PARCC Algebra Practice Test 2

Question 1

1. Simplify the expression (4^x + 2^2x) / (2^x)

Accepted Answer

2<sup><i>x+1</i></sup></li>

Answer

First, recognize that 2^(2x) can be rewritten as (2^2)^x or 4^x. So the expression becomes (4^x + 4^x) / (2^x), which simplifies to 2 * 4^x / 2^x. Since 4^x is (2^2)^x or 2^(2x), the expression is 2 * 2^(2x) / 2^x. Using exponent rules, this simplifies to 2^(1 + 2x - x), resulting in 2^(x+1).

Question 2

2. Simplify the expression (2x²-5x-12)/(2x²-4x-16).

Accepted Answer

(2x+3)/2(x+2)

Answer

To simplify the expression, factor both the numerator and the denominator. The numerator, 2x^2 - 5x - 12, factors into (2x+3)(x-4). The denominator, 2x^2 - 4x - 16, factors into 2(x^2 - 2x - 8), which further factors into 2(x-4)(x+2). Canceling the common factor (x-4) from both the numerator and denominator leaves the simplified expression (2x+3) / [2(x+2)].

Question 3

3. Suppose that the function f(x) is a quadratic function with roots at x=2-3i and x=2+3i. Find f(x).

Accepted Answer

f(x)=x²-4x+13

Answer

If the roots are x=2-3i and x=2+3i, the factors of the quadratic function are (x - (2-3i)) and (x - (2+3i)). Multiplying these factors gives (x - 2 + 3i)(x - 2 - 3i). This is a difference of squares, ( (x-2) + 3i ) ( (x-2) - 3i ), which simplifies to (x-2)^2 - (3i)^2. Expanding yields x^2 - 4x + 4 - 9i^2, and since i^2 = -1, the function is x^2 - 4x + 4 + 9, or f(x) = x^2 - 4x + 13.

Question 4

4. Solve the inequality for x. Select all that apply.

³

²

Accepted Answer

x<-4</li>

Answer

First, factor the polynomial 4x^3 + 10x^2 - 24x by taking out the common factor 2x, resulting in 2x(2x^2 + 5x - 12). Then, factor the quadratic expression to get 2x(2x-3)(x+4). The roots are x=0, x=3/2, and x=-4. By testing intervals around these roots, the expression 4x^3 + 10x^2 - 24x is less than 0 when x < -4 and when 0 < x < 3/2.

Question 5

5. A baseball is thrown up in the air from an initial height of 6 feet. Its height above the ground (in feet) t seconds after being thrown is given by the function h(t)=-16t^2+46t+6. How long will it take (in seconds) for the baseball to hit the ground?

Accepted Answer

4 seconds</li>

Answer

To find when the baseball hits the ground, set the height function h(t) to 0: -16t^2 + 46t + 6 = 0. Dividing by -2 simplifies the equation to 8t^2 - 23t - 3 = 0. Factoring this quadratic equation yields (8t+1)(t-3) = 0, which gives solutions t = -1/8 and t = 3. Since time cannot be negative, the baseball hits the ground after 3 seconds. (Note: There appears to be a discrepancy between the calculated answer of 3 seconds and the provided correct answer of 4 seconds for this specific function.)

PARCC Practice Test

PARCC Practice Test

PARCC Algebra Practice Test 2