Practice Test (Algebra 1 End-of-Course) Flashcards

Factor the trinomial: x² + 5x + 6

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

Find two numbers that multiply to 6 and add to 5; those are 2 and 3, giving (x + 2)(x + 3).

What are the solutions of x² − 9 = 0?

Answer: x = ±3

x² = 9 gives x = √9 = ±3, so both x = 3 and x = −3 are solutions.

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

Answer: x ≥ 4

The expression under a square root must be non-negative, so x − 4 ≥ 0, which means x ≥ 4.

An arithmetic sequence begins 3, 7, 11, 15, ... What is the 10th term?

Answer: 39

Using aₙ = a₁ + (n−1)d with a₁ = 3, d = 4, a₁₀ = 3 + 9(4) = 39.

Simplify: √75

Answer: 5√3

√75 = √(25 × 3) = √25 × √3 = 5√3.

Which equation represents exponential growth?

Answer: y = 2(1.5)ˣ

Exponential growth has the form y = a · bˣ where b > 1; y = 2(1.5)ˣ fits this pattern.

What is the vertex of f(x) = x² − 4x + 3?

Answer: (2, −1)

The x-coordinate of the vertex is x = −b/2a = 4/2 = 2, and f(2) = 4 − 8 + 3 = −1, giving vertex (2, −1).