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 5 Grid Ins Questions with Answer Keys | SAT Online Tutor AMBiPi.
SAT 2022 Math Practice Test 5 Grid Ins Questions with Answer Keys
SAT Math Practice Online Test Question No 1:
A garden, measuring 10 feet by 12 feet, contains individual plots that measure 1 foot by 1 foot. 30% of the plots contain bell peppers, 30% contain cherry tomatoes, 25% contain squash, and the remaining 15% contain eggplants. Each bell pepper plot produces 2 bell peppers every 5 days, a tomato plot produces 4 cherry tomatoes every 6 days, a squash plot produces 1 squash every 15 days, and an eggplant plot produces 3 eggplants every 10 days.
In a 30-day month, how many vegetables are produced by the 10 × 12 foot garden?
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Correct Answer: 1374
First, calculate the number of plots in the garden. Given that the garden measures 10 feet by 12 feet and each plot is one foot by one foot, there are 10 × 12 = 120 total plots.
Next, calculate the number of each type of vegetable plot as follows:
120 × 0.3 = 36 bell pepper plots
120 × 0.3 = 36 cherry tomato plots
120 × 0.25 = 30 squash plots
120 × 0.15 = 18 eggplant plots
According to the question, 2 bell peppers are grown every 5 days on each of the 36 pepper plots. That means that all the pepper plots together grow 2 × 36 = 72 peppers in 5 days. To determine how many peppers would grow in a month, set up a proportion.
72 peppers/5 days = x/30 days
Cross-multiply, and then divide by 5 to find that the garden produces 432 peppers for the month. Repeat these steps with the other 3 vegetables. The 36 tomato plots produce 144 tomatoes every 6 days. Together, they produce 720 tomatoes in the month. The 30 squash plots produce 30 squash every 15 days, for a total of 60 squash in a month.
Finally, the 18 eggplant plots grow 54 eggplants every 10 days, which means during a 30-day period the garden will produce 162 eggplants. The total number of vegetables can be calculated as 432 bell peppers + 720 cherry tomatoes + 60 squash + 162 eggplants = 1,374 vegetables.
SAT Math Practice Online Test Question No 2:
If tanθ = 12/5, then cos θ =
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Correct Answer: 5/13 or 0.384 or 0.385
Draw a right triangle and label a non-right angle θ. SOHCAHTOA tells you that the tangent is opposite/adjacent, so the leg opposite θ is 12 and the leg adjacent to θ is 5.
Cosine is adjacent/hypotenuse, so you need to find the hypotenuse of the triangle. You can use the Pythagorean theorem, or you can recognize this as a 5-12-13 Pythagorean triplet.
The hypotenuse is therefore 13. The leg adjacent to θ is still 5, so cos θ = 5/13.
SAT Math Practice Online Test Question No 3:
Given that the equation 3x2 + 2x – 8 = 0 has two distinct solutions, what is the value of the smaller solution subtracted from the larger solution?
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Correct Answer: 10/3
3x2 + 2x – 8 = (-2 – x)(4 – 3x) = 0. Solving -2 – x = 0 and 4 – 3x = 0 for x, we find that the two solutions for x are -2 and 4/3.
The question asks us to subtract the value of the smaller solution from the larger solution. This difference is 4/3-(-2) = 4/3 + 6/3 = 10/3.
SAT Math Practice Online Test Question No 4:
y = x
(y – 2)2 – 4 = -x
The system of equations above intersects at two points. What is the sum of the coordinates of the point of intersection in Quadrant I?
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Correct Answer: 6
Substitute x for y in the second equation to get (x – 2)2 – 4 = –x. Expand the left side of the equation to get (x – 2)(x – 2) – 4 = –x or x2 – 4x + 4 – 4 = –x.
Simplify the equation to get x2 – 4x = –x. Set the equation to 0 to get x2 – 3x = 0.
Factor an x out of the equation to get x(x – 3) = 0. Therefore, either x = 0 or x – 3 = 0, and x = 3.
According to the question, the point of intersection is in quadrant I, where the x and y values are both positive. Therefore, x = 3 and y = 3. The sum of 3 + 3 = 6. The correct answer is 6.
SAT Math Practice Online Test Question No 5:
Marty is planning which crops to plant on his farm for the upcoming season. He has enough seed to plant 4 acres of wheat and 7 acres of soybeans, but the total area of farmland he owns is only 9 acres. He earns $90 per acre for every acre of wheat planted and $120 for every acre of soybeans planted, and he must pay a 10% tax on all money he earns from selling his crops. What is the maximum profit, in dollars, that Marty can earn from planting wheat and soybeans this season?
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Correct Answer: 918
In order to find the greatest profit, maximize the number of acres of soybeans Marty plants, since soybeans bring in more money per acre than does wheat. At most, Marty can plant 7 acres of soybeans.
Therefore, the most money he can make on soybeans is 7 × 120 = 840. He then has 9 – 7 = 2 acres left on which to plant wheat. The money he makes from this wheat is 2 × 90 = 180.
The total amount Marty makes before taxes is therefore 840 + 180 = 1,020. The tax on this money equals 1,020 × 0.10 = 102.
Subtract the amount Marty pays in taxes to get 1,020 – 102 = 918 profit. The correct answer is 918.
