Question

60 minutes - 60 questions
directions: solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.
do not linger over problems that take too much time. solve as many as you can; then return to the others in the time you have left for this test.
you are permitted to use a calculator on this test. you may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.
note: unless otherwise stated, all of the following should be assumed.

1. illustrative figures are not necessarily drawn to scale.
2. geometric figures lie in a plane.
3. the word line indicates a straight line.
4. the word average indicates arithmetic mean.
5. the numbers 1 through 15 were each written on individual pieces of paper, 1 number per piece. then the 15 pieces of paper were put in a jar. one piece of paper will be drawn from the jar at random. what is the probability of drawing a piece of paper with a number less than 9 written on it?

a. $\frac{1}{9}$
b. $\frac{1}{15}$
c. $\frac{6}{15}$
d. $\frac{7}{15}$
e. $\frac{8}{15}$

1. which of the following expressions is equivalent to $-4x^{3}-12x^{3}+9x^{2}$?

f. $x^{8}$
g. $-7x^{8}$
h. $-8x^{3}+9x^{2}$
j. $-16x^{3}+9x^{2}$
k. $-16x^{6}+9x^{2}$

1. when $x = 2$, $10 + 3(12div(3x))=$?

a. 12
b. 16
c. 26
d. 34
e. 104

1. $|6 - 4|-|3 - 8|=$?

f. -7
g. -3
h. 3
j. 7
k. 21

1. the expression $(4c - 3d)(3c + d)$ is equivalent to:

a. $12c^{2}-13cd - 3d^{2}$
b. $12c^{2}-13cd + 3d^{2}$
c. $12c^{2}-5cd - 3d^{2}$
d. $12c^{2}-5cd + 3d^{2}$
e. $12c^{2}-3d^{2}$

1. of the 180 students in a college course, $\frac{1}{4}$ of the students earned an a for the course, $\frac{1}{3}$ of the students earned a b for the course, and the rest of the students earned a c for the course. how many of the students earned a c for the course?

f. 75
g. 90
h. 105
j. 120
k. 135

1. the number of fish, $f$, in skippers pond at the beginning of each year can be modeled by the equation $f(x)=3(2^{x})$, where $x$ represents the number of years after the beginning of the year 2000. for example, $x = 0$ represents the beginning of the year 2000, $x = 1$ represents the beginning of the year 2001, and so forth. according to the model, how many fish were in skippers pond at the beginning of the year 2006?

a. 96
b. 192
c. 384
d. 1,458
e. 46,656

Explanation:

1.

Step1: Count favorable outcomes

Numbers less than 9 from 1 - 15 are 1, 2, 3, 4, 5, 6, 7, 8. So there are 8 favorable outcomes.

Step2: Calculate probability

The total number of outcomes is 15. Probability $P=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}=\frac{8}{15}$.

Step1: Combine like - terms

Combine the terms with the same power of $x$. For the $x^{3}$ terms, $-4x^{3}-12x^{3}=(-4 - 12)x^{3}=-16x^{3}$, and the $x^{2}$ term remains as $9x^{2}$. So the expression is $-16x^{3}+9x^{2}$.

Step1: Evaluate the innermost parentheses

When $x = 2$, first evaluate $3x=3\times2 = 6$, then $12\div(3x)=12\div6 = 2$.

Step2: Multiply and add

Next, $3\times2=6$, and $10 + 6=16$.

Answer:

E. $\frac{8}{15}$

2.