Accuplacer College Placement ACCUPLACER Advanced Algebra and Functions Test 2 — Questions and Answers
Question 1: Solve the system: 2x + y = 7 and x − y = 2.
- x = 2, y = 3
- x = 3, y = 1 (Correct answer)
- x = 4, y = −1
- x = 1, y = 5
Correct answer: x = 3, y = 1
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)?
- All real numbers
- x > 4
- x ≠ 4 (Correct answer)
- x ≠ −4
Correct answer: x ≠ 4
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?
- y = 2(1.5)ˣ
- y = 3(0.8)ˣ (Correct answer)
- y = 5 + 2x
- y = x²
Correct answer: y = 3(0.8)ˣ
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)?
- 0
- 1
- 2
- 3 (Correct answer)
Correct answer: 3
By the Remainder Theorem, substitute x = 1: 1 − 2 + 4 = 3.
Question 5: Simplify: √(75)
- 5√3 (Correct answer)
- 15√3
- 3√5
- 5√15
Correct answer: 5√3
75 = 25 × 3, so √75 = √25 · √3 = 5√3.
Question 6: What is the amplitude of y = 4sin(2x)?
- 2
- 4 (Correct answer)
- 8
- π
Correct answer: 4
The amplitude of y = A·sin(Bx) is |A|, which is 4.
Accuplacer College Placement ACCUPLACER Advanced Algebra and Functions Test 2
Solve the system: 2x + y = 7 and x − y = 2.