SBAC High School Math 2 Practice Test — Questions and Answers
Question 1: The polynomial, x^3+7x^2-20x-96, has a factor of (x+8). Which of the following represents two of the zeros of the polynomial?
- x=-3 and x=4 (Correct answer)
- x=-6 and x=2
- x=-3 and x=-4
- x=6 and x=-2
Correct answer: x=-3 and x=4
If (x+8) is a factor of the polynomial, then x=-8 is one of its zeros. To find the other zeros, we can use synthetic division to divide the polynomial x^3+7x^2-20x-96 by (x+8). This division results in the quadratic expression x^2-x-12. Factoring this quadratic equation, we get (x-4)(x+3). Setting these factors to zero gives the remaining zeros: x=4 and x=-3.
Question 2: The possible combinations of candy bars and packages of suckers that Amanda may purchase are represented by the graph shown below.<br><br>Which of the following inequalities represents the possible combinations of candy bars and packages of suckers that she may purchase?
- 0.75x+1.5y≤20
- 0.5x+1.25y≤25
- 0.75x+1.25y≤25 (Correct answer)
- 1.25x+0.75y≤20
Correct answer: 0.75x+1.25y≤25
To find the correct inequality, we can identify the intercepts from the graph. The line crosses the x-axis (where y=0) at approximately x=33.33, and the y-axis (where x=0) at y=20. We can test these points with the given inequalities. For option C, 0.75x+1.25y≤25, if y=0, 0.75x≤25 means x≤25/0.75, which is x≤33.33. If x=0, 1.25y≤25 means y≤25/1.25, which is y≤20. Since the shaded region is below the line, indicating 'less than or equal to', this inequality correctly represents the graph.
Question 3: Ana solves the quadratic equation, x^2-6x=18, by completing the square. Which of the following equations may be used to find the solution, using this method?
- 〖(x+3)〗^2=27
- 〖(x-6)〗^2=24
- 〖(x+6)〗^2=24
- 〖(x-3)〗^2=27 (Correct answer)
Correct answer: 〖(x-3)〗^2=27
To solve the quadratic equation x^2-6x=18 by completing the square, we need to add a constant to both sides that makes the left side a perfect square trinomial. The constant needed is (b/2)^2, where b is the coefficient of the x term. In this equation, b=-6, so (b/2)^2 = (-6/2)^2 = (-3)^2 = 9. Adding 9 to both sides gives x^2-6x+9 = 18+9, which simplifies to (x-3)^2 = 27.
SBAC High School Math 2 Practice Test
The polynomial, x^3+7x^2-20x-96, has a factor of (x+8).
Which of the following represents two of the zeros of the polynomial?