Lesson 5.5-5.6

5.5-5.6 Differentiating and integrating inverse trigonometric functions Quiz: Pearson Edexcel Further Maths, Unit 5

20 questions

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Lesson 5.5-5.6, Differentiating and integrating inverse trigonometric functions: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 5: Further calculus, written with Revision Ninja.

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The 20 questions

  1. What is the derivative of arcsin x?

    • 1/sqrt(1 - x^2)
    • -1/sqrt(1 - x^2)
    • 1/(1 + x^2)
    • 1/(1 - x^2)
  2. What is the derivative of arctan x?

    • 1/(1 - x^2)
    • 1/sqrt(1 + x^2)
    • 1/(1 + x^2)
    • -1/(1 + x^2)
  3. What is the derivative of arccos x?

    • -1/(1 - x^2)
    • -1/(1 + x^2)
    • 1/sqrt(1 - x^2)
    • -1/sqrt(1 - x^2)
  4. Which result gives the integral of 1/sqrt(a^2 - x^2) dx?

    • arcsin(a/x) + C
    • ln|x + sqrt(a^2 - x^2)| + C
    • arcsin(x/a) + C
    • a arcsin x + C
  5. Which result gives the integral of 1/(a^2 + x^2) dx?

    • (1/a) arctan(x/a) + C
    • (1/a) ln(a^2 + x^2) + C
    • a arctan(x/a) + C
    • arctan(a x) + C
  6. What is the domain of arcsin x as a real function?

    • 0 <= x <= pi
    • -1 <= x <= 1
    • 0 < x < 1
    • all real numbers
  7. What is the range of the principal value of arctan x?

    • -pi/2 < y < pi/2
    • 0 < y < pi
    • 0 <= y <= pi
    • all real numbers
  8. What is the derivative of arcsin x + x sqrt(1 - x^2)?

    • 2/sqrt(1 - x^2)
    • 2 sqrt(1 - x^2)
    • -2 sqrt(1 - x^2)
    • 1/sqrt(1 - x^2)
  9. What is the derivative of (1/2) arctan(x^2)?

    • x^2/(1 + x^4)
    • 2x/(1 + x^4)
    • x/(1 + x^4)
    • x/(1 + x^2)
  10. What is the value of the integral from 0 to 1 of 1/sqrt(4 - x^2) dx?

    • pi/2
    • pi/6
    • pi/4
    • pi/3
  11. What is the value of the integral from 0 to 1 of 1/(1 + x^2) dx?

    • pi/6
    • pi/4
    • pi/2
    • pi/3
  12. What is the value of the integral from 0 to sqrt(3) of 1/(3 + x^2) dx?

    • pi/(4 sqrt(3))
    • pi/12
    • pi/(2 sqrt(3))
    • pi/4
  13. What is the derivative of arcsin(2x)?

    • -2/sqrt(1 - 4x^2)
    • 2/sqrt(1 - 4x^2)
    • 2/sqrt(1 - x^2)
    • 1/sqrt(1 - 4x^2)
  14. What is the derivative of arccos x at x = 0?

    • 1
    • -1
    • -pi/2
    • 0
  15. What is the value of the integral from 0 to 3/2 of 1/sqrt(9 - x^2) dx?

    • pi/3
    • pi/2
    • pi/4
    • pi/6
  16. What is the derivative of arctan(x/2)?

    • 1/(4 + x^2)
    • 2/(4 - x^2)
    • 2/(4 + x^2)
    • 1/(2 + x^2)
  17. What is the value of the integral from 0 to 2 of 1/(x^2 + 4) dx?

    • pi/8
    • pi/2
    • pi/4
    • pi/16
  18. What is the value of the integral from 0 to 1/2 of 1/sqrt(1 - 4x^2) dx?

    • pi/6
    • pi/2
    • pi/12
    • pi/4
  19. What is the derivative of x arcsin x?

    • arcsin x + x/sqrt(1 - x^2)
    • 1/sqrt(1 - x^2)
    • arcsin x - x/sqrt(1 - x^2)
    • x/sqrt(1 - x^2)
  20. Which expression is an antiderivative of arctan x?

    • arctan x/(1 + x^2)
    • x arctan x - (1/2) ln(1 + x^2)
    • x/(1 + x^2)
    • x arctan x + (1/2) ln(1 + x^2)

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