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Module I: Math
If 
=3, what is the value of 
?
3
18
54
What is the area of a rectangle with a length of 15 centimeters (cmcm) and a width of 5 cm?
35 cm2
45 cm2
75 cm2
100 cm
The function ff is defined by f(x)=5x+10. What is the x-intercept of the graph of y=f(x) in the xy-plane?
(0,−2)
(0,2)
(−2,0)
(2,0)
In the xy-plane, the x-coordinate of the y-intercept of the graph of the function f is c. Which of the following must be equal to c?
0
1
f(0)
f(1)
x−3=2
−2(x−3)+y=−4
The solution to the given system of equations is (x,y). What is the value of y?
Answer:
y=68
y= x2+4
The graphs of the given equations in the xy-plane intersect at the point (a,b). What is a possible value of a?
−8
−4
17
64
An oven operates for 480 minutes each day. It can bake either a small cake or a large cake, one at a time. It takes the oven 20 minutes to bake a small cake or 40 minutes to bake a large cake. Which equation represents the possible number of small cakes, x, and large cakes, y, the oven can make each day?
20x+40y=480
40x+20y=480
(x+y)(20+40)=480
(20+x)(40+y)=480
A linear function fis defined by the equation f(x)=mx+3, where m is a constant. If f(2)=
, what is the value of m?
Answer:
A cube has a volume of 27 cubic units. What is the surface area, in square units, of the cube?
Answer:
Each of the dot plots shown represents the number of apples consumed by each member of two groups, Group A and Group B. Which statement best compares the standard deviations of the numbers of apples consumed by each member of these two groups?
The standard deviation of the number of apples consumed by each member for Group A is less than the standard deviation of the number of apples consumed by each member for Group B.
The standard deviation of the number of apples consumed by each member for Group A is equal to the standard deviation of the number of apples consumed by each member for Group B.
The standard deviation of the number of apples consumed by each member for Group A is greater than the standard deviation of the number of apples consumed by each member for Group B.
There is not enough information to compare these standard deviations.
The total cost f(x), in dollars, to rent a machine for 50 hours from a particular rental company is given by f(x)=50x+200, where x is the hourly rental rate, in dollars. What is the total cost to rent the machine for 50 hours when the hourly rate is $10?
$500
$700
$800
$1,000
The graph of y=f(x) is shown, where
the function ff is defined by f(x)=a
+b
+cx+d, and a,b,c,d are constants.
For how many values of x is f(x)=0?
0
1
2
3
y=2x+12
One of the two linear equations in a system is given. If the system has no solution, which equation could be the second equation in the system?
y=2(x+2)
y=2(x+6)
y=6(x+2)
y=6(x+6)
10B+60P=820
At a local arcade, players can win different colored marbles that correspond to different point values. One player won B blue marbles and P purple marbles worth a total of 820 points. The given equation represents this situation. How many more points is a purple marble worth than a blue marble?
Answer:
A cylinder has a base diameter of 4 inches and a height of 6 inches. What is the volume, in cubic inches, of the cylinder?
16π
24π
36π
96π
A swimming pool contains 4,800 cubic feet of water. A drainage system starts to empty the water at a fixed rate of 80 cubic feet per minute. Once half of the initial volume of water has been drained, the drainage system's rate decreases to 60 cubic feet per minute. What is the total time, in minutes, it takes for the drainage system to completely empty the pool?
60
70
72
80
The expression 60x3− 40x2 is equivalent to rx2 (3x−2), where rr is a constant. What is the value of r?
10
20
40
60
In the system of equations below, a and b are constants.
1/2 x− 1/7y = 1/6
ax+y=b
If the system of equations has an infinite number of solutions (x,y), what is the value of a−b ?
0
7/3
(-7)/3
(-7)/2
Each value in the data set shown represents the weight, in grams, of different rocks:
8,8,10,14,14,11,12,12,10,11
What is the mean weight, in grams, of these rocks?
Answer:
Which of the following expressions is equivalent to the given expression, where x ≠ ±3?
,
x−3
=2
What is the smallest solution to the given equation?
Answer:
x−15=(x−a)(x−15)
Which of the following are solutions to the given equation, where aa is a constant and a>15?
I. a
II. a+1
III. 15
I and II only
I and III only
II and III only
III only
Check Your Work
On test day, you won't be able to move on to the next module until time expires.
For these practice tests, you can click Next when you're ready to move on.
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The questions in this section address a number of important reading and writing skills.
Each question includes one or more passages, which may include a table or graph. Read
each passage and question carefully, and then choose the best answer to the question
based on the passage(s).
All questions in this section are multiple-choice with four answer choices. Each
question has a single best answer.
The questions in this section address a number of important reading and writing skills.
Each question includes one or more passages, which may include a table or graph. Read
each passage and question carefully, and then choose the best answer to the question
based on the passage(s).
All questions in this section are multiple-choice with four answer choices. Each
question has a single best answer.
The questions in this section address a number of important math skills.
Use of a calculator is permitted for all questions. A reference sheet, calculator, and these directions can be accessed throughout the test.
Unless otherwise indicated:
- All variables and expressions represent real numbers.
- Figures provided are drawn to scale.
- All figures lie in a plane.
- The domain of a given function
fis the set of all real numbersxfor whichf(x)is a real number.
For multiple-choice questions, solve each problem and choose the correct answer from the choices provided. Each multiple-choice question has a single correct answer.
For student-produced response questions, solve each problem and enter your answer as described below:
- If you find more than one correct answer, enter only one answer.
- You can enter up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer.
- If your answer is a fraction that doesn't fit in the provided space, enter the decimal equivalent.
- If your answer is a decimal that doesn't fit in the provided space, enter it by truncating or rounding at the fourth digit.
- If your answer is a mixed number (such as
3
1
2
), enter it as an improper fraction (
7
2
) or its decimal equivalent (
3.5). - Don't enter symbols such as a percent sign, comma, or dollar sign.
The questions in this section address a number of important math skills.
Use of a calculator is permitted for all questions. A reference sheet, calculator, and these directions can be accessed throughout the test.
Unless otherwise indicated:
- All variables and expressions represent real numbers.
- Figures provided are drawn to scale.
- All figures lie in a plane.
- The domain of a given function
fis the set of all real numbersxfor whichf(x)is a real number.
For multiple-choice questions, solve each problem and choose the correct answer from the choices provided. Each multiple-choice question has a single correct answer.
For student-produced response questions, solve each problem and enter your answer as described below:
- If you find more than one correct answer, enter only one answer.
- You can enter up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer.
- If your answer is a fraction that doesn't fit in the provided space, enter the decimal equivalent.
- If your answer is a decimal that doesn't fit in the provided space, enter it by truncating or rounding at the fourth digit.
- If your answer is a mixed number (such as
3
1
2
), enter it as an improper fraction (
7
2
) or its decimal equivalent (
3.5). - Don't enter symbols such as a percent sign, comma, or dollar sign.