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

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.

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Relations, Functions & Inverse Trigonometry questions and exercises with answers

Showing questions 1–30 of 92.

The value of $\cos^{-1}(-1)$ is:Read the answer and worked solution →The value of $\sin(\tan^{-1}(3/4))$ is:Read 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 →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 →Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Read the answer and worked solution →Bayes' theorem is essentially used to: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 →In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:Read the answer and worked solution →For a binomial distribution B(n, p), the MEAN and VARIANCE are:Read 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 →If |A| = 3 and |B| = 4, then |A × B| equals:Read the answer and worked solution →For R = {(a,b) : a divides b} on ℕ, R is:Read the answer and worked solution →f(x) = 2x + 3 on ℝ is:Read the answer and worked solution →For a function f: A → B, range is always:Read the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →

Worked practice questions

The value of $\cos^{-1}(-1)$ is:

  1. $0$, since $\cos 0 = 1$ but we want $-1$ on chart
  2. $\pi$, since $\cos\pi = -1$ in the principal range
  3. $-\pi$, taking a negative angle on the chart instead
  4. $\pi/2$, the angle whose cosine is $0$ on the chart
Show answer and solution

Correct answer: B. $\pi$, since $\cos\pi = -1$ in the principal range

$\cos\pi = -1$ and $\pi \in [0, \pi]$, the principal range of $\cos^{-1}$.

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The value of $\sin(\tan^{-1}(3/4))$ is:

  1. $3/4$, the same number as the tangent argument here
  2. $4/5$, taking the cosine of the angle on the chart
  3. $1/2$, ignoring the triangle relationships on the school chart
  4. $3/5$, since opp = 3, adj = 4 gives hyp = 5 and sin = 3/5
Show answer and solution

Correct answer: D. $3/5$, since opp = 3, adj = 4 gives hyp = 5 and sin = 3/5

Right triangle with opp = 3, adj = 4, hyp = 5; $\sin = 3/5$.

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A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?

  1. $1/52$
  2. $2/52$
  3. $1/13$
  4. $1/26$
Show answer and solution

Correct answer: C. $1/13$

P(king | red) = P(red king) / P(red) = (2/52) / (26/52) = 2/26 = 1/13. Conditional probability reduces the sample space.

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