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Module I: Math
What is the maximum value of the function f defined by f(x)=−(x−5)2+25?
Answer:
If a line passes through the points (2,3) and (5,11), what is its slope?
Answer:
Line m is defined by y=4x+3. A line n is parallel to line m in the xy-plane. What is the slope of line n?
Answer:
The graph shown represents an exponential function in the xy-plane. The graph can represent the population of a species in a restricted habitat over time, x, in years. Assuming ideal conditions without any limiting factors, what is the best interpretation of the behavior of the graph as x increases?
The population decreases rapidly.
The population remains constant.
The population increases at a decreasing rate.
The population increases at an increasing rate.
If 5x−3=22, what is the value of x?
Answer:
Solve the equation 2∣4−x∣+3∣4−x∣=40. What is the positive solution for x?
12
15
Calculate the value x where f(x)=3x2+4x−5 is minimized.
Answer:
There are 80 members in a book club. A sample of the book club members was selected at random and asked whether they are interested in participating in a monthly online book discussion. Of those surveyed, 25% responded that they are interested in participating in the online discussion. Based on this survey, which of the following is the best estimate of the total number of book club members who are interested in participating in the online discussion?
20
40
60
80
The measure of angle C is 
radians.
The measure of angle D is 
radians
greater than the measure of angle C. What is the measure of
angle D , in degrees?
Answer:
The number x is 65% less than the positive number y. The number z is 50% greater than x. If w is 20% less than z, then w is how many times y?
Answer:
A local school conducted a survey among 500 students to determine their favorite extracurricular activity. The students could choose between sports and arts. The results were sorted by grade level and are summarized as follows: 120 Grade 9 students prefer sports and 30 prefer arts, 100 Grade 10 students prefer sports and 50 prefer arts, 80 Grade 11 students prefer sports and 70 prefer arts, and 20 Grade 12 students prefer sports and 30 prefer arts. The school has a total of 2,000 students. Based on this information, what is the best estimate of the number of students who prefer sports?
Answer:
The total area of a mountainous region is 180 square kilometers, of which 40 square kilometers are uninhabitable due to mountains. If the region had a population of 360,000 people in the year 2020, which of the following is closest to the population density, in people per square kilometer of habitable land area, of the region at that time?
2,571
4,542
5,542
10,542
A household consumes 300 kWh of energy at 15 degrees Celsius. When the temperature rises to 25 degrees Celsius, the consumption increases to 350 kWh. Assuming a linear relationship, what is the energy consumption, in kWh, at 20 degrees Celsius?
Answer:
The equation models the population, P, of a certain species of fish yy years after a conservation project begins: P=2,000(1.03)y. Of the following, which equation models the population of the species m months after the conservation project begins?
P=2,000(1.0025)12m
P=2,000(1.03)12m
P=
P=2,000(1.425)m
In a quiz, 8 participants scored an average of 35 points. After removing the participant with the lowest score, the average increases to 38 points. What was the lowest score?
Answer:
A circle in the xy-plane has its center at (−2,3). Line m is tangent to this circle at the point (1,5). What is the slope of line m?
Answer:
In an electrical circuit, the voltage V, in volts, across a resistor is related to the current I, in amperes, flowing through it and the resistance R, in ohms, of the resistor by the formula V=IR+6I2. Suppose the resistance R is 4 ohms, and the current I is 2 amperes. Find the voltage V across the resistor.
6 V
16 V
32 V
53 V
A survey was conducted with 500 pet owners to understand their preferences for pet food brands. The survey found that 46% of the respondents prefer Brand X for their pets, with a margin of error of 4.2%. What is the spread between the upper and lower limit of the preference for Brand X, written in percentages.(Input 1 as 1%).
Answer:
If 3(3x−2)=4(3x−2)+5, what is 3x−2?
Answer:
If a sphere has a volume of 36πx3 cubic units, find the surface area of the sphere in terms of x.
24πx2
36πx2
54πx2
65πx2
A bakery produces loaves of bread at a constant rate. It baked 250 loaves in the first 3 hours. What is the total number of hours needed to bake 750 loaves?
Answer:
The number of radians in a 225-degree angle can be written as aπ, where a is a constant. What is the value of a?
Answer:
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.