SAT Math Practice Online Test Question No 6:
The daily recommended serving of protein is 50 grams. A nutritional bar contains 32% of the daily recommended serving of protein and 10% of the daily recommended serving of fat. If the nutritional bar contains 700% more grams of protein than grams of fat, what is the daily recommended serving of fat, in grams? (Disregard units when gridding your answer.)
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Correct Answer: 20
First, determine the grams of protein in the bar. If the bar contains 32% of the daily recommended serving of protein, and the daily recommended serving of protein is 50 grams, then the bar contains 0.32 × 50 = 16 grams of protein.
Next, determine the grams of fat in the bar by using the percent change equation: percent change = difference/original x 100.
The percent change is 700, and the original is the grams of fat (because percent more means the original is the smaller number), which means 700 = (16 – x)/x *100.
Divide both sides by 100: 7 = (16 – x)/x. Multiply both sides by x to get 7x = 16 – x.
Add x to both sides to get 8x = 16. Divide both sides by 8 and you find x = 2. That is the number of grams of fat in the bar.
To find the daily recommended serving of fat, translate English to math. 2 is 10% of the daily recommended serving, so if the daily recommended serving is y, 2 = 0.10y. Divide both sides by 0.10, and you find that the daily recommended serving of fat is 20.
SAT Math Practice Online Test Question No 7:
1 < (c – 1)2 < 36
What is the greatest integer solution to the inequality above?
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Correct Answer: 6
Try Plugging In different values of c to see which ones work. Make a table to keep track of all the numbers. 
The largest value of c that works without hitting the boundaries of the inequality is 6, so the correct answer is 6.
SAT Math Practice Online Test Question No 8:
Set R consists of all the one-digit prime numbers. Set S contains all of the elements of Set R, as well as an additional positive integer, x.
Michael wants to change the value of x so that the mean of Set S is equal to the median of Set S and for Set S to have no mode. What value of x would accomplish his goal?
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Correct Answer: 8
The additional positive integer x cannot equal 2, 3, 5, or 7 (otherwise there would be a mode).
Next, determine what the median could be for various ranges of x. If x is less than 2, then the set would be, in consecutive order, {x, 2, 3, 5, 7}, making the median 3. Try this set. If the median equals the mean, then the sum of the elements divided by 5 (the number of elements) must equal 3: (x + 2 + 3 + 5 + 7)/5 = 3.
Multiply both sides by 5 and combine like terms: x + 17 = 15. Subtract 17 from both sides, and you find x = -2. However, x must be a positive integer, so this doesn’t work.
Try a new median. If x = 4, then the set is {2, 3, 4 (x), 5, 7), with a median of 4. However, the mean is (2 + 3 + 4 + 5 + 7)/5 = 5.25, not 4, so this doesn’t work.
If x is 6 or greater, the set would either be {2, 3, 5, 6 (x), 7} or {2, 3, 5, 7, x}. In either case, the median is 5. Set up the average equal to the median of 5: (2 + 3 + 5 + 7 + x)/5 = 5. Multiply both sides by 5 and combine like terms: 17 + x = 25. Subtract 17 from both sides, and you find that x = 8.
SAT Math Practice Online Test Question No 9:
3h – j = 7
2h + 3j = 1
Based on the system of equations above, what is the value of h?
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Correct Answer: 2
Whenever there are two equations with the same two variables, they can be solved simultaneously by adding or subtracting them. The key is to get one variable to disappear.
Multiply the first equation by 3 to get 9h – 3j = 21. Stack the equations and add them. [(9h – 3j = 21) + (2h + 3j = 1)] = (11h = 22). Therefore h = 2, and the correct answer is 2.
SAT Math Practice Online Test Question No 10:
Abeena is making punch for a winter party in a punch bowl that can hold at most 9 quarts. She wants to get as much vitamin C in her punch as possible, so she is using only orange juice and grape juice. She has 6 quarts of orange juice, which has 2 grams of vitamin C per quart, and 7 quarts of grape juice, which has 1 gram of vitamin C per quart. If there are 4 cups in a quart, what is the greatest possible amount of vitamin C, in grams, that Abeena can have in one cup of her punch?
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Correct Answer: 5/12 or 0.416 or 0.417
Start by calculating the amount of vitamin C in the entire punch bowl and then calculate what the equivalent in only one cup would be.
To maximize the amount of vitamin C in the punch bowl, Abeena will need to add as much orange juice, which has the highest concentration of vitamin C, as she can.
Given that the punch bowl holds 9 quarts, she will pour in 6 quarts of orange juice (which is all she has) and 3 quarts of grape juice. The amount of vitamin C can be calculated as follows: 
Therefore, the 9 quarts of a punch contain 15 grams of vitamin C. Next, convert the quarts to cups. The question tells us that there are 4 cups in 1 quart. Therefore, 9 × 4 = 36 cups in 9 quarts.
To figure out how much vitamin C is in one cup, set up the following proportion: 15 grams /36 cups = x grams/1 cup. Cross-multiply to get 36x =15, or x = 15/36 = 5/12.
The correct answer is 5/12. Only reduce a fraction if it is necessary to make it fit in the grid-in box.
