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 a+b=5 and ab=4, find a^3+b^3.

    Answer: 65

    a^3+b^3=(a+b)^3-3ab(a+b)=125-60=65.

  2. The polynomial x^3-6x^2+11x-6 has roots r, s, t. Find r+s+t.

    Answer: 6

    By Vieta's formulas, the sum of roots equals 6.

  3. Solve 3^(2x) - 4*3^x + 3 = 0. What are the solutions?

    Answer: x=0 or x=1

    Let u=3^x: u^2-4u+3=0 gives u=1 (x=0) or u=3 (x=1).

  4. If x + 1/x = 5, what is x^2 + 1/x^2?

    Answer: 23

    Squaring x+1/x=5 gives x^2+2+1/x^2=25, so x^2+1/x^2=23.

  5. A function satisfies f(2x)=2f(x) and f(1)=3. Find f(8).

    Answer: 24

    f(2)=6, f(4)=12, f(8)=24.

  6. For how many integers n is (n-1)/(n+1) also an integer?

    Answer: 4

    Writing n-1=(n+1)-2, n+1 must divide 2, so n+1 in {-2,-1,1,2} giving 4 integers.