8.1-8.2 Hyperbolic functions and their derivatives Quiz: Pearson Edexcel Further Maths, Unit 8

The 20 questions

1. How is cosh x defined in terms of exponentials?

   • e^x - e^(-x)
   • (e^x - e^(-x)) / 2
   • (e^x + e^(-x)) / (e^x - e^(-x))
   • (e^x + e^(-x)) / 2

2. What is the range of cosh x?

   • y >= 1
   • -1 < y < 1
   • y > 0
   • All real numbers

3. What is the range of tanh x?

   • -1 < y < 1
   • All real numbers
   • 0 <= y <= 1
   • y >= 1

4. Which identity holds for all real x?

   • cosh^2 x - sinh^2 x = 0
   • cosh x - sinh x = 1
   • cosh^2 x + sinh^2 x = 1
   • cosh^2 x - sinh^2 x = 1

5. What is the derivative of sinh x with respect to x?

   • sinh x
   • -cosh x
   • tanh x
   • cosh x

6. What is the derivative of cosh x with respect to x?

   • -sinh x
   • cosh x
   • sinh x
   • 1/cosh x

7. Which expression is the derivative of tanh x?

   • sech^2 x
   • cosh x
   • cosech^2 x
   • sech x tanh x

8. Find d/dx of tanh(3x).

   • sech^2(3x)
   • 3 sech(3x) tanh(3x)
   • 3 sech^2(3x)
   • 3 cosh^2(3x)

9. Find d/dx of cosh(2x).

   • 2 sinh(2x)
   • 2 cosh(2x)
   • -2 sinh(2x)
   • sinh(2x)

10. Find d/dx of x sinh x.

    • x cosh x
    • sinh x - x cosh x
    • sinh x + x cosh x
    • cosh x - x sinh x

11. Find d/dx of sinh(x^2).

    • 2x sinh(x^2)
    • x^2 cosh(x^2)
    • 2x cosh(x^2)
    • cosh(x^2)

12. If y = ln(cosh x), what is dy/dx?

    • sinh x / x
    • sech x
    • ln(sinh x)
    • tanh x

13. Evaluate cosh(ln 2).

    • 1/2
    • 2
    • 3/4
    • 5/4

14. Evaluate sinh(ln 3).

    • 8/3
    • 5/3
    • 4/3
    • 10/3

15. Find the value of x > 0 for which sinh x = 1.

    • ln(sqrt 2 - 1)
    • 1
    • ln(1 + sqrt 2)
    • ln 2

16. Given cosh x = 5/4 with x > 0, find sinh x.

    • 4/5
    • 3/4
    • 5/3
    • 9/16

17. Find d/dx of sech x.

    • -cosech x coth x
    • -sech^2 x
    • -sech x tanh x
    • sech x tanh x

18. Find d/dx of x tanh x.

    • tanh x + sech^2 x
    • tanh x + x sech^2 x
    • tanh x - x sech^2 x
    • x sech^2 x

19. Which statement about sinh x is true?

    • sinh x is an even function
    • sinh x has range -1 < y < 1
    • sinh x has range y >= 1
    • sinh x is an odd function

20. Where is the stationary point of y = cosh x?

    • There are no stationary points
    • At x = ln 2, which is a maximum
    • At x = 1, which is a point of inflection
    • At x = 0, which is a minimum

Related quizzes

• Proof by mathematical induction Quiz · 1.1 · 20 questions
• Quadratic equations and complex arithmetic Quiz · 2.1-2.2 · 20 questions
• Matrix arithmetic and inverses Quiz · 3.1-3.2 · 20 questions
• Expectation of discrete random variables Quiz · 3B.1.1 · 20 questions
• The Poisson distribution Quiz · 3B.2.1 · 20 questions
• Geometric and negative binomial models Quiz · 3B.3.1 · 20 questions
• Hypothesis tests for the Poisson distribution Quiz · 3B.4.1 · 20 questions
• Applying the Central Limit Theorem Quiz · 3B.5.1 · 20 questions
• Goodness of fit tests for discrete distributions Quiz · 3B.6.1 · 20 questions
• Definition and derivation of probability generating functions Quiz · 3B.7.1 · 20 questions