Math Quiz For High School

1. What value of x makes "2x + 3 = 15" a true statement?

-9

-6

6

9

To find the value of x that makes the equation "2x + 3 = 15" true, we need to solve for x. Subtracting 3 from both sides of the equation gives us 2x = 12. Dividing both sides by 2 gives us x = 6. Therefore, the value of x that makes the equation true is 6.

Explanation

To find the value of x that makes the equation "2x + 3 = 15" true, we need to solve for x. Subtracting 3 from both sides of the equation gives us 2x = 12. Dividing both sides by 2 gives us x = 6. Therefore, the value of x that makes the equation true is 6.

2. Which expression represents the use of the distributive property on 3(a + b)?

A + 3b

3a + b

3a + 3b

3ab

The expression 3(a + b) represents the use of the distributive property because the 3 is being multiplied to both terms inside the parentheses. This means that the 3 is being distributed or distributed across both a and b. Therefore, the correct answer is 3a + 3b.

Explanation

The expression 3(a + b) represents the use of the distributive property because the 3 is being multiplied to both terms inside the parentheses. This means that the 3 is being distributed or distributed across both a and b. Therefore, the correct answer is 3a + 3b.

3. What value of x makes "-6x = -42" a true statement?

-7

-6

6

7

To find the value of x that makes "-6x = -42" a true statement, we need to solve the equation. By dividing both sides of the equation by -6, we get x = 7. Substituting x = 7 back into the equation, we have -6(7) = -42, which is true. Therefore, the correct answer is 7.

Explanation

To find the value of x that makes "-6x = -42" a true statement, we need to solve the equation. By dividing both sides of the equation by -6, we get x = 7. Substituting x = 7 back into the equation, we have -6(7) = -42, which is true. Therefore, the correct answer is 7.

4. What is the greatest common factor of 9x, 3y, and 12z?

3x

3

3y

Xyz

The greatest common factor (GCF) is the largest number that divides evenly into all of the given terms. In this case, the GCF of 9x, 3y, and 12z is 3 because it is the largest number that can divide evenly into all of them. Each term has a factor of 3, so it is the common factor among them. Therefore, the correct answer is 3.

Explanation

The greatest common factor (GCF) is the largest number that divides evenly into all of the given terms. In this case, the GCF of 9x, 3y, and 12z is 3 because it is the largest number that can divide evenly into all of them. Each term has a factor of 3, so it is the common factor among them. Therefore, the correct answer is 3.

5. If x = 4, what is 3^x (3 to the power of x)?

81

64

27

243

When x = 4, 3^x (3 to the power of x) can be calculated by raising 3 to the power of 4. This can be done by multiplying 3 by itself 4 times. Therefore, 3^4 equals 81.

Explanation

When x = 4, 3^x (3 to the power of x) can be calculated by raising 3 to the power of 4. This can be done by multiplying 3 by itself 4 times. Therefore, 3^4 equals 81.

6. What is the square root of 28 in simplified form?

Square Root 14

2 Times The Square Root of 7

7 Times The Square Root of 2

Square Root 9

The square root of 28 can be simplified as 2 times the square root of 7. This is because 28 can be factored into 2 times 2 times 7, and the square root of 2 times 2 is 2, while the square root of 7 remains as it is. Therefore, the simplified form of the square root of 28 is 2 times the square root of 7.

Explanation

The square root of 28 can be simplified as 2 times the square root of 7. This is because 28 can be factored into 2 times 2 times 7, and the square root of 2 times 2 is 2, while the square root of 7 remains as it is. Therefore, the simplified form of the square root of 28 is 2 times the square root of 7.

7. What is the slope of y = -4x + 1?

1

-4

4

-1

The slope of a linear equation in the form y = mx + b represents the rate at which y changes with respect to x. In this equation, the coefficient of x is -4, which means that for every increase of 1 in x, y decreases by 4. Therefore, the slope of y = -4x + 1 is -4.

Explanation

The slope of a linear equation in the form y = mx + b represents the rate at which y changes with respect to x. In this equation, the coefficient of x is -4, which means that for every increase of 1 in x, y decreases by 4. Therefore, the slope of y = -4x + 1 is -4.

8. What kind of slope does the line 3x - 2y = 6 have?

Zero

Undefined

Positive

Negative

The line 3x - 2y = 6 can be rewritten as y = (3/2)x - 3. In this form, the coefficient of x is positive, indicating that the line has a positive slope. This means that as x increases, y also increases, and as x decreases, y decreases. Therefore, the correct answer is positive.

Explanation

The line 3x - 2y = 6 can be rewritten as y = (3/2)x - 3. In this form, the coefficient of x is positive, indicating that the line has a positive slope. This means that as x increases, y also increases, and as x decreases, y decreases. Therefore, the correct answer is positive.

