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 37 Grid Ins Questions with Answer Keys | SAT Online Tutor AMBiPi*.

### SAT 2022 Math Practice Test 37 Grid Ins Questions with Answer Keys

**SAT Math Practice Online Test Question No 1:**

Given f(x) = √(164 + 5x) and g(x) = x – 8, find the value of x for which f(x) = g(x).

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**Correct Answer: 25 **

When f(x) = g(x), √(164 + 5x) = x – 8.

To solve this equation, you need to square both sides, which gives you 164 + 5x = x² – 16x + 64. (Notice that I’m using the same cool formula from Question 8 of Section 3.) To solve the equation, you need it to equal zero, which you get by subtracting 164 and 5x from both sides.

That gives you x² – 21x – 100 = 0, which factors to (x – 25)(x + 4) = 0, which makes x either 25 or –4; go for 25 because you can’t grid a negative answer.

**SAT Math Practice Online Test Question No 2:**

Find a value of x that satisfies x^{2} = 3x + 10.

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**Correct Answer: 5 **

You first want to put everything on one side of the equation, so that you can factor: x² – 3x – 10 = 0.

To the factor, you’re looking for two numbers that multiply to –10 that also have a difference of 3. The numbers –5 and 2 will do the trick: (x – 5)(x + 2) = 0.

Now set each factor equal to 0 and solve for x. You find that x is 5 or –2. Because it’s impossible to? grid in negative numbers, the answer must be 5.

**SAT Math Practice Online Test Question No 3:**

The ratio of a rectangle’s length to its width is 5:3. If its area is 60 square inches, find its width, in inches.

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**Correct Answer: 6 **

Because the ratio of length to width is 5:3, you can represent the length as 5x and the width as 3x. You know that area equals length × width, so the area = (3x)(5x), which equals 60. Simplifying, you get that 15x² = 60, and then x² = 4.

Mathematically, this result means that x is either 2 or –2. It doesn’t make sense for a rectangle to have a negative dimension, so x is 2. You’re looking for the width of the rectangle, which you called 3x and which you now know is 3(2) = 6.

**SAT Math Practice Online Test Question No 4:**

If ab = 4 and a + b = 5, what is the value of a^{2} + b^{2}?

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**Correct Answer: 17**

Watch out! Make sure you don’t fall into the trap where you think that (a + b)² = a² + b².

You need to FOIL to square a + b. If a + b = 5, you can solve for a, and determine that a = 5

**SAT Math Practice Online Test Question No 5:**

Hiring a band for a party involves a flat fee and an hourly fee. If it costs $525 to hire a band for 3 hours, and $765 to hire them for 5 hours, what is the flat fee, in dollars?

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**Correct Answer: 165 **

It costs $525 to hire the band for 3 hours, and it costs $765 to hire the band for 5 hours.

You can see that 2 extra hours of music costs an additional $765 – $525 = $240, so each hour of music costs $120. The $525 is three times the hourly rate plus the flat fee (call the? flat fee? x), which can be represented as 525 = 3(120) + x.

Solve for x, and you learn that? the flat fee is $165. You can double-check your answer by checking that the flat fee plus 5?hours of music costs $765: 165 + 5(120) = 165 + 600 = 765.

**SAT Math Practice Online Test Question No 6:**

For all numbers g and h, let g & h be defined as [g^{2} + h^{2}]/2. For what value of h does 4 & h = 26?

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**Correct Answer: 6 **

Following the pattern given in the definition of & in the problem, you know that 4 & h = [4² + h²]/2 = [16 + h²]/2, which you want to set equal to 26.

Multiplying both sides of the equation by 2, you get that 16 + h² = 52, so h² = 36.

This result means that h equals 6 or –6. The answer must be 6 because you can’t grid in negative numbers.

**SAT Math Practice Online Test Question No 7:**

If d is the middle number of three consecutive odd integers whose sum is s, what is the value of d divided by s?

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**Correct Answer: 0.333 **

Just pick three consecutive odd integers, like 1, 3, and 5. Since d is the middle of these, d = 3.

Since s is the sum of these, s = 1 + 3 + 5 = 9. So d divided by s is 3/9 or 1/3.

**SAT Math Practice Online Test Question No 8:**

The measures of the four angles in a quadrilateral have a ratio of 3:4:5:6. What is the measure, in degrees, of the smallest of these angles?

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**Correct Answer: 60 **

The sum of the four angles in a quadrilateral is 360 °. The sum of the parts in the ratio is 3 + 4 + 5 + 6 = 18.

Therefore the angles are 3/18, 4/18, 5/18, and 6/18 of the whole, which is 360°. So the smallest angle measures (3/18)(360°) = 60°.

**SAT Math Practice Online Test Question No 9:**

If x and y are positive integers such that x^{2} + y^{2} = 41, then what is the value of (x + y)^{2}?

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**Correct Answer: 81 **

By guessing and checking positive integers, you should be able to see that the only positive integers that satisfy the equation are 5 and 4. Therefore (x + y)² = (5 + 4)² = 81.

**SAT Math Practice Online Test Question No 10:**

NUMBER OF BOOKS READ DURING SUMMER VACATION

The table above shows the number of books 20 students read over their summer vacation. What is the median number of books read by these students?

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**Correct Answer: 2.5 **

Notice that the question asks for the median of these numbers, not for their average or mode.

The median is the “middle” number when the numbers are listed in order, or the average of the two middle numbers if there are an even number of numbers. According to the table, there are 20 numbers representing the number of books each child has read:

1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5+, 5+

We don’t know the final two numbers in the list, only that they are integers greater than 4. That’s okay: to find the median, we don’t need these last two numbers; we only need to find the average of the two middle numbers (the 10^{th} and 11^{th}), which are 2 and 3.

Therefore the median is 2.5.