Welcome to AMBiPi (Amans Maths Blogs). SAT (Scholastic Assessment Test) is a standard test, used for taking admission to undergraduate programs of universities or colleges in the United States. In this article, you will get SAT 2022 Math Practice Test 16 Online Grid Ins Questions with Answer Keys | SAT Online Classes AMBiPi.
SAT 2022 Math Practice Test 16 Online Grid Ins Questions with Answer Keys
SAT Math Practice Online Test Question No 1:
Some doctors base the dosage of a drug to be given to a patient on the patient’s body surface area (BSA). The most commonly used formula for calculating BSA is BSA = √wh/√3,600, where w is the patient’s weight (in kg), h is the patient’s height (in cm), and BSA is measured in square meters. How tall (in cm) is a patient who weighs 150 kg and has a BSA of 2√2 m2?
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Correct Answer: 192
This looks like a word problem, but don’t let it intimidate you. Once you read it, you’ll see that it boils down to substituting a few given values for the variables and solving the equation.
Before you start substituting values, quickly check that the units given match the units required to use the equation—they do, so proceed. The patient’s weight (w) is 150 and the patient’s BSA is 2√2, so the equation becomes 2√2 = √150h/√3,600. The only variable left in the equation is h, and you are trying to find the patient’s height, so you’re ready to solve the equation. To do this, square both sides of the equation and then continue using inverse operations. Be careful when you square the left side—you must square both the 2 and the root 2.
2√2 = √150h/√3,600
(2√2)2 = (√150h/√3,600)2
22 (√2)2 = 150h/3,600
4(2) = 150h/3,600
28,800 = 150h
192 = h
SAT Math Practice Online Test Question No 2:
In the figure above, AB, CD, and EF are the diameters of the circle. If y = 2x – 12, and the shaded area is 1/5 of the circle, what is the value of x?
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Correct Answer: 40
Because AB, CD, and EF are diameters, the sum of x, y, and the interior angle of the shaded region is 180 degrees. The question tells you that the shaded region is 1/5 of the circle, so the interior angle must equal 1/5 of the degrees in the whole circle, or 1/5 of 360.
Getting to the Answer: Use what you know about y (that it is equal to 2x – 12) and what you know about the shaded region (that it is 1/5 of 360 degrees) to write and solve an equation.
x + y + 1/5(360) = 180
x + (2x – 12) + 72 = 180
3x + 60 = 180
3x = 120
x = 40
SAT Math Practice Online Test Question No 3:
Chemical Makeup of One Mole of Chloroform
A chemical solvent is a substance that dissolves another to form a solution. For example, water is a solvent for sugar. Unfortunately, many chemical solvents are hazardous to the environment. One eco-friendly chemical solvent is chloroform, also known as trichloromethane (CHCl3). The table above shows the chemical makeup of one mole of chloroform.
Carbon makes up what percent of the mass of one mole of chloroform? Round your answer to the nearest whole percent and ignore the percent sign when entering your answer.
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Correct Answer: 10
Getting to the Answer: To use the formula, find the part of the mass represented by the carbon; there is 1 mole of carbon, and it has a mass of 12.011 grams. Next, find the whole mass of the mole of chloroform; 1 mole carbon (12.011 g) + 1 mole hydrogen (1.008 g) + 3 moles chlorine (3 × 35.453 = 106.359 g) = 12.011 + 1.008 + 106.359 = 119.378.
Now use the formula: Percent = 12,011/119.378 x 100%
= 0.10053 x 100% = 10.053%
Before you grid in your answer, make sure you follow the directions—round to the nearest whole percent, which is 10.
SAT Math Practice Online Test Question No 4:
A company is buying two warehouses near their production plants in two states, New York and Georgia. As is always the case in the real estate market, geographic location plays a major role in the price of the property. Consequently, the warehouse in New York costs $30,000 less than four times the Georgia warehouse. Together, the two warehouses cost the company $445,000. How many more thousand dollars does the New York property cost than the Georgia property?
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Correct Answer: 255
Write a system of equations with N = the cost of the New York property in thousands of dollars (so you don’t have to deal with all the zeros) and G = the cost of the Georgia property in thousands of dollars. Before entering your final answer, check that you answered the right question (how much more does the New York property cost).
The New York property costs 30 thousand dollars less than four times the cost of the Georgia property, so N = 4G – 30; together, the two properties cost 445 thousand dollars, so N + G = 445.
The system of equations is: {N = 4G – 30, N + G = 445}
The top equation is already solved for N, so substitute 4G – 30 into the second equation for N and solve for G:
4G – 30 + G = 445
5G – 30 = 445
5G = 475
G = 95
The Georgia property costs 95 thousand dollars, so the New York property costs 4(95) – 30 = 350 thousand dollars. This means the New York property costs 350 – 95 = 255 thousand more dollars than the Georgia property.
