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Module I: Math
Consider a magnetic field passing through a flat circular surface perpendicular to it, where the magnetic flux through the surface is given by the product of the magnetic field's strength and the area of the surface. Suppose the surface consists of two adjacent circles. The radius of the larger circle is four times the radius of the smaller circle, measured in meters. A magnetic field with a strength of 15.00 teslas passes uniformly through this surface, which is perpendicular to the field. Given that the total magnetic flux through this surface is 7,000 teslas ⋅⋅square meters, determine the magnetic flux, in teslas ⋅⋅ square meters, through the larger circle, rounded to the nearest whole number.
The graph shows the height of a plant over time. The vertical axis represents the height of the plant in centimeters, while the horizontal axis represents time in weeks. Given that the curve represents the growth of the plant, which of the following best describes the plant's growth pattern?
The plant grows at a constant rate.
The plant grows at an increasing rate.
The plant grows at a decreasing rate.
The plant does not grow at all.
In a survey of 12,345 randomly selected homeowners in a large city, those surveyed reported an average monthly electricity bill of 120 dollars in the summer months, as compared to 110 dollars per month in the summer two years ago. Both estimates had a margin of error of 5 dollars at the 95% confidence level. Which of the following is a reasonable claim to make based on this sample?
All homeowners in the city had monthly electricity bills between 115 dollars and 125 dollars last summer.
95% of homeowners in the city had monthly electricity bills between 115 dollars and 125 dollars last summer.
It is plausible that the average monthly electricity bill of homeowners in the city remained the same in the summer months of last year as it was in the summer two years ago.
The average monthly electricity bill for homeowners in the city last summer was 15 dollars higher than in the summer two years ago, with a 95% confidence interval between 115 dollars and 125 dollars.
A bakery sells three types of cupcakes: chocolate, vanilla, and strawberry. On a certain day, the bakery made a batch consisting of 120 cupcakes in total. The number of chocolate cupcakes is twice the number of vanilla cupcakes, and the number of strawberry cupcakes is five more than the number of chocolate cupcakes. How many vanilla cupcakes did the bakery make?
3x−y=7. x+y=15. If the ordered pair (x,y) satisfies the system of equations, what is the value of x?
A fair 6-sided die is rolled four times. What is the probability of rolling an odd number at least once?
1−
1− (
)4
()4
In triangle ABC, angle C is a right angle, and the lengths of the sides are such that AB = 10 units, and AC = 8 units. What is the sine of angle B?
A cone has a diameter of 8 inches and a height of 12 inches. What is the volume, in units of π cubic inches, of the cone?
Sarah’s house is a 12-minute bike ride or an 8-minute car ride away from her friend’s house. The car service arrives once every 10 minutes, and the number of minutes, t, that Sarah waits for the car varies between 0 and 10. Which of the following inequalities gives the values of t for which it would be faster for Sarah to ride her bike to her friend’s house?
t−8<12
t−8>12
t+8<12
t+8>12
Square T has a side length of c meters. Square U has a perimeter that is 160 meters more than the perimeter of square T. What is the expression for the area of square U in terms of c?
(c+40)2
(c+50)2
(c+80)2
(c+160)2
A factory allocates 160 hours to produce two types of widgets, X and Y. The equation 5x+3y=160 represents this, where x and y are the numbers of widgets X and Y produced, respectively. If 20 units of Y are produced, how many more hours are spent producing X compared to Y?
If the polynomial p(x)=x3−6x2+11x−6 is divided by x−2, what is the remainder?
Each side of a 40-sided polygon has one of three lengths. The number of sides with length 10 cm is 4 times the number of sides n with length 5 cm. There are 8 sides with length 6 cm. Which equation must be true for the value of n?
n+4n+8=28
n+4n+8=40
8n−8=40
40n+8=48
In two stores, Store A and Store B, the following numbers of shoes were sold: Store A sold 40 casual shoes, 20 sports shoes, and 10 formal shoes, while Store B sold 30 casual shoes, 25 sports shoes, and 20 formal shoes. A customer buys a shoe at random from Store A. What is the probability that the shoe bought is a sports shoe?
What is the maximum value of the function f defined by f(x)=−(x−2)2+16?
0
4
16
18
A group of friends decided to create a large painting made up of smaller square tiles. Each tile has a side length of 5 centimeters. They arrange the tiles in a rectangular pattern, 4 tiles wide and 6 tiles long. Calculate the total area of the painting in square meters. (Note: 1 meter = 100 centimeters)
Mia drives an average of 150 miles each week. Her car can travel an average of 30 miles per gallon of gasoline. Mia would like to reduce her weekly expenditure on gasoline by 10 dollars. Assuming gasoline costs 3 dollars per gallon, how many miles (rounded to nearest whole number) less does she need to drive each week.
Two lines, L1 and L2, are represented by the equations L1:y=2x+3 and L2:y=ax+5, where a is a constant. These lines intersect at the point (1,5). What is the value of a?
A scientist is studying a population of bacteria that doubles every 3 hours. If the initial population is 500 bacteria, and a medicine introduced into the environment removes 10% of the bacteria population every 3 hours, how many bacteria will there be after 18 hours?
16,004
17,006
64,002
128,005
On February 10, 2021, there were 85 million tablet users in Country Z. The major providers were Sigma, Tau, Upsilon, Phi, and Psi. By June 15, 2021, the number of tablet users in Country Z increased to 120 million. If a tablet user in Country Z on June 15, 2021 is randomly selected, the probability they are a Sigma user is 0.25. There were q million Sigma users in Country Z on June 15, 2021. Rounded to the nearest million, what is the value of q?
A car rental service charges a flat fee of 50 dollars per rental and then an additional 0.25 dollars per mile driven. If Emily rents a car and is charged a total of 137.50 dollars, how many miles did she drive the car?
The graph of y = g(x) is shown in the xy-plane and has x-intercepts at x = -2, 0, and 4. What is the value of g(-2)+g(0)+g(4)?
−2
0
2
4
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.