Algebra 1 Final Review Quiz

1. Find the volume of a figure with length of 4 feet, width of 6 feet, and height of 8 feet.

192 feet cubed

14 feet cubed

20 feet cubed

The volume of a figure can be calculated by multiplying its length, width, and height. In this case, the length is 4 feet, the width is 6 feet, and the height is 8 feet. Multiplying these values together (4 x 6 x 8) gives us a volume of 192 feet cubed.

Explanation

The volume of a figure can be calculated by multiplying its length, width, and height. In this case, the length is 4 feet, the width is 6 feet, and the height is 8 feet. Multiplying these values together (4 x 6 x 8) gives us a volume of 192 feet cubed.

2. 2 out of 6 is the same as:

4 out of 12

3 out of 7

5 out of 10

The given question is asking for an equivalent fraction to 2 out of 6. To find an equivalent fraction, we can multiply both the numerator and denominator by the same number. In this case, we can multiply both 2 and 6 by 2, resulting in 4 out of 12. Therefore, 4 out of 12 is the same as 2 out of 6.

Explanation

The given question is asking for an equivalent fraction to 2 out of 6. To find an equivalent fraction, we can multiply both the numerator and denominator by the same number. In this case, we can multiply both 2 and 6 by 2, resulting in 4 out of 12. Therefore, 4 out of 12 is the same as 2 out of 6.

3. What is the simplified form of this expression?
8y+x-y

9y

7y-x

7y+x

The expression 8y+x-y can be simplified by combining like terms. The terms that have y can be combined by adding the coefficients, which gives us 8y-y = 7y. The terms that have x can also be combined by adding the coefficients, which gives us x. Therefore, the simplified form of the expression is 7y+x.

Explanation

The expression 8y+x-y can be simplified by combining like terms. The terms that have y can be combined by adding the coefficients, which gives us 8y-y = 7y. The terms that have x can also be combined by adding the coefficients, which gives us x. Therefore, the simplified form of the expression is 7y+x.

4. Factor the following trinomial:

x² + 6x + 8

(x + 3) (x + 3)

(x + 2) (x + 4)

(x + 2) (x - 4)

The given trinomial is x^2 + 6x + 8. To factor it, we need to find two binomials that multiply together to give us the trinomial. We can do this by looking for two numbers whose sum is 6 and whose product is 8. The numbers that satisfy these conditions are 2 and 4. Therefore, the correct answer is (x + 2) (x + 4) because when we multiply these binomials, we get x^2 + 6x + 8.

Explanation

The given trinomial is x^2 + 6x + 8. To factor it, we need to find two binomials that multiply together to give us the trinomial. We can do this by looking for two numbers whose sum is 6 and whose product is 8. The numbers that satisfy these conditions are 2 and 4. Therefore, the correct answer is (x + 2) (x + 4) because when we multiply these binomials, we get x^2 + 6x + 8.

5. Which of the following equations has a negative slope?

Y = 4x - 3

Y = 4x + 3

Y = -4x + 3

The equation y = -4x + 3 has a negative slope because the coefficient of x, which is -4, is negative. In general, the slope of a linear equation is determined by the coefficient of x. If the coefficient is positive, the slope is positive, and if the coefficient is negative, the slope is negative. Therefore, y = -4x + 3 has a negative slope.

Explanation

The equation y = -4x + 3 has a negative slope because the coefficient of x, which is -4, is negative. In general, the slope of a linear equation is determined by the coefficient of x. If the coefficient is positive, the slope is positive, and if the coefficient is negative, the slope is negative. Therefore, y = -4x + 3 has a negative slope.

6. What is the mean of the following set of data?
12, 12, 13, 14, 15, 18

*remember mean = average
add up ALL the numbers and divide by the total ( 6 )

12

14

13

The mean of a set of data is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values in the set. In this case, the set of data is 12, 12, 13, 14, 15, and 18. Adding up all the numbers gives us a sum of 84. Since there are 6 numbers in the set, we divide the sum by 6 to find the mean. 84 divided by 6 equals 14, so the mean of the set of data is 14.

Explanation

The mean of a set of data is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values in the set. In this case, the set of data is 12, 12, 13, 14, 15, and 18. Adding up all the numbers gives us a sum of 84. Since there are 6 numbers in the set, we divide the sum by 6 to find the mean. 84 divided by 6 equals 14, so the mean of the set of data is 14.

7. Which expression represents six less than four times a number?

6 - 4n

4n - 6

4/n - 6

The expression "4n - 6" represents six less than four times a number. This is because "4n" represents four times a number, and subtracting 6 from it gives the result of six less than that.

Explanation

The expression "4n - 6" represents six less than four times a number. This is because "4n" represents four times a number, and subtracting 6 from it gives the result of six less than that.

8. Y < 3

Which of the following is true?

Y is equal to all numbers less than 3

Y is equal to all numbers less than or equal to 3

Y is greater than 3

The statement "y is equal to all numbers less than 3" is true because the inequality y

Explanation

The statement "y is equal to all numbers less than 3" is true because the inequality y

9. What is the slope of the following line?

y = x + 4

4

0

1

The slope of a line is the coefficient of the x-term in its equation. In the given equation y = x + 4, the coefficient of x is 1. Therefore, the slope of the line is 1.

Explanation

The slope of a line is the coefficient of the x-term in its equation. In the given equation y = x + 4, the coefficient of x is 1. Therefore, the slope of the line is 1.

10. A jacket originally cost $75. It is on sale for $50. What is the percent of discount for the jacket?

25%

33%

35%

The discount for the jacket can be calculated by finding the difference between the original price and the sale price, which in this case is $75 - $50 = $25. To find the percentage of the discount, we divide this amount by the original price and multiply by 100: ($25 / $75) * 100 = 33.33%. Rounded to the nearest whole number, the percentage of discount for the jacket is 33%.

Explanation

The discount for the jacket can be calculated by finding the difference between the original price and the sale price, which in this case is $75 - $50 = $25. To find the percentage of the discount, we divide this amount by the original price and multiply by 100: ($25 / $75) * 100 = 33.33%. Rounded to the nearest whole number, the percentage of discount for the jacket is 33%.