Practice Test GeeksAIME - American Invitational Mathematics Examination Practice Test
← All AIME Flashcard Decks

Polynomials and Functions 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 Polynomials and Functions flashcards as text

  1. For f(x) = x^2 - 4x + 7, what is the minimum value?

    Answer: 3

    Complete the square: f(x)=(x-2)^2+3; minimum value is 3 at x=2.

  2. How many real roots does x^4 + 4 = 0 have?

    Answer: 0

    x^4=-4 has no real solutions since x^4≥0 for all real x.

  3. Simplify (x^2 - 9)/(x^2 - x - 6) for x ≠ 3 and x ≠ -2.

    Answer: (x+3)/(x+2)

    Factor numerator as (x-3)(x+3) and denominator as (x-3)(x+2); cancel (x-3) to get (x+3)/(x+2).

  4. The function f(x) = 3/(x-2) has a vertical asymptote at:

    Answer: x = 2

    A vertical asymptote occurs where the denominator is zero: x-2=0 gives x=2.

  5. If g(x) = x^2 and h(x) = x + 1, find (g ∘ h)(3).

    Answer: 16

    (g∘h)(3)=g(h(3))=g(4)=16.

  6. Find the product of the roots of 2x^2 - 6x + 3 = 0.

    Answer: 3/2

    By Vieta's, product of roots = c/a = 3/2.