SAT Math Practice Online Test Question No 5:
A company conducted a study comparing the overall job performance of its regional managers with the length of time each one spent in the company’s management-training program. The scatterplot above shows the results of the study. What is the length of the time spent in training, in months, of the manager represented by the data point that is the greatest distance from the line of best fit (not shown)?
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Correct Answer: 8
The line of best fit is shown as follows:
Look for the point that is farthest from the line you drew, which is (8, 6). Because time is plotted along the horizontal axis, this point represents a manager who spent 8 months in the training program.
SAT Math Practice Online Test Question No 6:
If 0.004 ≤ m ≤ 0.4 and 1.6 ≤ n ≤ 16, what is the maximum value of m/n?
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Correct Answer: 1/4 or .25
The question is asking about m/n, so think about how fractions work. Large numerators result in larger values (3/2, for example is larger than 1/2,) and smaller denominators result in larger values (1/2, for example is greater than 1/4).
Getting to the Answer: The largest possible value of m/n is found by choosing the largest possible value of m and the smallest possible value for n: 0.4/1.6 = 0.25
SAT Math Practice Online Test Question No 7:
A company conducts a survey among its employees and categorizes the results based on gender and longevity (the number of years the employee has been working for the company). The Director of Human Resources wants to conduct a small follow-up focus group meeting with a few employees to discuss the overall survey results. If the HR Director randomly chooses four employees that participated in the initial survey, what is the probability that all of them will have been with the company for longer than 3 years? Enter your answer as a fraction.
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Correct Answer: 1/16
First, find the probability that if an employee is chosen at random, it will be one who has been with the company for longer than 3 years. The total number of employees who participated in the study is 38 + 30 + 15 + 19 + 54 + 48 = 204. The total number of both females and males who have been with the company longer (greater) than 3 years is 54 + 48 = 102. Therefore, the probability of choosing one employee who has been with the company longer than 3 years is: 102/204 = 1/2. This means the probability that all 4 employees would have been with the company longer than 3 years is 1/2 x 1/2 x 1/2 x 1/2 = 1/16.
SAT Math Practice Online Test Question No 8:
The Great Depression began in 1929 and lasted until 1939. It was a period of extreme poverty, marked by low prices and high unemployment. The main catalytic event to the Great Depression was the Wall Street Crash (stock market crash). The Dow, which measures the health of the stock market, started Black Thursday (October 24, 1929) at approximately 306 points.
The stock market had been in steady decline since its record high the month before. If the market had declined by 19.5% between its record high and opening on Black Thursday, what was the approximate value of the Dow at its record high? Round your answer to the nearest whole point.
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Correct Answer: 380
The question is asking for the Dow value before the 19.5% decrease to 306. This means that 306 represents 100 – 19.5 = 80.5% of what the stock market was at its record high. Fill these amounts into the equation and solve for the original whole, the record high Dow value.
0.805 x w = 306
w = 306/0.805
w = 380.124
Rounded to the nearest whole point, the record high was approximately 380 points.
SAT Math Practice Online Test Question No 9:
The table above shows the seating configuration for several commercial airplanes. The day before a particular flight departs, a travel agent books the last seat available for a client. If the seat is on one of the two Boeing 777s, what is the probability that the seat is a Business Class seat, assuming that all seats have an equal chance of being the last one available?
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Correct Answer: 1/6 or .166 or .167
To find the probability that the seat is a Business Class seat, find the total number of seats in that category (in only the bottom two rows), and divide by the total number of seats on the planes (in only the bottom two rows):
P(Business Class) = (37 + 52) / (194 + 37 + 16 + 227 + 52 + 8)
= 89/534 = 1/6 = 0.16
Grid in your answer as 1/6 or .166 or .167.
SAT Math Practice Online Test Question No 10:
When the top of a pyramid (or a cone) is cut off, the remaining bottom part is called a frustum. Suppose the top third (based on the height) of the square pyramid shown above is cut off and discarded. What will be the volume, in cubic meters, of the remaining frustum?
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Correct Answer: 9984
The figure shows a right triangle inside the pyramid. The bottom leg is given as 18 and the slant height, or hypotenuse of the triangle, is given as 30. You might recognize this as a multiple of the Pythagorean triplet, 3-4-5, which is in this case 18-24-30. This means the height of the original pyramid is 24. You now have enough information to find the volume of the original pyramid.
V = (1/3)lwh
V = (1/3)(36)(36)(24)
V = (1/3)(31,104)
V = 10,368
To determine the dimensions of the top piece that is cut off, use similar triangles.
One-third of the original height is 24 ÷ 3 = 8, resulting in a 6-8-10 triangle, making the length of the smaller leg 6, which means the length of the whole cutoff pyramid is 6 × 2 = 12. Substitute this into the formula for volume again.
V = (1/3)lwh
V = 1/3(12)(12)(8)
V = 1/3(1,152)
V = 384
Thus, the volume of the frustum is 10,368 – 384 = 9,984 cubic meters.
