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 Exam Math Test 4 Grid Ins Questions with Answer Keys | SAT Online Classes AMBiPi*.

### SAT 2022 Exam Math Test 4 Grid Ins Questions with Answer Keys

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

If -1 ≤ a ≤ 2 and -3 ≤ b ≤ 2, what is the greatest possible value of (a + b)(b – a)?

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**Correct Answer: 9 **

This looks suspiciously like a quadratic equation, and if you multiply it out, its equivalent is b^{2} – a^{2}.

You want to make this as large as possible, so you want b^{2} to be large and a^{2} to be small. If b = -3, b^{2} = 9; if a = 0, a^{2} = 0. So b^{2} – a^{2} can be as large as 9.

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

In the figure above, AB is the arc of the circle with center O. Point A lies on the graph of y = x^{2} – b, where b is a constant. If the area of shaded region AOB is π, then what is the value of b?

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**Correct Answer: 4 **

This question looks tough, so work it one step at a time, and start with what you know.

Sector AOB is a quarter-circle (it covers an angle of 90 out of 360 degrees), so multiplying its area (π) by 4 gives you the area of the whole circle (4π).

Plugging this into the equation for the area of a circle, A = πr^{2}, gives you 4π = πr^{2}, and the radius must be a positive value, so r = 2. This means that the coordinates of point A must be (-2, 0). Because A is on both the circle and the parabola, you can plug its x- and y-coordinates into the given equation of the parabola, y = x^{2} – b. This becomes 0 = (-2)^{2} – b, so b = 4.

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

13r + 8v = 47

22v = 63 – 17r

Based on the system of equations above, what is the sum of r and v?

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**Correct Answer: 11/3 or 3.66 or 3.67 **

Whenever there are two equations with the same two variables, they can be solved simultaneously by adding or subtracting them. Take the second equation and rewrite it so that the variables are on the left side of the equation: 17r + 22v = 63. Stack the equations and add them together.

[(13r + 8v = 47) + (17r + 22v) = 63] = (30r + 30v = 110).

Divide the entire equation by 30 to get r + v = 110/30. This is too big for the grid, so reduce it to 11/3.

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

During a presidential election, a high school held its own mock election. Students had the option to vote for Candidate A, Candidate B, or several other candidates. They could also choose to spoil their ballot. The table below displays a summary of the election results.

614 students voted for Candidate A. Approximately how many students attend the school?

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**Correct Answer: 1279 **

614 students voting for Candidate A represent 0.48 of the population out of 1.

Set up a proportion: 0.48/1.00 = 614/x where x is the total number of students in the school. Cross-multiply: 0.48x = 614. Divide both sides by 0.48 and you get approximately 1,279.

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

Professor Malingowski, a chemist and teacher at a community college, is organizing his graduated cylinders in the hopes of keeping his office tidy and setting a good example for his students. He has beakers with diameters, in inches, of 1/2, 3/4, 4/5, 1, and 5/4.

With his original five cylinders, Professor Malingowski realizes that he is missing a cylinder necessary for his upcoming lab demonstration for Thursday’s class. He remembers that the cylinder he needs, when added to the original five, will create a median diameter value of 9/10 for the set of six total cylinders. He also knows that the measure of the sixth cylinder will exceed the value of the range of the current five cylinders by a width of anywhere from

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**Correct Answer: 1 ≤ y ≤ 1.25 **

A set with an even number of elements will have as its median the average of the middle two terms. In the current set, 4/5 and 1 have an average of 9/10, so the new cylinder must be equal to or greater than 1, so the median will be the average of 4/5 and 1.

The range of the set of five cylinders is the greatest minus the least: 5/4 – 1/2 = 3/4. Because the new cylinder must be 1/4 inches to 1/2 greater than 3/4, the cylinder must be between 1 and 5/4 inches in diameter.

