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 Online 33 Grid Ins Questions with Answer Keys | SAT Online Course AMBiPi*.

### SAT 2022 Math Practice Test Online 33 Multiple Choice Questions with Answer Keys

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

Lauren took four exams. Her scores on the first three are 89, 85, and 90. If her average (arithmetic mean) on all four exams is 90, what did she get on the fourth exam?

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**Correct Answer: 96 **

This problem is simple if you remember an easy trick: total = number × average. In this case, the total must equal 4 × 90 = 360. Adding up Lauren’s first three scores gives you 264, and 360 – 264 = 96.

Another good way to solve this problem is to play the over/under game. For each score, figure out how much it is over or under the average. In this case, you get –1, –5, and 0. Adding up these numbers gives you –6, so Lauren is 6 points under average before she takes her last exam. Thus, she needs 6 points over her average, or a 96, on the last exam.

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

Find the value of x that satisfies √4x – √8 + 1 = 7.

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**Correct Answer: 11 **

In a radical or absolute-value problem, you first need to isolate the radical or absolute value. Therefore, you have to subtract 1 from both sides of the given equation before doing anything else; doing so gives you this equation: √4x – √8 = 6.

Now you can square both sides to eliminate the radical: 4x

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

Renting a private party room in a restaurant can be modeled as a linear function. If the cost of a party of 8 is $270, and the cost of a party of 10 is $320, find the cost, in dollars, of a party of 18.

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**Correct Answer: 520 **

A linear function has the form y = mx + b. In this problem, x is the number of people, while y is the cost.

You can choose from several ways to work out this problem, but here I focus on the slope, which is the change in y divided by the change in x. When the number of people increases by 2, the cost increases by $50.

Therefore, the slope m = 50?2 = 25. Now, because a party for 10 costs $320, a party of 18 adds 8 people, for 8 × $25 = $200 more. So a party of 18 costs $520.

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

If a – b = 8 and ab = 10, then a^{2} + b^{2 }= ?

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**Correct Answer: 84 **

You can try to figure out what a and b are equal, but doing so isn’t worth the energy.

(a – b)² = a² – 2ab + b². You know that (a – b) = 8, so (a – b)² = a² – 2ab + b² = 64. This question asks you for a² + b², which is (a²– 2ab + b²) + 2ab, or 64 + 2(10) = 84.

Pat yourself on the back if you got this one right; I think it’s the hardest problem in this section.

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

If 21/2 sticks of butter measure 20 tablespoons, how many tablespoons are in 4 sticks of butter?

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**Correct Answer: 32 **

This question is best done as a proportion problem: 2(1/2)/20 = 4/x.

So 21?2x = 80. Dividing by 21?2 gives you x = 80 ÷ 21?2 = 80 ÷ 5?2 = 80 × 2?5 = 160?5 = 32.

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

A certain fraction is equivalent to 2/3. If the fraction’s denominator is 12 less than twice its numerator, find the denominator of the fraction.

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**Correct Answer: 36 **

If you let the numerator equal n, then the denominator is 2n – 12, not 12 – 2n. Thus, 2/3 = n/(2n – 12). So, 2(2n – 12) = 3n, or 4n – 24 = 3n.

Subtracting 4n from both sides gives you –24 = –n, and dividing by –1 gives you n = 24. But wait! That’s not the answer: n is the numerator, but the problem asks for the denominator.

So plug 24 into 2n – 12: 2(24) – 12 = 36. If you have time, take a minute to check that 24? 36 really does equal 2? 3.

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

A sequence of numbers begins 1, 5, 4, 8, 7, 11, 10. What would be the 21st term of this sequence?

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**Correct Answer: 31 **

This problem is an example of an alternating sequence; it alternates between adding 4? and subtracting 1 from each term.

You could just follow the pattern out to the 21st term, but there’s an easier way. Look at all the odd terms: 1, 4, 7, 10. Each term is 3 more than the previous term. So, the 21st term must follow this pattern.

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

If xy = 120, and 1/x + 1/y = 1/4, find x + y.

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**Correct Answer: 30 **

This question is all about working with fractions. Consider 1/x + 1/y = 1/4.

When you’re working with fractions, getting a common denominator on each side is a good idea. Do the following to get a common denominator:

(y/y)(1/x) + (1/y)(x/x) = 1/4

y/xy + x/xy = 1/4

x + y/xy = 1/4

Notice how I always put the letters in alphabetical order; that’s standard practice in algebra. Does anything about the fraction on the left side look familiar? It should: The numerator is x + y, which is what you’re looking for; the denominator is xy, which equals 120. Now you can write x + y/120 = 1/4, so 4(x + y) = 120, and x + y = 30.

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

A rectangle’s length is twice its width. If its area is 32 square inches, find its width, in inches.

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**Correct Answer: 4 **

You can solve this problem by using trial and error or by letting l = 2w, writing (2w)(w) = 32, and then solving for w.

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

If 20 percent of half a number is 17, what was the original number?

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**Correct Answer: 170 **

20 percent is one-fifth, and one-fifth of one-half is one-tenth, so the original number was 10 × 17 = 170.