Algebra & Functions Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Algebra & Functions flashcards as text
If r, s, t are the roots of x^3 - 3x^2 + 5x - 7 = 0, what is r^2 + s^2 + t^2?
Answer: -1
r^2 + s^2 + t^2 = (r + s + t)^2 - 2(rs + st + tr) = 9 - 10 = -1.
What is the sum of the coefficients of the expansion of (2x - 1)^5?
Answer: 1
The sum of coefficients equals P(1) = (2 - 1)^5 = 1.
Which of the following functions is even?
Answer: f(x) = x^4 - 3x^2 + cos x
Every term of x^4 - 3x^2 + cos x is unchanged when x is replaced by -x.
What is log_3(81) + log_2(1/8)?
Answer: 1
log_3(81) = 4 and log_2(1/8) = -3, so the sum is 1.
What is i^2026, where i^2 = -1?
Answer: -1
Since 2026 ≡ 2 (mod 4), i^2026 = i^2 = -1.
If x and y are positive with x + 2y = 10, what is the maximum value of xy?
Answer: 25/2
xy = (10 - 2y)y peaks at y = 5/2, x = 5, giving 25/2.
How many integers x satisfy x^2 < 20?
Answer: 9
The integers -4 through 4 satisfy it, which is 9 values.
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