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 Practice Test 1 Math Grid Ins Questions with Answer Keys | SAT Online Tutor AMBiPi*.

### SAT 2022 Practice Test 1 Math Grid Ins Questions with Answer Keys

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

If a^{b} = 4^{ }and 3b = 2, what is the value of a?

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**Correct Answer: 8 **

Given 3b = 2 ⇒ b = 2/3.

Thus, a^{2/3} = 4 ⇒ ∛a^{2} = 4 ⇒ a^{2} = 4^{3} = 64 ⇒ a = 8.

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

n = 12 x 2^{t/3}

The number of mice in a certain colony is shown by the formula above, such that n is the number of mice and t is the time, in months, since the start of the colony. If 2 years have passed since the start of the colony, how many mice does the colony contain now?

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**Correct Answer: 3072 **

Given n = 12 x 2^{t/3 }

Now, put 2 years = 24 months,

Thus, n = 12 x 2^{24/3 }= 12 × 2^{8} = 12 × 256 = 3072.

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

A rectangular box has sides 3, 4, and x and a volume of 18. What is the value of x?

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**Correct Answer: 1.5 or 3/2 **

Given Volume = 18 ⇒ (3)(4)(x) ⇒ 18 = 12x ⇒ x = 18/12 ⇒ x = 3/2 = 1.5.

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

In the expression (6/5) / [(12/2y) – (5/y)] = 1, what is the value of y?

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**Correct Answer: 5/6 or 0.83 **

Given (6/5) / [(12/2y) – (10/2y)] = 1 ⇒ (6/5)/(2/2y) = 1 ⇒ (6/5)/(1/y) = 1 ⇒ 6y/5 = 1 ⇒ y = 5/6

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

A square is inscribed in a circle. The area of the square is what percent of the area of the circle? (Disregard the percent symbol when gridding your answer.)

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**Correct Answer: 63.6% **

Draw a square of side as s = 1 unit inscribed in a circle.

Then, the diameter of the circle is equal to the diagonal of the square.

Thus, d = 2√2 ⇒ r = √2

Now, Area of the square A = 4.

And, Area of the Circle A = π(√2)^{2 }⇒ A = 2π.

Now, let area of square is x % of the area of the circle.

Therefore, 4 = (x/100)2π. ⇒ x = 63.6.

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

If twice a number is equal to that number minus five, what is three times that number plus seventeen minus that number?

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**Correct Answer: 7 **

Let x equal the number.

Then, 2x = x – 5 ⇒ x = -5.

Three times that number plus seventeen minus that number is 3(-5) + 17 – (-5) = 7.

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

Twelve Smooth-Glide pens and eight Easy-Write pencils cost exactly $16.00 at Office World. Six Smooth-Glide pens and ten Easy-Write pencils cost $11.00 at the same location. How much will nine Smooth-Glide pens and nine Easy-Write pencils cost at Office World? (Disregard the dollar sign when gridding your answer.)

**Show/Hide Answer Key**

**Correct Answer: 13.5 **

Let s be the price of Smooth-Glide pens and e be the price of Easy-Write pencils.

If 12 pens and 8 pencils cost $16, then 12s + 8e = 16 … (i)

Similarly, if 6 pens and 10 pencils cost $11, then 6s + 10e = 11 …(ii)

On Adding (i) and (ii), 18s + 18e = 27 ⇒ 9s + 9e = 13.5.

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

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Find the number of apples he had.

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**Correct Answer: 700**

Suppose originally he had *x* apples. Then, (100 – 40)% of *x* = 420 ⇒ x = 700

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

Squares ABCD and WXYZ define two parallel planes such that AW = BX = CY = DZ = 5. Additionally, AB = WX = 4. Point Q lies between the two parallel planes such that it is equidistant from points A, B, C, and D and also equidistant from points W, X, Y, and Z. Lines AQY, BQZ, CQW, and DQX are drawn to create two pyramids. What is the total volume of the two pyramids?

**Show/Hide Answer Key**

**Correct Answer: 80/3**

First draw the diagram from given information.

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Volume of Both Pyramid = 2 x (1/3)(Base Area)(Height) = 2 x 1/3 x 16 x 5/2 = 80/3

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

In the figure, AC is bisected by BD. If BC is 7, then what is the length of BD?

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**Correct Answer: 6 **

BD = AE / 2 = 12 / 2 = 6.