Start learning →

AP Intermediate 2nd Year Relations, Functions & Inverse Trigonometry — practice questions — page 2

Explore 92 free Relations, Functions & Inverse Trigonometry questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Relations, Functions & Inverse Trigonometry with Quill →

Relations, Functions & Inverse Trigonometry questions and exercises with answers

Showing questions 31–60 of 92.

Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →Trace how trigonometry travelledRead the answer and worked solution →True or false: the historical noteRead the answer and worked solution →If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Read the answer and worked solution →$\tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) = $Read the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?Read the answer and worked solution →For a function f: A → B, range is always:Read the answer and worked solution →$\sin^{-1}\left(\sin\tfrac{2\pi}{3}\right)$ equalsRead the answer and worked solution →$\cot^{-1}\left(-\tfrac{1}{\sqrt{3}}\right) = $Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Read the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →The number of ways to choose 3 books out of 5 (order does NOT matter) is:Read the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Bayes' theorem is essentially used to:Read the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(X) is:Read the answer and worked solution →For R = {(a,b) : a divides b} on ℕ, R is:Read the answer and worked solution →If |A| = 3 and |B| = 4, then |A × B| equals:Read the answer and worked solution →f(x) = 2x + 3 on ℝ is:Read the answer and worked solution →

Worked practice questions

Complete the rule about restricting a domain

Read exercise and reference answers
Missing parts
  1. Answer
    one-one and onto
    Choices
    1. one-one and onto
    2. continuous
    3. increasing
  2. Answer
    bijective
    Choices
    1. bijective
    2. periodic
    3. bounded
  3. Answer
    principal value branch
    Choices
    1. principal value branch
    2. natural domain
    3. range of definition
Complete the statement
An inverse exists only when a function is {0}. Trigonometric functions are not, so the domain is restricted until the function becomes {1}, and the agreed choice is called the {2}.
This sentence is the argument of the whole chapter in one line. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

Open this exercise →

Three of these are wrong. Find the one that holds.

Read exercise and reference answers
Questions
  1. Question
    Three of these statements about sin⁻¹ are false.
    Choices
    1. Item
      Its principal range is [−π/2, π/2]
      Correct
      Yes
    2. Explanation
      That is the range of cos⁻¹, not sin⁻¹.
      Item
      Its principal range is [0, π]
    3. Explanation
      That is (sin x)⁻¹. The −1 here means inverse function.
      Item
      It equals 1/sin x
    4. Explanation
      Sine only outputs [−1, 1], so the inverse accepts only that.
      Item
      It is defined for every real x
  2. Question
    Three of these statements about sec⁻¹ are false.
    Choices
    1. Item
      Its principal range is [0, π] − {π/2}
      Correct
      Yes
    2. Explanation
      sec is undefined at π/2, so that point must be removed.
      Item
      Its principal range is [0, π]
    3. Explanation
      That is where sec⁻¹ is NOT defined. Its domain is R − (−1, 1).
      Item
      Its domain is [−1, 1]
    4. Explanation
      cosec⁻¹ removes 0. sec⁻¹ removes π/2.
      Item
      It removes 0 from its range
Each wrong option is a real exam trap: a swapped range, a reciprocal confusion, or an unrestricted domain. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

Open this exercise →

Principal values worked in the chapter

Read exercise and reference answers
Questions
  1. Question
    Principal value of sin⁻¹(1/√2)
    Choices
    1. π/3
    2. π/6
    3. π/4
    Correct choice
    π/4
  2. Question
    Principal value of cot⁻¹(−1/√3)
    Choices
    1. 2π/3
    2. −π/3
    3. π/3
    Correct choice
    2π/3
  3. Question
    Why is cot⁻¹(−1/√3) not −π/3?
    Choices
    1. cot(−π/3) is undefined
    2. −π/3 is outside (0, π)
    3. −π/3 is not a real number
    Correct choice
    −π/3 is outside (0, π)
Both values are computed in full in your syllabus Examples 1 and 2: sin⁻¹(1/√2) = π/4 because sin(π/4) = 1/√2 and π/4 lies in [−π/2, π/2] cot⁻¹(−1/√3) = 2π/3 because cot(2π/3) = −1/√3 and 2π/3 lies in (0, π). Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

Open this exercise →

How to practise

  1. Choose a Relations, Functions & Inverse Trigonometry question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Relations, Functions & Inverse Trigonometry practice for AP Intermediate 2nd Year. Read explanations as you go. No signup form needed to start.

Practise Relations, Functions & Inverse Trigonometry →

More Mathematics topics

Vector Algebra and 3D GeometryContinuity, Differentiability & DerivativesIntegrals and ApplicationsLinear ProgrammingDifferential EquationsDeterminantsMatrices and DeterminantsProbability