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. What is tan(45) + tan(225)?

    Answer: 2

    tan has period 180, so tan(225)=tan(45)=1; sum=1+1=2.

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

    Answer: 1

    This is the fundamental Pythagorean identity: sin^2(x)+cos^2(x)=1 for all x.

  3. What is the maximum value of y = 2cos(x) - 1?

    Answer: 1

    cos(x) achieves maximum 1, giving y_max=2(1)-1=1.

  4. In a triangle with a=7, b=8, and angle C=60, what is the area?

    Answer: 14sqrt(3)

    Area=(1/2)*a*b*sin(C)=(1/2)(7)(8)(sqrt(3)/2)=14sqrt(3).

  5. What is sin(pi/4) * cos(pi/4)?

    Answer: 1/2

    (sqrt(2)/2)*(sqrt(2)/2)=2/4=1/2.

  6. What is the range of y = arcsin(x)?

    Answer: [-pi/2,pi/2]

    The principal value range of arcsin is [-pi/2,pi/2] by definition.