Advanced High School Algebraic Mastery

Q: Which of the following describes the behavior of a polynomial function f(x) = ax^n + ... as x approaches infinity if a < 0 and n is an even integer?

f(x) approaches negative infinity

Mathematics

A comprehensive assessment of challenging high school algebra concepts including functions, systems, and polynomial theory.

algebra high school curriculum

10 Questions Hard Ages 15+ Apr 4, 2026

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This study set covers Mathematics through 10 practice questions. A comprehensive assessment of challenging high school algebra concepts including functions, systems, and polynomial theory. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

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1 Which of the following describes the behavior of a polynomial function f(x) = ax^n + ... as x approaches infinity if a < 0 and n is an even integer?

A f(x) approaches infinity
B f(x) approaches negative infinity
C f(x) approaches 0
D f(x) oscillates indefinitely

2 Given the system of equations 2x + y - z = 3, x - y + 2z = 4, and 3x - 2z = 1, what is the value of x?

3 What is the discriminant of the quadratic equation 3x^2 - 5x + 4 = 0?

A -23
B 7
C 23
D 49

4 According to the Remainder Theorem, what is the remainder when the polynomial P(x) = x^3 - 2x^2 + x - 5 is divided by (x - 3)?

A 3
B 7
C 10
D 13

5 For the function f(x) = log_b(x), which condition must be satisfied for the function to be defined as a real-valued function?

A x > 0, b > 0, b ≠ 1
B x ≥ 0, b > 0
C x ≠ 0, b > 1
D x > 0, b ≠ 0

6 Which expression is equivalent to the simplified form of (i^10 + i^20) where i is the imaginary unit?

A 0
B 1
C 2i
D -2

7 What are the vertical asymptotes of the rational function f(x) = (x^2 - 4) / (x^2 - x - 6)?

A x = 3
B x = -2
C x = 2, x = -3
D x = 3, x = -2

8 If log_2(x) + log_2(x - 2) = 3, what is the valid solution for x?

A 4
B -2
C 4 and -2
D None of these

9 What is the expansion of (x + y)^5 using the Binomial Theorem?

A x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5
B x^5 + x^4y + x^3y^2 + x^2y^3 + xy^4 + y^5
C x^5 + 5x^4y + 5x^3y^2 + 5x^2y^3 + 5xy^4 + y^5
D x^5 + 10x^4y + 10x^3y^2 + 10x^2y^3 + 10xy^4 + y^5

10 For a geometric series with first term a=2 and common ratio r=0.5, what is the sum to infinity?

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