Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Trigonometry & Precalculus Flashcards

6 cards from real AMC12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. Which expression equals cos^2(x) - sin^2(x)?

    Answer: cos(2x)

    The double angle identity states cos(2x)=cos^2(x)-sin^2(x).

  2. In triangle ABC with A=45 deg, B=60 deg, and c=10, what is side a by the Law of Sines?

    Answer: 10sin(45)/sin(75)

    C=75 deg; a/sin(A)=c/sin(C) gives a=10sin(45)/sin(75).

  3. What is the exact value of cos(75 degrees)?

    Answer: (sqrt(6)-sqrt(2))/4

    cos(75)=cos(45+30)=cos45*cos30-sin45*sin30=(sqrt(6)-sqrt(2))/4.

  4. If tan(alpha)=2 and tan(beta)=3, what is tan(alpha+beta)?

    Answer: -1

    tan(alpha+beta)=(2+3)/(1-2*3)=5/(-5)=-1.

  5. What is the inverse of f(x) = e^(2x)?

    Answer: (1/2)ln(x)

    Setting y=e^(2x) and solving for x gives x=(1/2)ln(y), so f^(-1)(x)=(1/2)ln(x).

  6. How many solutions does sin(x) = sqrt(3)/2 have in [0, 2pi)?

    Answer: 2

    sin(x)=sqrt(3)/2 at x=pi/3 and x=2pi/3, giving 2 solutions.