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
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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)
-
What is the derivative of arctan x?
- 1/(1 - x^2)
- 1/sqrt(1 + x^2)
- 1/(1 + x^2)
- -1/(1 + x^2)
-
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)
-
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
-
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
-
What is the domain of arcsin x as a real function?
- 0 <= x <= pi
- -1 <= x <= 1
- 0 < x < 1
- all real numbers
-
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
-
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)
-
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)
-
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
-
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
-
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
-
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)
-
What is the derivative of arccos x at x = 0?
- 1
- -1
- -pi/2
- 0
-
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
-
What is the derivative of arctan(x/2)?
- 1/(4 + x^2)
- 2/(4 - x^2)
- 2/(4 + x^2)
- 1/(2 + x^2)
-
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
-
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
-
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)
-
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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