Accuplacer College Placement ACCUPLACER Advanced Algebra and Functions Test 2

Question 1

Solve the system: 2x + y = 7 and x − y = 2.

Accepted Answer

x = 3, y = 1

Answer

Add the two equations to eliminate y: 3x = 9, so x = 3; then y = 7 − 2(3) = 1.

Question 2

What is the domain of f(x) = 1/(x − 4)?

Accepted Answer

x ≠ 4

Answer

The function is undefined when the denominator equals zero, i.e., when x = 4, so the domain is all real numbers except 4.

Question 3

Which equation represents exponential decay?

Accepted Answer

y = 3(0.8)ˣ

Answer

A base between 0 and 1 (like 0.8) causes the function to decrease, representing exponential decay.

Question 4

What is the remainder when x³ − 2x + 4 is divided by (x − 1)?

Accepted Answer

3

Answer

By the Remainder Theorem, substitute x = 1: 1 − 2 + 4 = 3.

Question 5

Simplify: √(75)

Accepted Answer

5√3

Answer

75 = 25 × 3, so √75 = √25 · √3 = 5√3.

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