Pre Algebra Tutor Competency Quiz

1. Classify the given expression as a monomial, a binomial, a trinomial or not a polynomial 19f² – 11f – 9

Monomial

Binomial

Trinomial

Not a polynomial

The given expression has three terms: 19f^2, -11f, and -9. Since it has three terms, it is classified as a trinomial.

Explanation

The given expression has three terms: 19f^2, -11f, and -9. Since it has three terms, it is classified as a trinomial.

2. Find the sum of - 25, -15, and 18.

8

58

-22

28

The sum of -25, -15, and 18 can be found by adding all the numbers together. -25 + (-15) + 18 = -22.

Explanation

The sum of -25, -15, and 18 can be found by adding all the numbers together. -25 + (-15) + 18 = -22.

3. Solve - 5 - ( - 24)

29

-19

19

-29

To solve the expression -5 - (-24), we can simplify it by removing the double negative. When we subtract a negative number, it is the same as adding the positive version of that number. Therefore, -5 - (-24) becomes -5 + 24, which equals 19.

Explanation

To solve the expression -5 - (-24), we can simplify it by removing the double negative. When we subtract a negative number, it is the same as adding the positive version of that number. Therefore, -5 - (-24) becomes -5 + 24, which equals 19.

4. Evaluate the expression xy for x = 0, y = - 34

34

-34

0

Undefined

The given expression is xy, where x = 0 and y = -34. When we substitute these values into the expression, we get 0 * (-34) = 0. Therefore, the answer is 0.

Explanation

The given expression is xy, where x = 0 and y = -34. When we substitute these values into the expression, we get 0 * (-34) = 0. Therefore, the answer is 0.

5. Identify the degree of the given polynomial 6h² + h⁶ + 13

13

6

2

1

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of the variable "h" is 6, so the degree of the polynomial is 6.

Explanation

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of the variable "h" is 6, so the degree of the polynomial is 6.

6. Find the square root √81

6561

11

18

9

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 81 is 9 because 9 multiplied by itself equals 81.

Explanation

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 81 is 9 because 9 multiplied by itself equals 81.

7. 16 is 1% of what number?

160

16

1600

16,000

To find 1% of a number, we divide the number by 100. In this case, dividing 1600 by 100 gives us 16. Therefore, 16 is 1% of 1600.

Explanation

To find 1% of a number, we divide the number by 100. In this case, dividing 1600 by 100 gives us 16. Therefore, 16 is 1% of 1600.

8. Write the prime factorization of 968?

2 • 2 • 11 • 11 • 11

2 • 2 • 2 • 2 • 11

2 • 2 • 2 • 11 • 11

8 • 121

The prime factorization of 968 is 2 • 2 • 2 • 11 • 11. In order to find the prime factorization, we need to break down the number into its prime factors. We start by dividing 968 by the smallest prime number, which is 2. This gives us 484. We continue dividing by 2 until we can no longer divide evenly, which gives us 11 • 22. Next, we divide by the smallest prime number again, which is 2, giving us 11 • 2 • 11. Finally, we have the prime factorization of 968 as 2 • 2 • 2 • 11 • 11.

Explanation

The prime factorization of 968 is 2 • 2 • 2 • 11 • 11. In order to find the prime factorization, we need to break down the number into its prime factors. We start by dividing 968 by the smallest prime number, which is 2. This gives us 484. We continue dividing by 2 until we can no longer divide evenly, which gives us 11 • 22. Next, we divide by the smallest prime number again, which is 2, giving us 11 • 2 • 11. Finally, we have the prime factorization of 968 as 2 • 2 • 2 • 11 • 11.

9. The angles in Triangle ABC measure 100º, 50º, 30º. What kind of triangle is ABC?

Acute

Obtuse

Right

Equilateral

The angles in Triangle ABC measure 100°, 50°, 30°. In a triangle, the sum of all angles is always 180°. Since the largest angle in this triangle is 100°, which is greater than 90°, it is an obtuse triangle.

Explanation

The angles in Triangle ABC measure 100°, 50°, 30°. In a triangle, the sum of all angles is always 180°. Since the largest angle in this triangle is 100°, which is greater than 90°, it is an obtuse triangle.

