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 Test 13 Grid Ins Questions with Answer Keys | SAT Online Tutor AMBiPi.
SAT 2022 Math Test 13 Grid Ins Questions with Answer Keys
SAT Math Practice Online Test Question No 1:
An exponential function is given in the form f(x) = a • bx . If f(0) = 3 and f(1) = 15, what is the value of f(–2)?
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Correct Answer: 3/25 or .12
Difficulty: Hard
Category: Passport to Advanced Math / Functions
Strategic Advice: When a question involving a function provides one or more ordered pairs, substitute them into the function to see what information you can glean.
Getting to the Answer: Start with x = 0 because doing so often results in the elimination of a variable.
f(x) = a ⦁ bx.
f(0) = a ⦁ b0
3 = a ⦁ b0
3 = a ⦁ 1
3 = a
Now you know the value of a, so the equation looks like f(x) = 3 o bx. Substitute the second pair of values into the new equation:
f(x) = 3 ⦁ bx
f(x) = 3 ⦁ b1
15 = 3 ⦁ b1
15 = 3b
5 = b
The exponential function is f(x) = 3 o 5x. The final step is to find the value being asked for, f(-2). Substitute -2 for x and simplify: f(-2) = 3 ⦁ 5-2 = 3/52 = 3/25
Grid this in as 3/25 or .12.
SAT Math Practice Online Test Question No 2:
Many sailboat manufacturers sell kits that include instructions and all the materials needed to build a simple sailboat. The figure shows the finished dimensions of a sailboat from such a kit. The instructions indicate that cosx° = b, but do not give the value of b. What is the value of b?
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Correct Answer: 2/3 or .666 or .667
Difficulty: Hard
Category: Additional Topics in Math / Trigonometry
Strategic Advice: Trig functions usually apply to right triangles, so draw in the altitude of the triangle to get a better picture of which parts of the triangle are useful. Then use the identity cos x = adj/hyp.
Getting to the Answer: Two angles of the triangle have equal measures, so the triangle is isosceles, which means that drawing an altitude from the top to the base will bisect the base, resulting in two smaller right triangles as shown here:
Now, use the identity cosx° = adjacent/hypotenuse = 8/12, so b = 8/12, which can be simplified to 2/3.
SAT Math Practice Online Test Question No 3:
Body mass index, or BMI, is one of several measures used by doctors to determine a person’s health as indicated by weight and height. Low-density lipoprotein, or LDL cholesterol, known as the “bad” cholesterol, is another health indicator and consists of fat proteins that clog arteries. Following are the results of a study showing the relationship between BMI and LDL for 12 individuals and the line of best fit for the data.
How many of the 12 people have an actual LDL that differs by 10 or more mg/dL from the LDL predicted by the line of best fit?
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Correct Answer: 3
Difficulty: Easy
Category: Problem Solving and Data Analysis / Scatterplots
Strategic Advice: This question takes just a bit of patience and careful reading and interpretation of the graph.
Getting to the Answer: Each grid line along the vertical axis represents 5 units, so look for points that are at least two grid lines away from the line of best fit. The people who have BMIs of 20, 25, and 28 have LDLs that are 10 or more mg/dL greater than the LDLs predicted by the line of best fit. This represents 3 people.
SAT Math Practice Online Test Question No 4:
In recent years, car manufacturers have started producing hybrid vehicles, which run on both electricity and gasoline, resulting in significantly higher gas mileage. Suppose the odometer of a hybrid car, which shows how many miles the car has traveled, reads 4,386 miles. If the car averages 48 miles to the gallon of gas and currently has 12 gallons in the tank, what should the odometer reading be when the tank is empty?
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Correct Answer: 4962
Difficulty: Easy
Category: Heart of Algebra / Linear Equations
Strategic Advice: Create a linear equation to keep the information straight. The total number of miles driven by the car is equal to the miles per gallon times the number of gallons in the tank added to the existing number of miles on the odometer.
Getting to the Answer: The equation is y = 48x + 4,386. You are given the x-value, 12 gallons, so simply substitute it for x and solve for y.
y = 48(12) + 4,386
y = 576 + 4,386
y = 4,962
SAT Math Practice Online Test Question No 5:
Rasha volunteers at a charity that helps feed the homeless. He collects donations and then uses the money to buy food for care packages. This week, he collected $145. Each care package will include canned vegetables and bags of rice in the ratio of 3:1. The cans cost $0.89 each, and the bags of rice cost $3.49 each. Using the given ratio, what is the maximum number of complete vegetable/rice care packages Rasha can make? ≤
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Correct Answer: 23
Difficulty: Medium
Category: Heart of Algebra / Inequalities
Strategic Advice: When a question asks about a maximum (or minimum) amount, it usually means you need to create and solve an inequality.
Getting to the Answer: Write the inequality in words first. The cost of 3 cans of vegetables plus the cost of 1 bag of rice, all multiplied by the number of care packages Rasha makes, must be less than or equal to the amount of money he collected, $145. Because you are not asked to differentiate between cans and rice, they can be represented by the same variable. Just don’t forget to multiply the cost of 1 can by 3 first ($0.89 × 3 = $2.67). Let p represent the number of care packages:
(2.67 + 3.49)p ≤ 145
6.16p ≤ 145
p ≤ 23.54
Be careful, the question asks for complete care packages, so he can make only 23.
SAT Math Practice Online Test Question No 6:
(4 + √-16)/(2 + √-4)
Use the definition √-1 = i to write the expression above in simplest form.
