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 8 Grid Ins Questions with Answer Keys | SAT Online Classes AMBiPi*.

### SAT 2022 Math Practice Test Online 8 Grid Ins Questions with Answer Keys

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

x ≥ 0

3y – 2x ≥ -12

2x + 5y ≤ 20

What is the area of the triangle formed in the xy-plane by the system of inequalities above?

**Show/Hide Answer Key**

**Correct Answer: 30 **

Since no picture has been provided, start by drawing the picture. To do so, change each of the equations into the slope-intercept form of an equation y = mx + b, where m is the slope and b is the y-intercept

The second equation becomes 3y ≥ 2x – 12, or y ≥ (2/3)x – 4. The third equation becomes 5y ≤ -2x + 20, or y ≤ – (2/5)x + 4. The ≥ sign in the second equation means that everything above the line should be shaded, and the ≤ sign in the third equation means that everything below that line should be shaded. To graph the first equation x ≥ 0, shade everything to the right of the y-axis. The resulting picture should l look like this:

The formula for the area of a triangle is A = (1/2)b x h. It is easiest to think of the side that is along the y-axis as the base. That side goes from a y-coordinate of 4 to -4, for a length of 8. The height of the triangle is the x-coordinate of the point where the two slanted lines meet; set the two equations equal to find it. Start with (2/3)x – 4 = (-2/5)x + 4 and multiply everything by 15 to get 10x – 60 = – 6x + 60. Then add 6x and 60 to both sides to get 16x = 120, so x = 7.5, and the height is 7.5. The resulting figure should look like this:

Plug the measurements for the base and the height into the area formula to get A = 1/2(8)(7.5) = 30. The correct answer is 30.

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

The Nile is a track & field athlete at North Sherahan High School. He hopes to qualify for the Olympic Games in his best field event, the javelin throw. He experiments with different javelin weights to build his arm strength and currently measures the results in feet.

During his preparations, Nile realizes that the upcoming Olympic qualifying competition will be judged in meters, rather than feet or yards. The Nile wants to make sure he can throw the javelin the minimum required distance so he can advance in the competition. If his current best throw is 60 yards, and one yard is approximately 0.9144 meters, how much further, to the nearest yard, must he throw to achieve the minimum required distance of 68.58 meters to qualify for the Olympics? (Disregard units when gridding your answer.)

**Show/Hide Answer Key**

**Correct Answer: 15 **

Start by converting the qualifying distance of 68.58 meters into yards. Set up a proportion: 1 yard/0.9144 meters = x yards/68.58 meters.

Cross-multiply to get 0.9144x = 68.58. Divide both sides by 0.9144 to find that the qualifying distance is 75 yards. If his current best is 60 yards, he needs to throw 75 – 60 = 15 more yards.

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

If (4 + 3i)(1 – 2i) = a + bi, then what is the value of a? (Note that i = √-1.)

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**Correct Answer: 10 **

Difficulty: Medium

Category: Additional Topics in Math / Imaginary Numbers

Strategic Advice: Multiply the two complex numbers just as you would two binomials (using FOIL). Then, combine like terms. The question tells you that i = √-1.

If you square both sides of the equation, this is the same as i2 = -1, which is a more useful fact.

Getting to the Answer:

(4 + 3i)(1 – 2i) = 4(1 – 2i) + 3i(1 – 2i)

= 4 – 8i + 3i – 6i^{2}

= 4 – 5i – 6(-1)

= 4 – 5i + 6 = 10 – 5i

The question asks for a in a + bi, so the correct answer is 10.

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

18 – (3x)^{1/2}/2 = 15

What value of x satisfies the equation above?

**Show/Hide Answer Key**

**Correct Answer: 12 **

Difficulty: Medium

Category: Passport to Advanced Math / Exponents

Strategic Advice: Solving an equation that has a fractional exponent can be very intimidating, so rewrite that part of the equation using a radical instead. Then, solve the equation the same way you would any other: Isolate the variable using inverse operations, one step at a time.

Getting to the Answer: After rewriting the equation using a radical, start by subtracting 18 from both sides. Next, multiply both sides of the equation by -2. Then, square both sides to remove the radical. Finally, divide both sides by 3.

18 – (3x)^{1/2}/2 = 15

18 – √3x/2 = 15

–√3x/2 = 15

√3x = 6

3x = 36

x = 12

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

If the equation that represents the graph shown above is written in standard form, Ax + By = C, and A = 6, what is the value of B?

**Show/Hide Answer Key**

**Correct Answer: 12 **

Difficulty: Easy

Category: Heart of Algebra / Linear Equations

Strategic Advice: The two things you can glean from the equation of a line are its slope and its y-intercept. In this question, you’re given information about A and asked about B. Try writing the equation in slope-intercept form to see how A and B are related. Then look at the graph and see what you can add to this relationship.

Getting to the Answer: Start by writing the equation in slope-intercept form, y = mx + b.

Ax + By = C

By = -Ax + C

y = (-A/B)x + C/B

So, together A and B (specifically A over B) define the slope of the line. Look at the graph: Reading from left to right, the line falls 1 unit for every 2 units that it runs to the right, so the slope is -1/2.

Don’t forget-the question tells you that A = 6, so set the slope equal to -6/B and solve for B:

-1/2 = -6/B

B = 12

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

A toy saber is stuck at a right angle into the ground 4 inches deep. It casts a shadow that is 4 feet long. The brick wall casts a shadow three times that long. If the wall is 7 feet 6 inches tall, how many inches long is the toy saber?

