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SHS Core Mathematics · Year 2

Vectors and Trigonometry (Advanced) practice questions

Position vectors, vector addition/subtraction/scalar multiplication, resultant vectors via the cosine rule, inverse trigonometric ratios, and angles of elevation and depression.

29 questions in this topic: 12 recall, 8 applying skills and concepts, 8 strategic thinking and 1 extended thinking. Every one carries a written explanation.

Sample questions

5 of 29 questions in this topic. Sign up to answer them and see the explanations.

  1. Question 1Strategic thinking

    Two forces of 12 N and 16 N act on an object with an angle of 140° between them (once the vectors are aligned tail-to-head). Using the cosine rule R² = A² + B² − 2AB cos θ, the value of R² is

    • a694.16
    • b400
    • c88
    • d112
  2. Question 2Recall

    A scalar quantity is one that has

    • amagnitude only, with no direction, such as mass, time or temperature
    • bboth magnitude and direction, such as force or velocity
    • cdirection only, with no magnitude
    • dneither magnitude nor direction
  3. Question 3Recall

    The inverse trigonometric ratio cotangent is defined as

    • acotθ = 1/tanθ = Adjacent/Opposite
    • bcotθ = 1/sinθ
    • ccotθ = tanθ
    • dcotθ = 1/cosθ
  4. Question 4Recall

    The inverse trigonometric ratio secant is defined as

    • asecθ = 1/cosθ = Hypotenuse/Adjacent
    • bsecθ = 1/sinθ
    • csecθ = cosθ
    • dsecθ = 1/tanθ
  5. Question 5Skills & concepts

    The cosine rule is used to find the magnitude of a resultant vector, rather than the sine rule, when

    • athe magnitudes of both original vectors and the angle between them are known
    • bonly one vector's magnitude is known
    • cnone of the angles are known
    • dthe vectors are perpendicular only

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