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Correct Answer: 2
Difficulty: Medium
Category: Additional Topics / Imaginary Numbers
Strategic Advice: Because √-1 = i, rewrite each number under the radical as a product of –1 and itself. Then take the square root of each. If possible, cancel any factors that are common to the numerator and the denominator.
Getting to the Answer: (4 + √-16)/(2 + √-4)
= 4 + [√16 x √(-1)] / 2 + [√4 x (-1)]
= 4 + 4i/2 + 2i
= 2
SAT Math Practice Online Test Question No 7:
A restaurant sent out surveys to determine how long customers are willing to wait for a table on Friday night versus Saturday night. Participants randomly received either a Friday night or a Saturday night survey. Results are shown in the bar graph below.
If a customer is chosen at random from all of the survey respondents, what is the probability that the customer is willing to wait at least 30 minutes for a table?
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Correct Answer: 49
Difficulty: Medium
Category: Problem Solving and Data Analysis / Statistics and Probability
Strategic Advice: Identify the parts of the bar graph that you will need to answer this question. You need to find a probability, which is always given by the number of favorable outcomes (willing to wait at least 30 minutes) divided by the total number of outcomes (all the responses to the survey).
Getting to the Answer: First, total the number of customers willing to wait 30 minutes or more. Be careful—the question doesn’t specify Friday or Saturday, so use both days:
38 + 45 + 33 + 43 + 20 + 40 + 9 + 17 = 245
Now, find the total number of people who responded to the survey. You don’t need to start over—just add the previous sum to the number of people willing to wait less than 30 minutes:
245 + 70 + 75 + 46 + 64 = 500
This means the probability that someone will be willing to wait more than 30 minutes is 245/500 = 49/100. This fraction won’t fit in the answer grid, so enter your answer as a decimal, .49.
SAT Math Practice Online Test Question No 8:
The graph above shows Umberto’s distance from home over a one-hour period, during which time he first went to the bank, then went to the post office, and then returned home. How many minutes did Umberto spend at the bank and at the post office combined?
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Correct Answer: 25
Difficulty: Easy
Category: Passport to Advanced Math / Functions
Strategic Advice: Pay careful attention to the axis labels as you read the answer choices. Time is graphed on the x-axis and distance is graphed on the y-axis. Try to visualize what is happening as Umberto runs his errands.
Getting to the Answer: Umberto was inside the bank and inside the post office when time was passing, but his distance was not changing (because he was stopped). This means you’re looking for the portions of the graph where the line is horizontal (because distance is graphed on the vertical axis and you want no vertical change). This occurs from (10, 4) to (20, 4) and from (35, 6) to (50, 6). This means he spent 10 minutes in the bank and 15 minutes in the post office, for a total of 25 minutes in both.
SAT Math Practice Online Test Question No 9:
A bag valve mask is used to resuscitate patients who have stopped breathing. It consists primarily of a bag attached to a mask. The mask is fitted to the patient’s nose and mouth. Squeezing the bag pushes air through the mask and into the patient’s lungs. For sanitary reasons, most of these masks are disposable. Suppose a hospital’s mask supplier sells them in boxes of 48 or 144, and the supplier has 35 boxes in stock. If the supplier has 2,832 total masks in stock, how many masks would the hospital receive if it ordered all of the boxes of 144 that the supplier has in stock?
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Correct Answer: 1728
Difficulty: Hard
Category: Heart of Algebra / Systems of Linear Equations
Strategic Advice: You can tell from the length of the question that you can simply skim the first couple of sentences. You also need to make sure you answer the right question (how many masks the hospital would receive if it ordered all of the boxes of 144 the supplier has in stock).
Getting to the Answer: Create a system of linear equations where x represents the number of boxes with 48 masks and y represents the number of boxes with 144 masks. The first equation should represent the total number of boxes, x + y = 35. The second equation should represent the total number of masks. Because x represents boxes with 48 masks and y represents boxes with 144 masks, the second equation is 48x + 144y = 2,832. Now solve the system using substitution. Solve the first equation for either variable; then substitute the result into the second equation:
x + y = 35
x = 35 – y
48(35 – y) + 144y = 2,832
1,680 – 48y + 144y = 2,832
96y = 1,152
y = 12
So 12 boxes have 144 masks. Because the question asks about boxes of 144, you don’t need to find the value of x—but you’re not done yet. The question asks how many masks the hospital would receive if it buys all of the boxes of 144 the supplier has, not the number of boxes. The hospital would receive 12 × 144 = 1,728 masks.
SAT Math Practice Online Test Question No 10:
A company sponsors a health program for its employees by partnering with a local gym. If employees pay for a yearlong membership at this gym, then for every day the employee uses his or her swipe card to enter the gym (and work out), the company reimburses the employee 0.2% of the cost of the $220 membership. Additionally, any employee who goes to the gym more than 60% of the days in the year gets one bonus paid day off of work. The company uses a 365-day year.
Giving employees additional paid time off also costs the company money because it is paying the salary of an employee who is not actually doing any work on that day. The pie graph below shows gym usage for the 246 employees who participated in health program.
If the average salary of workers who participated was $14.90 per hour and one day off equals 8 hours, how much did the health program day-off benefit cost the company? Round your answer to the nearest whole dollar.
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Correct Answer: 4887
Difficulty: Hard
Category: Problem Solving and Data Analysis / Rates, Ratios, Proportions, and Percentages
Strategic Advice: Again, break the question into short steps so that your calculations don’t get jumbled up.
Getting to the Answer: Step one: Determine how many days an employee needed to visit the gym to earn the bonus day off by multiplying the number of days in the year, 365, by 60%. The result is 219, but the question says more than 60% of the days, so an employee must have gone 220 days to qualify for the bonus day off.
