SHS Core Mathematics · Year 1

Vectors and Trigonometry practice questions

Representing vectors geometrically and algebraically, and the three basic trigonometric ratios (sine, cosine, tangent) of acute angles including the special angles 30°, 45° and 60°.

25 questions in this topic: 10 recall, 5 applying skills and concepts, 9 strategic thinking and 1 extended thinking. Every one carries a written explanation.

Sample questions

5 of 25 questions in this topic. Sign up to answer them and see the explanations.

Question 1Strategic thinking
The vector u has an initial point at (−2, 1) and an endpoint at (4, −2). Its components are (4−(−2), −2−1) = (6, −3), so its length is
- a3√5 units
- b6 units
- c9 units
- d3 units
Question 2Recall
Two vectors are said to be equal when they have
- athe same magnitude and the same direction
- bthe same magnitude only, regardless of direction
- cthe same direction only, regardless of magnitude
- ddifferent magnitudes but the same starting point
Question 3Skills & concepts
A zero vector is unusual among vectors because
- ait has no defined direction, since it does not point anywhere — it is essentially a point at the origin
- bit always has the largest magnitude of any vector
- cit can only exist in three dimensions
- dit is always parallel to every other vector except itself
Question 4Strategic thinking
A skier travels down a beginner slope that makes a 15° angle with the ground, covering a horizontal distance of 120 m. Using cos(15°) = 120/distance travelled, the distance travelled down the slope is approximately
- a124.2 m
- b120 m
- c31 m
- d116 m
Question 5Recall
In the 30-60-90 special right triangle (with sides 1, √3 and 2 units), the exact value of sin 30° is
- a1/2
- b√3/2
- c1/√3
- d√3

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Vectors and Trigonometry practice questions

Sample questions

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