1.
MM1A1a. Given f(x) = -2x^{2} + 1, evaluate f(-2).
Correct Answer
B. -7
Explanation
You must plug -2 in for x in the function. Square -2 first and get 4. Multiply 4 by -2 and get -8. Add 1 to -8 and get -7.
2.
MM1A1b. The function below is what type of function?
Correct Answer
E. Rational
Explanation
The given function is a rational function because it is in the form of a fraction, where both the numerator and the denominator are polynomials. In this case, the function may have variables in the numerator and/or the denominator, and the degree of the numerator can be different from the degree of the denominator.
3.
MM1A1c. Which of the following is the description of the transformations from the parent function? f(x) = -(x+5)^{3}
Correct Answer
B. Shift left 5, followed by a reflection across the x-axis.
Explanation
(-) Reflection across the x-axis
(+5) Left five
4.
MM1A1d. Which of the following describes the interval of increase for the function below?
Correct Answer
C. [3, oo]
Explanation
Interval of increase is the values of x at which the function is increasing (going uphill). This function does not begin increasing until x=3 and continues to forever (oo).
5.
MM1A1e. Given 13, 10, 7, ... find S(6).
Correct Answer
A. -2
Explanation
S(6) is the sixth term. Three is being subtracted to find the next term. Therefore, you get 13, 10, 7, 4, 1, -2. The sixth term here is -2.
6.
MM1A1f. Given the function g(x) = 3x^{2} find the rate of change when the input changes from -5 to -2.
Correct Answer
A. -21
Explanation
Rate of Change: (Change in Y)/(Change in X)
x = -5 -2, Plug both values into g(x) = 3x^2 to get y
y = 75 12
Change in Y = 75 - 12 = 63
Change in X = -5 - -2 = -3
63/-3 = -21
7.
MM1A1g. The function m(x) = 15x - 500 represents Amanda's monthly paycheck after benefits, where x is the number of hours worked in a month. What is the independent quantity?
Correct Answer
B. Number of hours worked in a month
Explanation
X is always the independent quantity and you are told that x represents the number of hours worked in a month.
8.
MM1A2a. Simplify the expression sqrt(48x^{3}).
Correct Answer
B. 4xsqrt(3x)
Explanation
The largest perfect square in 48 is 16 and the largest perfect square in x^3 is x^2. So you get sqrt(16*3*x^2*x). The square root of 16 is 4 and the square root of x^2 is x, leaving 3 and x under the radical. Hence, your answer is 4xsqrt(3x).
9.
MM1A2b. Simplify 2sqrt(6) - 3sqrt(6).
Correct Answer
B. -1sqrt(6)
Explanation
Radicand and index must be the same when adding or subtracting radical expressions. In this case they are, so all you need to do is subtract coefficients and rewrite the radical.
10.
MM1A2b. -2sqrt(3)(sqrt(3) + 5)
Correct Answer
D. -6 -10sqrt(3)
Explanation
Distribute the -2sqrt(3) to both sqrt(3) and 5. Then simplify.
11.
MM1A2c. (-14x^{3} - 9x + 3) - (5x^{2} + 3x - 1)
Correct Answer
A. -14x^3 - 5x^2 - 12x + 4
Explanation
Change the subtraction to addition, and change the sign of everything in the parenthesis to the right. Then add like terms.
(-14x^3 - 9x + 3) + (-5x^2 - 3x + 1)
12.
MM1A2c. Divide (x^{2} - 8x + 12) by (x - 2)
Correct Answer
C. (x - 6)
Explanation
Use long division.
13.
MM1A2c. Multiply (2x - 5)(x + 3)
Correct Answer
B. 2x^2 + x - 15
Explanation
FOIL - You must multiply the first terms in each parenthesis, then the outer terms, then the inner terms, then the last terms. Then combine any like terms.
14.
MM1A1a. Given f(x) = -sqrt(x - 3) + 2, evaluate f(12).
Correct Answer
D. -1
Explanation
You must first subtract 3 from 12, which gives you 9. Then take the square root of 9, which is 3. The 3 then becomes negative, giving you -3. Lastly, you must add 2 to -3, which is -1.
15.
MM1A1b. Which parent function has the following characteristics?Domain: {All real numbers}Range: {All real numbers}
Correct Answer
D. Cubic
Explanation
A cubic function is the only parent function that has a domain of all real numbers and a range of all real numbers. This is because a cubic function is a polynomial function of degree 3, which means it can take on any real number as input and produce any real number as output. Linear, quadratic, absolute value, and square root functions all have restrictions on their domains and ranges, so they do not meet the given criteria.
16.
MM1A1c. A transformation that flips a function across the x-axis is a _______________.
Correct Answer
A. Vertical Reflection
Explanation
A vertical reflection flips a function across the x-axis, which means that the positive values of the function become negative and vice versa. This transformation does not involve any movement along the x-axis or a change in the shape of the function, only a reflection across the x-axis. Therefore, the correct answer is Vertical Reflection.
17.
MM1A1d. How many zeros are there for the quadratic function with the following conditions?Domain: {All real numbers}Range: {All real numbers greater than or equal to negative one}
Correct Answer
B. 2
Explanation
Since this is a quadratic with a range of all real numbers greater than or equal to negative one, it has a vertex at (0,-1) and is opening upward. Therefore the function crosses the x-axis twice.
18.
MM1A1e. Given S(n) = 4^{n+2}, find t_{0}.
Correct Answer
D. 64
Explanation
t0 is the first term of a sequence. Therefore n=1, so we need to find S(1). When you plug 1 in for n, you get 4^3, which is 64.
19.
MM1A1f. Which of the following is NOT true of the function below?
Correct Answer
C. The rate of change is constant.
Explanation
The function described in the question does not have a constant rate of change. This means that the rate at which the function is changing is not consistent throughout its domain. Instead, the rate of change is increasing, indicating that the function is becoming steeper or more steeply sloped as the input values increase. Therefore, the statement "The rate of change is constant" is not true for this function.
20.
MM1A1g. The function p(c) = 18c represents the profit from selling cases of coke, where c is the number of cases sold. What does p(6) = 108 mean?
Correct Answer
B. The profit is $108 when 6 cases are sold.
Explanation
c represents the number of cases sold and p(c) represents the profit. In p(6)= 108, c has been replaced with 6 and p(c) = 108, therefore 6 represents the number of cases sold and 108 is the profit.