Practice What Is A Normal? (2.1) - Tangents and Normals - IB 10 Mathematics

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9 questions

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2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the definition of a normal line?
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Think about the relationship between tangents and normals.
Question 2.
If the slope of the tangent is 3, what is the slope of the normal?
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Remember the relationship between slopes of perpendicular lines.
3Question 3.
What is the slope of a normal line if the slope of the tangent is 5?
- -1/5
- -5
- 1/5
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Recall the formula for slopes of perpendicular lines.
4Question 4.
True or False: The normal line intersects the curve at more than one point.
- True
- False
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Think about the definition of a normal line.
Question 5.
Prove that the normal line to the circle x^2 + y^2 = r^2 at the point (rcos(θ), rsin(θ)) is perpendicular to the tangent line.
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Construct the derivative of the curve to find the slopes.
Question 6.
Derive the equation of a normal line to a parabola y = x^2 at the vertex.
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Consider what happens to slopes at extremities.

5 more questions in this section. Enroll free to practise them all.