Drawing Tangents to Curves: 15 flashcards
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1. What is a tangent to a curve?
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A straight line that touches the curve at exactly one point, called the point of tangency.
2. What is the point of tangency?
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The single point where a tangent line touches the curve.
3. Does a tangent line cross the curve at the point of tangency?
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No, it only touches the curve at that point; it does not cross it there.
4. What does the gradient of a tangent line represent?
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The instantaneous rate of change of the curve at the point of tangency.
5. On a distance-time graph, what does the gradient of the tangent give?
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The instantaneous speed at that point in time.
6. On a height-time graph, what does the gradient of the tangent give?
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The instantaneous vertical velocity at that moment.
7. What is the formula for the gradient of a tangent line?
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$m = \frac{y_2 - y_1}{x_2 - x_1}$
8. Do the two points used to calculate a tangent's gradient need to lie on the original curve?
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No, they only need to lie on the tangent line itself.
9. What is the first step in drawing a tangent to a curve?
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Locate the specific point on the curve where you want the tangent (the point of tangency).
10. How should a ruler be positioned to draw a tangent?
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So that it touches the curve only at the chosen point, without crossing it.
11. What is a common mistake when drawing a tangent?
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Drawing a line that crosses the curve at the point of tangency instead of only touching it.
12. Why is drawing tangents important in physics?
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It allows calculation of instantaneous rates like speed or velocity from a graph.
13. What does 'instantaneous rate of change' mean?
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The rate of change at one exact point or moment in time, given by the tangent's gradient.
14. If a curve is momentarily straight at a point, what line represents that straightness?
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The tangent line at that point.
15. What does the tangent capture about a curve at a single point?
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The momentary direction or 'straightness' of the curve at that point.
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