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 Prep Test 36 Grid Ins Questions with Answer Keys | SAT Online Course AMBiPi*.

### SAT 2022 Math Prep Test 36 Grid Ins Questions with Answer Keys

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

If w^{2} – v^{2} = 54 and w – v = 9, find the value of 2w + 2v.

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**Correct Answer: 12 **

The expression w^{2} – v^{2} is a difference of two squares, which factors into (w – v)(w + v) = 54.

Because you know that w – v = 9 and that the whole thing equals 54, you can say that w + v = 6, so 2w + 2v = 12. Notice that you don’t know what w and v are individually but that you don’t really care, either.

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

Car rental company A charges $80 per day, plus 25 cents per mile driven. Car rental company B charges $100 per day, plus 10 cents per mile driven. If you plan on renting a car for 3 days, for what number of miles would the costs of the two cars be equivalent?

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**Correct Answer: 400 **

Car A costs 80d + 0.25m, where d is days and m is miles. Car B costs 100d + 0.10m. If?you plug in 3 for d and make the equations equal, you get 240 + 0.25m = 300 + 0.10m. Combining like terms gives you 0.15m = 60, and dividing gives you m = 400.

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

Lorraine jogged for 8 minutes at a rate of 400 feet per minute, then walked for 2 minutes at a rate of 200 feet per minute. What was her average speed during this time, in feet per minute?

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**Correct Answer: 360 **

8 × 400 = 3,200 feet, and 2 × 200 = 400 feet. That makes 3,600 feet in 10 minutes or 360 feet per minute.

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

At South Side High School, one-half of the juniors have English class second period, one-third of the juniors have English class fifth period, and 12 students have English class sixth period. If every student has exactly one English class, how many students are in the junior class?

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**Correct Answer: 72 **

The 12 students represent the whole class minus one-half plus one-third of the class.

Because 1/2 + 1/3 = 3/6 + 2/6 = 5/6 and 1 – 5/6 = 1/6, 12 students are one-sixth of the class, and 12 × 6 = 72 students are in the whole class.

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

Find a value of x which satisfies x^{2} + x = 72.

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**Correct Answer: 8 **

It is a quadratic equation, so to solve it, you have to make it equal to zero. Doing so gives you x^{2} + x – 72 = 0, which factors to (x + 9)(x – 8) = 0; this equation is true when x is either –9 or 8. You can’t grid a negative answer, so go with 8.

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

The polygon shown has nine sides. How many additional lines must be drawn to make sure that every vertex (corner) is connected to every other vertex?

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**Correct Answer: 27 **

Imagine that you have only the 9 vertices, and none of them are connected yet. Pick a vertex and connect it to each of the others, drawing 8 lines. Now pick another vertex and connect it to all the vertices.

It was already connected to the first vertex, so you draw 7 new lines. The third vertex will already be connected to the first and third, so it needs only 6 new lines. After all the vertices are completely connected, you will have 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36 lines.

The original drawing already has 9 of those lines drawn in, so you need 36 – 9 = 27 more lines.

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

Given that point P in the drawing above lies on the graph of y = x^{2}, and that the area of triangle NOP is 108, find a.

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**Correct Answer: 6 **

NOP is a triangle, so its area is one-half its base times its height. You know from the diagram that its base has a length of a; because P is on y = x^{2}, its height must be a^{2}. Using those numbers, you get a(a^{2})/2 = 108, so a^{3} = 216, and a = 6.

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

Julie ran the 100-yard dash four times. Her times for the first three dashes were 16 seconds, 18 seconds, and 15 seconds. If her average time on all four dashes was 15.5 seconds, what was her time, in seconds, on the fourth dash?

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**Correct Answer: 13 **

Because the average time over four dashes was 15.5, the total time for all four races is 4 × 15.5 = 62 seconds. You can now subtract each of the three dash times that you know to determine the missing time: 62 – 16 – 18 – 15 = 13 seconds for the final dash.

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

The line y = mx + b passes through the points (0, 7) and (-2, 3). Determine the value of m + b.

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**Correct Answer: 9**

Hopefully, you remember that in y = mx + b, m represents the slope of the line, and b represents the y-intercept of the line.

It gives you the y-intercept: (0, 7), so you know that b = 7. To find the slope, remember that slope = rise/run = y₂ – y₁/x₂ – x₁ = 7 – 3/0 -(-2) = 4/2 = 2, so m = 2. With some simple addition, you find that m + b = 2 + 7 = 9.

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

When a certain number is divided by 5, the remainder is 2. When the number is divided by 7, the remainder is 6. If you know that the number is positive and less than 50, what is one possible value for the number?

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**Correct Answer: 27 **

A chart is probably the easiest way to solve this problem. If you know that when you divide a number by 5 you get a remainder of 2, then you know that the number is two more than a multiple of 5. Similarly, the number can be represented as six more than a multiple of 7. Because you know the number is less than 50, you know where to stop your chart.

Because the number 27 shows up in both columns of the chart, that must be the answer! You can double-check: 27 divided by 5 is 5 with a remainder of 2 (check!), and 27 divided by 7 is 3 with a remainder of 6 (check!).