SBAC High School Math 1 Practice Test — Questions and Answers
Question 1: Which of the following represents the difference of (3x^3-9x^2+6x)-(8x^3+4x^2-3x)?
- -5x^3-13x^2+9x (Correct answer)
- 11x^3-13x^2+3x
- -5x^3-5x^2+3x
- 5x^3+13x^2+9x
Correct answer: -5x^3-13x^2+9x
To find the difference between the two polynomials, distribute the negative sign to each term in the second polynomial and then combine like terms. This results in (3x^3 - 9x^2 + 6x - 8x^3 - 4x^2 + 3x), which simplifies to -5x^3 - 13x^2 + 9x.
Question 2: A polynomial has factors of x-3, x+6, and x+2. Which of the following represents the graph of the polynomial?
- A. (Correct answer)
- B.
- C.
- D.
Correct answer: A.
The factors of a polynomial directly correspond to its x-intercepts, also known as its zeros. If (x-3) is a factor, then x=3 is an x-intercept. Similarly, if (x+6) is a factor, x=-6 is an x-intercept, and if (x+2) is a factor, x=-2 is an x-intercept. Therefore, the graph of the polynomial must cross the x-axis at x=3, x=-6, and x=-2, which is represented by graph A.
Question 3: Which of the following expressions is equivalent to the expression, (x-3)/(x^3-6x^2-9x+54)?
- (x-3)/(x-6)
- 1/((x+3)(x-6)) (Correct answer)
- 1/(x-6)
- (x-3)/((x+3)(x-6))
Correct answer: 1/((x+3)(x-6))
To simplify the expression, we need to factor the denominator, x^3-6x^2-9x+54. Since (x-3) is in the numerator, we can test if it's a factor of the denominator using synthetic division or by checking if x=3 is a root. Dividing the polynomial by (x-3) yields (x^2-3x-18). Factoring this quadratic gives (x-6)(x+3). Thus, the original expression becomes (x-3)/((x-3)(x-6)(x+3)). Canceling out the common factor (x-3) from the numerator and denominator leaves 1/((x+3)(x-6)).
Question 4: Rewrite using fractional exponents: 5√(3&2^2 ) +√(7& 3^2 ).
- 5∙2⅔+3
- 5∙2^⅔+3^(2⁄7) (Correct answer)
- 5^3∙2^½+7∙3^½
- 〖10〗^⅔+3^(2⁄7)
Correct answer: 5∙2^⅔+3^(2⁄7)
To rewrite radical expressions using fractional exponents, we use the rule that the nth root of x^m is equivalent to x^(m/n). For the first term, 5 times the cube root of 2 squared (5√(3&2^2)), this translates to 5 multiplied by 2 raised to the power of 2/3, or 5∙2^(2/3). For the second term, the 7th root of 3 squared (√(7&3^2)), this becomes 3 raised to the power of 2/7, or 3^(2/7). Combining these, the expression is 5∙2^(2/3) + 3^(2/7).
SBAC High School Math 1 Practice Test
Which of the following represents the difference of (3x^3-9x^2+6x)-(8x^3+4x^2-3x)?