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**Correct Answer: 34**

Difficulty: Hard

Category: Additional Topics in Math / Geometry

Strategic Advice: Drawing on the diagram is a great strategy to get started on a question like this. There are two right triangles-the smaller one formed by the saber, the path of the sun’s rays, and the ground; and the larger one formed by the brick wall, the path of the sun’s rays, and the ground. The two triangles share one angle (the small angle on the left side), and each has a 90-degree angle (where the saber and the brick wall each meet the ground), making the third pair of corresponding angles also congruent. This means the triangles are similar to AAA, and the sides of the triangles are proportional.

Getting to the Answer: Add information from the question to the diagram. You’ll need to convert the height of the wall to inches because the question asks for the length of the saber in inches. (You could also convert the base lengths to inches, but it is not necessary because you can compare feet to feet in that ratio.)

Now that you have a more detailed drawing, set up and solve a proportion:

(base of small triangle/ base of the large triangle) = length of saber(in inches)/ height of the wall(in inches)

4/12 = h/90

4(90) = 12h

360 = 12h

30 = h

Don’t forget to add the 4 inches that are stuck in the ground to find that the length of the saber is 30 + 4 = 34 inches.

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

0 ≤ (1 – k)/2 < 7/8

If k lies within the solution set of the inequality shown above, what is the maximum possible value of k?

**Show/Hide Answer Key**

**Correct Answer: 1 **

Difficulty: Medium

Category: Heart of Algebra / Inequalities

Strategic Advice: Whenever expressions involve fractions, you can clear the fractions by multiplying each term in the expression by the least common denominator. Don’t forget-when working with inequalities, if you multiply or divide by a negative number, you must flip the inequality symbol(s).

Getting to the Answer: The inequality in this question is a compound inequality, but you don’t need to break it into parts. Just be sure that anything you do to one piece of the inequality, you do to all three pieces. Start by multiplying everything by 8 to clear the fractions.

0 ≤ (1 – k)/2 < 7/8

0 ≤ 4(1 – k) < 7

0 ≤ 4 – 4k < 7

-4 ≤ -4k < 3

-4/-4 ≥ -4k/-4 > 3/-4

1 ≥ k > -3/4

Turn the inequality around so the numbers are increasing from left to right: -3/4 < k ≤ 1. This tells you that k is less than or equal to 1, making 1 the maximum possible value of k.

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

In medicine, when a drug is administered in pill form, it takes time for the concentration in the bloodstream to build up, particularly for pain medications. Suppose for certain pain medication, the function C(t) = 1.5t/t^{2} + 4 is used to model the concentration, where t is the time in hours after the patient takes the pill. For this particular medication, the concentration reaches a maximum level of 0.375 about two hours after it is administered and then begins to decrease. If the patient isn’t allowed to eat or drink until the concentration drops back down to 0.3, how many hours after taking the pill must the patient wait before eating or drinking?

**Show/Hide Answer Key**

**Correct Answer: 4**

Difficulty: Hard

Category: Passport to Advanced Math / Functions

Strategic Advice: Sometimes in a real-world scenario, you need to think logically to get a mental picture of what is happening. Think about the concentration of the medicine-it starts at 0, increases to a maximum of 0.375, and then decreases again as it begins to wear off. This means the concentration is 0.3 two times once before it hits the max and once after. In this case, you’re looking for the second occurrence.

Getting to the Answer: Set the function equal to 0.3 and solve for t. Don’t stress out about the decimals-as soon as you have the equation in some kind of standard form, you can move the decimals to get rid of them.

0.3 = 1.5t/t^{2} + 4

0.3(t^{2} + 4) = 1.5t

0.3t^{2} + 1.2 = 1.5t

To make the equation easier to work with, move the decimal one place to the right in each term. The result is a fairly nice quadratic equation. Move everything to the left side, factor out a 3, and go from there.

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

(√x ⦁ x^{5/6} ⦁ x)/∛x

If xn is the simplified form of the expression above, what is the value of n?

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**Correct Answer: 2 **

Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Strategic Advice: Rewrite the radicals as fraction exponents: √x = x^{1/2} and ∛x = x^{1/3}

Getting to the Answer: Write each factor in the expression in exponential form. Then use the rules of exponents to simplify the expression. Add the exponents of the factors that are being multiplied and subtract the exponent of the factor that is being divided:

(x ⦁ x^{5/6} ⦁ x)/∛x = (x^{1/2} ⦁x^{5/6}⦁ x^{1})/x

= x^{1/2 + 5/6 + 1/1 – 1/3}

= x^{3/6 + 5/6 + 6/6 – 2/6}

= x^{12/6} = x^{2}

Because n is the power of x, the value of n is 2.

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

The figure above shows the solution for the system of inequalities { y < -3x + 2 , y > x – 6}. Suppose (a, b) is a solution to the system. If a = 0, what is the greatest possible integer value of b?

**Show/Hide Answer Key**

**Correct Answer: 1 **

Difficulty: Medium

Category: Heart of Algebra / Inequalities

Strategic Advice: If (a, b) is a solution to the system, then a is the x-coordinate of any point in the region where the shading overlaps and b is the corresponding y-coordinate.

Getting to the Answer: When a = 0 (or x = 0), the maximum possible value for b lies on the upper boundary line, y < -3x + 2. (You can tell which boundary line is the upper line by looking at the y-intercept.) The point on the boundary line is (0, 2), but the boundary line is dashed (because the inequality is strictly less than), so you cannot include (0, 2) in the solution set. This means 1 is the greatest possible integer value for b when a = 0.