cm5 \text{ cm}, and height 6 cm6 \text{ cm}.

    A.

    120 cm2120 \text{ cm}^2

    B.

    74 cm274 \text{ cm}^2

    C.

    148 cm2148 \text{ cm}^2

    D.

    150 cm2150 \text{ cm}^2

  2. 2.

    Calculate the volume of a sphere with a radius of 1.5 cm1.5 \text{ cm} in terms of π\pi.

    A.

    4.5π cm34.5\pi \text{ cm}^3

    B.

    3π cm33\pi \text{ cm}^3

    C.

    2.25π cm32.25\pi \text{ cm}^3

    D.

    9π cm39\pi \text{ cm}^3

  3. 3.

    Find the volume of a cylinder with radius 4 cm4 \text{ cm} and height 3 cm3 \text{ cm}, in terms of π\pi.

    A.

    12π cm312\pi \text{ cm}^3

    B.

    48π cm348\pi \text{ cm}^3

    C.

    36π cm336\pi \text{ cm}^3

    D.

    16π cm316\pi \text{ cm}^3

Download the worksheet for Geometry and Trigonometry - Surface area and volume of prisms, cylinders, pyramids, cones, and spheres to practice offline. It includes additional chapter-level practice questions.

Geometric transformations: translation, reflection, rotation, and enlargement

Subtopic

Geometric transformations: translation, reflection, rotation, and enlargement under Geometry and Trigonometry for Grade 9 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the scale factor of an enlargement centered at the origin that maps point (2,2)(2, 2) to (8,8)(8, 8)?

    A.

    k=2k = 2

    B.

    k=6k = 6

    C.

    k=10k = 10

    D.

    k=4k = 4

  2. 2.

    Point S(1,4)S(1, 4) is reflected in the line y=xy = x. What are the coordinates of the image S′S'?

    A.

    (−1,−4)(-1, -4)

    B.

    (−4,−1)(-4, -1)

    C.

    (4,1)(4, 1)

    D.

    (1,−4)(1, -4)

  3. 3.

    Point R(5,5)R(5, 5) is rotated 90∘90^\circ clockwise about the origin. What are the coordinates of the image R′R'?

    A.

    (−5,5)(-5, 5)

    B.

    (5,−5)(5, -5)

    C.

    (−5,−5)(-5, -5)

    D.

    (0,0)(0, 0)

Download the worksheet for Geometry and Trigonometry - Geometric transformations: translation, reflection, rotation, and enlargement to practice offline. It includes additional chapter-level practice questions.

Geometry and Trigonometry - Grade 9 Maths (IB) | Krit.club