8th Grade Math Formulas Quiz

1) Which of these is the Pythagorean Theorem formula?

A2 + b2 = c2

A2 + b2 = c3

A + b2 = c2

A2 + b = c2

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, the correct formula is a^2 + b^2 = c^2, where a and b represent the lengths of the two shorter sides, and c represents the length of the hypotenuse.

Explanation

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, the correct formula is a^2 + b^2 = c^2, where a and b represent the lengths of the two shorter sides, and c represents the length of the hypotenuse.

2) How to calculate the perimeter for a square?

S - s - s - s

S + s + s x s

S + s + s

S + s + s + s

To calculate the perimeter of a square, we add up all four sides. In the given answer, "s" represents the length of one side of the square. By adding "s" four times, we are essentially adding up all four sides of the square, which gives us the correct perimeter.

Explanation

To calculate the perimeter of a square, we add up all four sides. In the given answer, "s" represents the length of one side of the square. By adding "s" four times, we are essentially adding up all four sides of the square, which gives us the correct perimeter.

3) The area for triangle is

B*h

2xb*h

B*h 2/1

B*h 1/2

The correct answer is "b*h 1/2". This is because the formula for finding the area of a triangle is (base * height) / 2.

Explanation

The correct answer is "b*h 1/2". This is because the formula for finding the area of a triangle is (base * height) / 2.

4) What's the formula for the area of the semicircle?

1/4(πr2 )

πr2

1/2(πr2 )

2(πr2 )

The formula for the area of a semicircle is given by 1/2(πr^2). This formula is derived by taking half of the formula for the area of a full circle, which is πr^2. Since a semicircle is exactly half of a circle, the area is also halved. Therefore, the correct answer is 1/2(πr^2).

Explanation

The formula for the area of a semicircle is given by 1/2(πr^2). This formula is derived by taking half of the formula for the area of a full circle, which is πr^2. Since a semicircle is exactly half of a circle, the area is also halved. Therefore, the correct answer is 1/2(πr^2).

5) "πr^2h" is the

Volume of cylinder

Volume of cone

Volume of pyramid

None of these

The formula "πr^2h" represents the volume of a cylinder. The letter "r" represents the radius of the base of the cylinder, and "h" represents the height of the cylinder. By multiplying the area of the base (πr^2) by the height, we can calculate the volume of the cylinder.

Explanation

The formula "πr^2h" represents the volume of a cylinder. The letter "r" represents the radius of the base of the cylinder, and "h" represents the height of the cylinder. By multiplying the area of the base (πr^2) by the height, we can calculate the volume of the cylinder.

6) LWH is the

Height of cuboid

Volume of cuboid

Weight of cuboid

Area of cuboid

The correct answer is "Volume of cuboid". This is because LWH refers to the dimensions of a cuboid, with L representing the length, W representing the width, and H representing the height. When these dimensions are multiplied together, they give the volume of the cuboid.

Explanation

The correct answer is "Volume of cuboid". This is because LWH refers to the dimensions of a cuboid, with L representing the length, W representing the width, and H representing the height. When these dimensions are multiplied together, they give the volume of the cuboid.

7) The formula for the area of rectangle

A = a + b

A = a - b

A = ab

None of these

The given options are different formulas for calculating the area of a rectangle. However, the correct formula for the area of a rectangle is A = ab, where 'a' represents the length of one side of the rectangle and 'b' represents the length of the other side. This formula calculates the area by multiplying the length and width of the rectangle. Therefore, the correct answer is A = ab.

Explanation

The given options are different formulas for calculating the area of a rectangle. However, the correct formula for the area of a rectangle is A = ab, where 'a' represents the length of one side of the rectangle and 'b' represents the length of the other side. This formula calculates the area by multiplying the length and width of the rectangle. Therefore, the correct answer is A = ab.

8) The formula for the volume of the pyramid is

1/3(b+h)h

1/3(b*h)h

1/3(b--h)h

1/4(b*h)h

The correct answer is 1/3(b*h)h. This formula is derived from the general formula for the volume of a pyramid, which is 1/3 times the base area times the height. In this case, the base area is represented by b (base length) multiplied by h (base width), and the height of the pyramid is also h. Therefore, the formula becomes 1/3(b*h)h.

Explanation

The correct answer is 1/3(b*h)h. This formula is derived from the general formula for the volume of a pyramid, which is 1/3 times the base area times the height. In this case, the base area is represented by b (base length) multiplied by h (base width), and the height of the pyramid is also h. Therefore, the formula becomes 1/3(b*h)h.

9) Which of these is the reflection across the y-axis?

(x, -y) --> (-x, y)

(x, y) --> (-x, y)

(-x, y) --> (-x, y)

(x, y) --> (-y, y)

The correct answer is (x, y) --> (-x, y) because reflecting a point across the y-axis involves changing the sign of the x-coordinate while keeping the y-coordinate the same. This is exactly what the transformation (x, y) --> (-x, y) does. It flips the point across the y-axis by negating the x-coordinate, while leaving the y-coordinate unchanged.

Explanation

The correct answer is (x, y) --> (-x, y) because reflecting a point across the y-axis involves changing the sign of the x-coordinate while keeping the y-coordinate the same. This is exactly what the transformation (x, y) --> (-x, y) does. It flips the point across the y-axis by negating the x-coordinate, while leaving the y-coordinate unchanged.

10) Rotation (90-degree counter-clock)

(x,y) (-y,x)

(x,-y) (-y,x)

(-x,y) (-y,x)

(x,y) (y,x)

The given answer (x,y) (-y,x) represents the result of rotating a point (x,y) 90 degrees counter-clockwise. In this transformation, the x-coordinate of the original point becomes the negation of the y-coordinate, and the y-coordinate becomes the x-coordinate. This can be seen by substituting the values of x and y into the expression (-y,x). Therefore, the answer (x,y) (-y,x) correctly represents the 90-degree counter-clockwise rotation of a point (x,y).

Explanation

The given answer (x,y) (-y,x) represents the result of rotating a point (x,y) 90 degrees counter-clockwise. In this transformation, the x-coordinate of the original point becomes the negation of the y-coordinate, and the y-coordinate becomes the x-coordinate. This can be seen by substituting the values of x and y into the expression (-y,x). Therefore, the answer (x,y) (-y,x) correctly represents the 90-degree counter-clockwise rotation of a point (x,y).