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Module I: Math
The revenue g(x) of a corporation is determined by g(x)=−300x2+18,000x, where x denotes the unit cost in dollars. The graph intersects the x-axis at points 0 and m. What is m?
Answer:
Theequation x2−14x+y2+8y=56 describes a circle in the coordinate plane. Determine the center of this circle.
(7,4)
(−7,−4)
(7,−4)
(−7,4)
P=2N−3
P=tN+5
In the system of equations, t is a constant. If the system has no solution, what is the value of t?
2
3
4
5
Find an equivalent expression
for 
?
A comprehensive survey was administered to 50 art history professors at Texan public colleges, asking which online platforms they prefer for conducting virtual classes. What is the broadest group to which the findings of this survey can be extrapolated?
All professors in Texan public colleges
All art history professors in Texan public colleges
All art history professors in the United States
All professors in the United States
In County Y, Mrs. Smith's seventh-grade class of 32 students participated in a health survey. It was found that 25% of the students ate fruits daily. If there are 2,200 seventh-grade classes in the county, each having an average of 32 students, what is the most accurate estimation for the number of seventh-grade students who do not consume fruits daily?
48,000
50,000
52,800
55,000
A bookstore sells a book for 12 dollars and sells 80 copies per day. When the price is lowered to 10 dollars, they sell 100 copies. Assuming a linear price-quantity relationship, what will be the quantity sold per day if the price is $11?
Answer:
In a law firm with 15 employees, the average number of years they've worked is 9. After a senior member retires, the average experience drops to 8.2 years. How many years did the senior member work at the law firm?
18.4
19.6
20.2
21.5
For the system of equations y=2x+1 and y=4x−1, how many solutions exist?
Exactly One
Exactly Two
Infinitely many
Zero
A bookstore sells two types of books: hardcovers for 20 dollars each and paperbacks for 10 dollars each. If the store sold a total of 25 books for a combined value of 400 dollars, how much money in dollars was made from the sale of hardcover books?
100
200
300
400
A bakery produces cakes and cookies. The oven can bake up to 50 items per hour. Each cake takes 2 slots in the oven, and each cookie takes 1 slot. The bakery wants at least twice as many cakes as cookies. Let k represent the number of cakes and c represent the number of cookies. What system of inequalities represents this?
2k+c≤50,k≤2c
2k+c≥50,k≤2c
2k+c≥50,k≥2c
2k+c≤50,k≥2c
Given the equation z=50x+100, if z=400, what is the value of x?
6
7
8
9
An
isosceles right triangle has a perimeter that can be represented as 236+ 118
inches. What is the length of a
single leg of this triangle?
67
118
128
236
You stumble upon a drawer filled with 8 black socks and 12 white socks. If you had to grab a sock blindly, what's the probability that it's a black sock?
The function g(x) is defined by g(x)=(x+3)(x+1). The graph of g(x) in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of g?
−6<x<−4
−4<x<−1
−1<x<1
3<x<4
Imagine a cuboid with dimensions 50 cm by 60 cm by 70 cm. A solid cylinder with a radius of 20 cm and height of 50 cm is situated inside the cuboid such that the cylinder's base touches the bottom of the cuboid. How much space, rounded to the nearest cubic centimeter, in the cuboid is not occupied by the cylinder?
62,832cm3
210,000cm3
147,168cm3
145,000cm3
Given theequation 5(3x2+qx+7)−20x(q+2)=15x2−130x+35, where q is a constant. Determine the value of q.
Answer:
Two cubes are made of different materials. Cube A has a density of 590 kg/m³ and an edge length of 1.1 m, while Cube B has a density of 690 kg/m³ and an edge length of 1.4 m. Using the density formula ρ = m/V or m = ρV and knowing that the volume of a cube is given by V = (edge length)³, determine the ratio of the mass of Cube A to the mass of Cube B. Round your answer to the nearest tenth.
0.2
0.3
0.4
0.5
What is the value of x when 5x−8=2x+1?
3
2
1
0
Given the algebraic expression 
where q and p are integers, and it simplifies to x+q for x≠q, what could p be?
q2
2q
q+1
q-1
The circle shown has two secants that pass through the center of the circle. Angles a and b are formed from the two secants and are a=60° and b=120° respectively. Assuming the radius of the circle is 10 units, what is the arc length of the minor arc?
10.47
12.41
13.24
15.43
The function f(x) is shown in the graph with an x-intercept of −1 and a y intercept of 2. If a function g (not shown) is defined as g(x)=ax+b, what is one possible value of a such that the x-intercept and y-intercept of f(x) is the same as the x-intercept and y-intercept of g(x).
4
2
−2
−5
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.