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

Danielle is a civil engineer for Dastis Dynamic Construction, Inc. She must create blueprints for a wheelchair-accessible ramp leading up to the entrance of a mall that she and her group are building. The ramp must be exactly 100 feet in length and make a 20° angle with the level ground. What is the horizontal distance, in meters, from the start of the ramp to the point level with the start of the ramp immediately below the entrance of the mall, rounded to the nearest meter? (Disregard units when inputting your answer.)

(Note: sin 20° ≈ 0.324, cos 20° ≈ 0.939, tan 20° ≈ 0.364)

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**Correct Answer: 94 **

The question describes a 100-foot ramp that forms a triangle.

The length of this ramp corresponds to the hypotenuse of a triangle. The height of the ramp is the length of the side of the triangle opposite the 20° angle; the horizontal distance from the start of the ramp immediately below the entrance of the mall is the side of the triangle adjacent to the 20° angle.

The function that relates the adjacent and the hypotenuse is cosine: cosθ = opposite/hypotenuse. In this problem, cos 20° = x/100. where x is the horizontal distance. Solve by multiplying both sides by 100: cos 20° = x. Next,replace cos 20° with the value given in the problem, 0.939: 100(0.939) = x. Multiply 100 by 0.939 to get x = 93.9, which rounds to 94.

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

In a certain ancient farming community, anthropologists determine that new dwellings were constructed monthly as modeled by the function f(x) = 2x + 100, where x is the current month of the year and f(x) is the number of dwellings constructed by the end of that month. Additionally, they determine that the population grew exponentially each month, thanks to the discovery of more fertile land for farming. This growth is modeled by the equation g(x) = 3^{x}, where g(x) represents the current population at the end of a given month. What is the smallest integer value of x, with 1 representing the end of January and 12 representing the end

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**Correct Answer: 5 **

Since you are looking for the value of x for which the population surpassed the number of dwellings, you can set up an inequality: 3^{x} > 2x + 100. Now, simply plug in values for x starting with x = 1 until the left-hand side of the inequality is larger than the right-hand side.

Using the values x = 1, x = 2, x = 3, and x = 4, you will find that the left-hand side of the inequality is less than the right-hand side. Using x = 5, 3^{5} = 243, and 2(5) + 100 = 110, making the left-hand of the inequality greater than the right-hand side. Therefore, the answer is 5.

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

p/3 + q/2 = 1

p – 3q = 1

Based on the system of equations above, what is the value of p?

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**Correct Answer: 7/3 or 2.33 **

Get rid of the fractions in the first equation by multiplying the entire equation by 6, to get 2p + 3q = 6. Whenever there are two equations with the same two variables, they can be solved simultaneously by adding or subtracting them.

The key is to get one variable to disappear. Stack the equations and add them. [(2p + 3q = 6) + (p – 3q = 1)] = (3p = 7). Therefore p = 7/3.

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

Hayoung is competing in a triathlon comprised of swimming, running, and biking. She starts by swimming m miles. Next, she runs 11 times the distance that she swims. Finally, she bikes 18 times the distance that she swims. If Hayoung swims 2.5 miles, what is the total distance, in miles, Hayoung travels as she competes?

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**Correct Answer: 75 **

Hayoung swims 2.5 miles.

She runs 11 × 2.5 = 27.5 miles, and she bikes 18 × 2.5 = 45 miles.

Her total triathlon mileage = 2.5 + 27.5 + 45 = 75 miles. The correct answer is 75.

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

What is the area of the shaded region of the circle, bound by the x-axis and the line y = –x, rounded to the nearest whole number?

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**Correct Answer: 19 **

The formula for the area of a circle is A = πr^{2}. If a full circle was shown, its radius would be 4, so the area of the full circle would be A = π4^{2} = 16π. The interior angle of the fraction of the circle shown can be calculated as 90 + 45 = 135 degrees.

Therefore, the figure shown is 135/360 of the area of a full circle. The area of the figure can be calculated as (135/360)(16π) = 0.375(16π) = 6π ≈ 18.8 ≈ 19. The correct answer is 19.