10. The lengths of two sides of a parallelogram are 5x + 4 and 2x + 3y. Identify an expression for the perimeter of the parallelogram.

7x + 3y + 4

12x +3y + 8

14x + 6y + 8

9x + 6y + 4

The perimeter of a parallelogram is found by adding the lengths of all four sides. In this case, the lengths of the two sides are given as 5x + 4 and 2x + 3y. To find the perimeter, we add these two lengths together and then double the result since the opposite sides of a parallelogram are equal in length. Therefore, the expression for the perimeter is (5x + 4) + (2x + 3y) + (5x + 4) + (2x + 3y), which simplifies to 14x + 6y + 8.

Explanation

The perimeter of a parallelogram is found by adding the lengths of all four sides. In this case, the lengths of the two sides are given as 5x + 4 and 2x + 3y. To find the perimeter, we add these two lengths together and then double the result since the opposite sides of a parallelogram are equal in length. Therefore, the expression for the perimeter is (5x + 4) + (2x + 3y) + (5x + 4) + (2x + 3y), which simplifies to 14x + 6y + 8.

11. Johnny teaches karate lessons for $55 per student for a 6-week session. From one group of students, he collected $1650. Find how many students are in the group.

34 students

20 students

32 students

30 students

If Johnny collected $1650 from one group of students and charges $55 per student for a 6-week session, we can divide the total amount collected by the cost per student to find the number of students. In this case, $1650 divided by $55 equals 30 students. Therefore, there are 30 students in the group.

Explanation

If Johnny collected $1650 from one group of students and charges $55 per student for a 6-week session, we can divide the total amount collected by the cost per student to find the number of students. In this case, $1650 divided by $55 equals 30 students. Therefore, there are 30 students in the group.

12. The length of a door is 12 inches less than twice the width. Identify the length and width of the door if its area is 4032 in².

L = 84 in. , w = 48 in.

L = 96 in., w = 42 in.

L = 84 in., w = 42 in.

L = 96in., w = 48in.

The area of a rectangle is given by the formula length times width. In this case, the area is given as 4032 in2. We are also given that the length of the door is 12 inches less than twice the width. Let's assume the width of the door is w. According to the given information, the length would be 2w - 12. We can set up the equation w * (2w - 12) = 4032 and solve for w. By solving the equation, we find that w = 48. Substituting this value back into the expression for the length, we get l = 2(48) - 12 = 84. Therefore, the length is 84 inches and the width is 48 inches.

Explanation

The area of a rectangle is given by the formula length times width. In this case, the area is given as 4032 in2. We are also given that the length of the door is 12 inches less than twice the width. Let's assume the width of the door is w. According to the given information, the length would be 2w - 12. We can set up the equation w * (2w - 12) = 4032 and solve for w. By solving the equation, we find that w = 48. Substituting this value back into the expression for the length, we get l = 2(48) - 12 = 84. Therefore, the length is 84 inches and the width is 48 inches.

13. What is the solution to 2x + 5 < 17?

X = 6

0

X < 6

X > 6

To find the solution to the inequality 2x + 5

Explanation

To find the solution to the inequality 2x + 5

14. Circle A has a diameter of 8 feet. The area of circle A is closest to:

200.96 sq ft

25.12 sq ft

12.56 sq ft

50.24 sq ft

The area of a circle is calculated using the formula A = πr², where r is the radius of the circle. In this case, the diameter of circle A is given as 8 feet, so the radius would be half of that, which is 4 feet. Plugging this value into the formula, we get A = π(4)² = 16π. Since π is approximately 3.14, the area of circle A is closest to 16 × 3.14 = 50.24 sq ft.

Explanation

The area of a circle is calculated using the formula A = πr², where r is the radius of the circle. In this case, the diameter of circle A is given as 8 feet, so the radius would be half of that, which is 4 feet. Plugging this value into the formula, we get A = π(4)² = 16π. Since π is approximately 3.14, the area of circle A is closest to 16 × 3.14 = 50.24 sq ft.