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Algebra Flashcards

6 cards from real AIME 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. Find the remainder when x^3 - 4x + 2 is divided by x - 2.

    Answer: 2

    By the Remainder Theorem, substitute x=2: 8-8+2=2.

  2. 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 is 5+(-2)=3.

  3. The roots of 3x^2 - 5x + 1 = 0 are r and s. Find r^2 + s^2.

    Answer: 19/9

    r+s=5/3, rs=1/3; r^2+s^2=(r+s)^2-2rs=25/9-2/3=25/9-6/9=19/9.

  4. For what value of c does cx^2 + 8x + 4 = 0 have a double root?

    Answer: 4

    A double root requires discriminant=0: 64-16c=0 gives c=4.

  5. If x + 1/x = 3, what is x^2 + 1/x^2?

    Answer: 7

    Square x+1/x=3: x^2+2+1/x^2=9, so x^2+1/x^2=7.

  6. How many integer solutions does x^2 < 16 have?

    Answer: 7

    x can be -3,-2,-1,0,1,2,3, giving 7 integer solutions.