Drawing Tangents to Curves: 18 MCQs
All 18 multiple-choice questions from this kit, free and with no sign-up.
Warm-up · 6 questions
Q1. Which of the following best defines a tangent line to a curve at a point?
BeginnerAnswers and explanations are in the Veda app.
Q2. What does the gradient of a tangent line to a curve at a point represent?
BeginnerAnswers and explanations are in the Veda app.
Q3. On a distance-time graph, what does the gradient of the tangent line at a specific time represent?
BeginnerAnswers and explanations are in the Veda app.
Q4. Which formula correctly calculates the gradient $m$ of a tangent line using two points $(x_1, y_1)$ and $(x_2, y_2)$ on the line?
BeginnerAnswers and explanations are in the Veda app.
Q5. What is the first step in drawing a tangent line to a curve?
BeginnerAnswers and explanations are in the Veda app.
Q6. The gradient of a tangent line to a curve at a specific point gives the instantaneous rate of change of the function at that point.
BeginnerAnswers and explanations are in the Veda app.
Building up · 7 questions
Q7. A student draws a line that touches a curve at one point but also crosses the curve at another point far away. Is this line a tangent at the first point?
IntermediateAnswers and explanations are in the Veda app.
Q8. On a velocity-time graph, the gradient of the tangent line at a given time gives which quantity?
IntermediateAnswers and explanations are in the Veda app.
Q9. A car's distance-time graph is a curve. To find the car's speed at $t = 3$ seconds, what should you do?
IntermediateAnswers and explanations are in the Veda app.
Q10. Which of the following is a common mistake when drawing a tangent line?
IntermediateAnswers and explanations are in the Veda app.
Q11. In economics, the gradient of the tangent to a total cost curve at a certain production level gives:
IntermediateAnswers and explanations are in the Veda app.
Q12. A population growth curve shows the number of individuals over time. What does the gradient of the tangent at a specific time represent?
IntermediateAnswers and explanations are in the Veda app.
Q13. A tangent line is drawn to a curve at point P. Which statement must be true?
IntermediateAnswers and explanations are in the Veda app.
Topper level · 5 questions
Q14. Given a curve, which of the following is the best way to estimate the instantaneous rate of change at a point?
AdvancedAnswers and explanations are in the Veda app.
Q15. A student calculates the gradient of a tangent line using two points that are not on the tangent line but on the curve near the point of tangency. What is the likely outcome?
AdvancedAnswers and explanations are in the Veda app.
Q16. The tangent line to a curve at a point is horizontal. What is the instantaneous rate of change at that point?
AdvancedAnswers and explanations are in the Veda app.
Q17. A curve represents the distance traveled by a car over time. If a tangent line is drawn at the point where $t = 4$ seconds with coordinates $(4, d)$, what does the gradient of this tangent line represent?
AdvancedAnswers and explanations are in the Veda app.
Q18. Given a curve representing total cost in production, if a tangent line is drawn at the point corresponding to producing 100 units, how would you calculate the marginal cost at that production level?
AdvancedAnswers and explanations are in the Veda app.
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