9. What value of x makes 4x - 2 = 2(x + 1) a true statement?

-2

1

2

0

To find the value of x that makes the equation true, we need to solve for x. By distributing 2 to (x + 1), we get 4x - 2 = 2x + 2. Combining like terms, we have 2x = 4. Dividing both sides by 2, we find that x = 2. Therefore, the value of x that makes the equation true is 2.

Explanation

To find the value of x that makes the equation true, we need to solve for x. By distributing 2 to (x + 1), we get 4x - 2 = 2x + 2. Combining like terms, we have 2x = 4. Dividing both sides by 2, we find that x = 2. Therefore, the value of x that makes the equation true is 2.

10. What percent of a circle is 75 degrees?

20.83%

15%

25%

75%

The measure of an angle in a circle is directly proportional to the percentage of the circle it represents. Since 75 degrees is 20.83% of 360 degrees (a full circle), the correct answer is 20.83%.

Explanation

The measure of an angle in a circle is directly proportional to the percentage of the circle it represents. Since 75 degrees is 20.83% of 360 degrees (a full circle), the correct answer is 20.83%.

11. What kind of slope does the line "3x + 2y = 6" have?

Negative

Zero

Undefined

Positive

The line "3x + 2y = 6" has a negative slope. This can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m represents the slope. By isolating y, we get y = -3/2x + 3. The negative coefficient of x indicates that the slope is negative.

Explanation

The line "3x + 2y = 6" has a negative slope. This can be determined by rearranging the equation into slope-intercept form, y = mx + b, where m represents the slope. By isolating y, we get y = -3/2x + 3. The negative coefficient of x indicates that the slope is negative.

12. What kind of slope does y = 4 have?

Undefined

Negative

Zero

Positive

The equation y = 4 represents a horizontal line that is parallel to the x-axis. Since the slope of a horizontal line is always zero, the correct answer is zero.

Explanation

The equation y = 4 represents a horizontal line that is parallel to the x-axis. Since the slope of a horizontal line is always zero, the correct answer is zero.

13. What is the y-intercept of 4x + 2y = -8?

(-2, 0)

(2, 0)

(0, -4)

(0, 4)

The y-intercept is the point where the graph of a function crosses the y-axis. To find the y-intercept of the equation 4x + 2y = -8, we set x = 0 and solve for y. When x = 0, the equation becomes 2y = -8, which gives us y = -4. Therefore, the y-intercept is (0, -4).

Explanation

The y-intercept is the point where the graph of a function crosses the y-axis. To find the y-intercept of the equation 4x + 2y = -8, we set x = 0 and solve for y. When x = 0, the equation becomes 2y = -8, which gives us y = -4. Therefore, the y-intercept is (0, -4).

14. What is the midpoint of the line segment with endpoints at (-1, 1) and (7, -3)?

(3, -1)

(6,3)

(5,1)

(1,-3)

The midpoint of a line segment is the point that is equidistant from both endpoints. To find the midpoint, we average the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (-1 + 7)/2 = 3 and the y-coordinate is (1 + -3)/2 = -1. Therefore, the midpoint of the line segment with endpoints at (-1, 1) and (7, -3) is (3, -1).

Explanation

The midpoint of a line segment is the point that is equidistant from both endpoints. To find the midpoint, we average the x-coordinates and the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (-1 + 7)/2 = 3 and the y-coordinate is (1 + -3)/2 = -1. Therefore, the midpoint of the line segment with endpoints at (-1, 1) and (7, -3) is (3, -1).

15. What is the solution of 4x - 7(x - 1) > 3(x + 1)?

X > -2/3

X > 2/3

X < -2/3

X < 2/3

To solve the given inequality, we first distribute the -7 and 3 to the terms inside the parentheses. This gives us 4x - 7x + 7 > 3x + 3. Simplifying further, we combine like terms to get -3x + 7 > 3x + 3. Next, we subtract 3x from both sides to isolate the variable. This gives us -6x + 7 > 3. Then, we subtract 7 from both sides to further isolate the variable. This gives us -6x > -4. Finally, we divide both sides by -6, remembering to flip the inequality sign since we are dividing by a negative number. This gives us x

Explanation

To solve the given inequality, we first distribute the -7 and 3 to the terms inside the parentheses. This gives us 4x - 7x + 7 > 3x + 3. Simplifying further, we combine like terms to get -3x + 7 > 3x + 3. Next, we subtract 3x from both sides to isolate the variable. This gives us -6x + 7 > 3. Then, we subtract 7 from both sides to further isolate the variable. This gives us -6x > -4. Finally, we divide both sides by -6, remembering to flip the inequality sign since we are dividing by a negative number. This gives us x