Math Questions 15.8 - Gradient of Curves

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Gradient of Curves Revision Questions

1. . The gradient of a function at a narrow section AB of its graph is -2 and the coordinates of point A are (1, 1). What is the x-coordinate of point B if the y-coordinate of this point is 0.8?

1. x_B = 0.1
2. x_B = 0.8
3. x_B = 0.9
4. x_B = 1.1

Reveal AnswerCorrect Answer: D

2. . What is the gradient of the function f(x) = x² at the point A if x_A = -3?

1. -6
2. -3
3. 3
4. 6

Reveal AnswerCorrect Answer: A

3. . A small part of the graph of an unknown function f(x) is shown in the figure below.

What is the gradient of this function at the point A?

1. -2
2. -1
3. -0.5
4. 0.5

Reveal AnswerCorrect Answer: A

4. . The gradient of f(x) = 2x² - 3mx + 8 at the point A with horizontal coordinate x_A = -1 is k = 5. What is the value of m?

1. -3
2. -1
3. 1
4. 3

Reveal AnswerCorrect Answer: A

5. . The gradient k of an unknown function is always twice the corresponding horizontal coordinate of that function. What is this unknown function?

1. f(x) = 2x
2. f(x) = x²
3. f(x) = 2x²
4. f(x) = 2

Reveal AnswerCorrect Answer: B

6. . What is the gradient k of the function f(x) = 2x³ - 4x² - 3x + 1 at the point of the graph with horizontal coordinate x = -1?

1. -5
2. -1
3. 11
4. 17

Reveal AnswerCorrect Answer: C

7. . What is the equation of the tangent to the graph of f(x) = x² - 3x + 2 at the point A with horizontal coordinate x_A = 4?

1. y = 2x - 3
2. y = 5x + 2
3. y = 2x + 6
4. y = 5x - 14

Reveal AnswerCorrect Answer: D

8. . The line y = 3x - 1 is tangent to the point A of a quadratic function y = ax² + bx + c with horizontal coordinate x_A = 2. What is the constant c of this quadratic function?

1. 2
2. 3
3. 4
4. 5

Reveal AnswerCorrect Answer: B

9. . What is the equation of the tangent to the point A for the function shown in the figure?

1. y = 3x - 2
2. y =3x - 3
3. y = 9x + 21
4. y = 20x - 2

Reveal AnswerCorrect Answer: C

10. . What is the gradient of the function shown in the figure at the point A with horizontal coordinate x_A = 2?

1. 0
2. 1
3. 2
4. 4

Reveal AnswerCorrect Answer: C

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5. Continuing learning types of graphs - read our next math tutorial: Quadratic Graphs Part One

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