Practice Test GeeksAMC12 - American Mathematics Competition 12 Practice Test
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Algebra 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.

Read the first 6 Algebra flashcards as text

  1. If 2^x = 3, what is the value of 4^x?

    Answer: 9

    4^x = (2^2)^x = (2^x)^2 = 3^2 = 9.

  2. The roots of x^2 - 5x + 6 = 0 are r and s. What is r^2 + s^2?

    Answer: 13

    By Vieta's, r+s=5 and rs=6, so r^2+s^2=(r+s)^2-2rs=25-12=13.

  3. If log2(x) + log2(x-2) = 3, find x.

    Answer: 4

    x(x-2)=8 gives x^2-2x-8=0, so (x-4)(x+2)=0 and x=4.

  4. For what positive k does 3x^2 + kx + 12 = 0 have exactly one real solution?

    Answer: 12

    The discriminant k^2-144=0 gives k=12.

  5. If f(x) = 2x+1 and g(x) = x^2, what is f(g(3))?

    Answer: 19

    g(3)=9 and f(9)=2(9)+1=19.

  6. Solve |2x-3|=7. What is the sum of all solutions?

    Answer: 3

    2x-3=7 gives x=5 and 2x-3=-7 gives x=-2; sum=3.