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AP Calculus AB Unit 1A3: Function Composition and Inverses — practice questions

Explore 95 free Unit 1A3: Function Composition and Inverses questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1A3: Function Composition and Inverses questions and exercises with answers

Showing questions 1–30 of 95.

The identity $1 + \tan^2\theta$ equals:Read the answer and worked solution →The expression $\sin(90^\circ - \theta)$ is equal to:Read the answer and worked solution →The value of tan 0° is:Read the answer and worked solution →Which set is FINITE?Read the answer and worked solution →For the equation x² + x − 2 = 0, the solution set in roster form is:Read the answer and worked solution →Set X = letters in 'ALLOY'; set B = letters in 'LOYAL'. Compare:Read the answer and worked solution →In mathematics, a SET is defined as:Read the answer and worked solution →Which symbol denotes 'belongs to' / 'is an element of' in set theory?Read the answer and worked solution →The set of all letters in the word 'SCHOOL' in roster form is:Read the answer and worked solution →Which of the following is an EMPTY set?Read the answer and worked solution →Which statement about the EMPTY SET ∅ is INCORRECT?Read the answer and worked solution →Which collection is NOT a well-defined set?Read the answer and worked solution →A = {1, 3, 5} and B = {x : x is an odd natural number less than 6}. What is the relationship?Read the answer and worked solution →For A = {1, 2, 3}, identify which is a PROPER subset of A.Read the answer and worked solution →The set A = {x : x is a positive integer and x² < 40} in roster form is:Read the answer and worked solution →Set A = {x : x = n/(n+1), where n is a natural number and 1 ≤ n ≤ 6} in roster form is:Read the answer and worked solution →Let A = {n ∈ ℤ : n² ≤ 4} and B = {x ∈ ℝ : x² − 3x + 2 = 0}. Are A and B equal?Read the answer and worked solution →Let A = {x : x is a natural number which divides 42}. Set-builder form A in roster form is:Read the answer and worked solution →If $n(A)=3$ and $n(B)=2$, then $n(A\times B)$ equals:Read the answer and worked solution →The Cartesian product $A\times B$ is the set of all:Read the answer and worked solution →The value of $\tan\dfrac{\pi}{4}$ is:Read the answer and worked solution →The relationship between degree measure and radian measure is:Read the answer and worked solution →In a circle of radius r, an arc of length l subtends a central angle θ (in radians) such that:Read the answer and worked solution →For all real x, the value of sin²x + cos²x is:Read the answer and worked solution →Convert 40°20′ to radian measure.Read the answer and worked solution →A wheel makes 360 revolutions in one minute. Through how many RADIANS does it turn in one second?Read the answer and worked solution →The minute hand of a watch is 1.5 cm long. The distance the tip moves in 40 minutes is (use π = 3.14):Read the answer and worked solution →The radius of a circle where a central angle of 60° intercepts an arc of length 37.4 cm (use π = 22/7) is:Read the answer and worked solution →If two arcs of equal length subtend angles of 65° and 110° at the centres of two circles, the ratio of the radii r₁ : r₂ is:Read the answer and worked solution →If cos x = -3/5 and x lies in the THIRD quadrant, then sin x equals:Read the answer and worked solution →

Worked practice questions

The identity $1 + \tan^2\theta$ equals:

  1. $\cot^2\theta$
  2. $\csc^2\theta$
  3. $\sec^2\theta$
  4. $\cos^2\theta$
Show answer and solution

Correct answer: C. $\sec^2\theta$

Dividing sin²+cos²=1 by cos²θ gives 1 + tan²θ = sec²θ.

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The expression $\sin(90^\circ - \theta)$ is equal to:

  1. cos θ
  2. cosec θ
  3. tan θ
  4. sin θ
Show answer and solution

Correct answer: A. cos θ

Complementary-angle identity: sin(90°−θ) = cos θ.

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The value of tan 0° is:

  1. 1/2
  2. 1
  3. 0
  4. ∞
Show answer and solution

Correct answer: C. 0

We have tan 0° = sin0/cos0. That is tan 0° = 0/1. So tan 0° = 0.

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More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A1: Relations, Functions and GraphsUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits