Polynomials and Properties of Exponents Unit Test Part 1
Please only use this to check your answers.
Equations with / are fractions and ^ are for exponents.
1. Which polynomial does the model represent
A. -x^3 + 2x^2 - 3x + 2
B. x^2 + x - 2
C. -x^2 - x + 2
D. -x^2 + x - 2 ***
For questions 2-3, simplify each polynomial.
2. 3x^2 + 6 - 2x + 5x - 4x^2 + 9
A. -x^2 + 3x + 15 ***
B. 7x^2 + 3x + 3
C. x^2 - 3x + 15
D. -x^2 + 7x + 15
3. 4x^2 + 8x - 11x + 6 - 5x^2 + 2
A. -x^2 - 3x + 8 ***
B. -x^2 + 3x + 8
C. x^2 - 3x + 8
D. x^2 + 3x + 8
4. What are the coefficients in the polynomial
7x^2 - 4x + 6?
A. -7, 4
B. 7, 4, -6
C. 7, -4, 6
D. 7, -4 ***
5. (m^2 - m - 4)+(m - 5)
A. m^2 - 2m + 9
B. m^2 + 2m - 9
C. m^2 - 2m - 9
D. m^2 - 9 ***
6. (7x^2 - x - 2)-(-6x^3 + 3)
A. 6x^3 + 7x^2 - x - 5 ***
B. -6x^3 + 7x^2 - x + 1
C. -x^3 - x - 5
D. x^2 - x + 1
7. Suppose you earned 8t - 3 dollars on Monday and 6t + 5 dollars on Tuesday. What were your total earnings? Simplify your answer.
A. 2t + 2
B. 2t - 8
C. 14t + 2 ***
D. 14t - 8
8. f^7 x f^1
A. f^8 ***
B. f^7
C. (2f)^8
D. (2f)^7
9. 64^10/64^5
A. 64^10/5
B. 64^50
C. 64^15
D. 64^5 ***
10. x^11/x^4
A. x^7 ***
B. x^15
C. x^44
D. x^11/4
11. Which of the following expressions is true?
A. 4^3 x 4^5 < 4^12 ***
B. 5^2 x 5^3 > 5^5
C. 3^2 x 3^4 = 3^2
D. 5^2 x 5^4 = 5^8
12. Which of the following expressions is true?
A. 2^4 x 2^3 = 12
B. 3^3 x 3^6 > 3^8 ***
C. 4^2 x 4^2 > 4^4
D. 5^5 x 5^2 = 5^10
Write the value of the expression.
13. 2^3/2^3
A. 0
B. 1 ***
C. 2
D. 3
14. 3^3/3^6
A. 1/27 ***
B. 1/9
C. 9
D. -27
Multiply Write the result in scientific notation.
15. (2.3 x 10^1)(7 x 10^6)
A. 1.61 x 10^7
B. 1.61 x 10^8 ***
C. 9.3 x 10^6
D. 9.3 x 10^7
16. (1.7 x 10^-4)(5 x 10^-5)
A. 8.5 x 10^-9 ***
B. 8.5 x 10^20
C. 6.7 x 10^-9
D. 6.7 x 10^20
17. 8t^5 x 8t^5
A. 64t^25
B. 64t^10 ***
C. 16t^10
D. 16t^5
18. -x(7x - 8)
A. 6x^2 - 9x
B. -7x - 8x
C. -7x^2 + 8x ***
D. 7x + 8x
19. 3k^2(-2k^2 - 4k + 7)
A. -6k^3 - k + 10k
B. -6k^4 - 12k^3 + 21k^2 ***
C. k^4 - k^3 + 10k^2
D. 6k^4 - 12^3 + 10k^2
20. (3k + 2)(k - 3)
A. 3k^2 - 7k - 5
B. 3k^2 - 7k - 6 ***
C. 3k^2 - 4k - 6
D. 3k^2 - 4k - 5
21. (-3y + 2)(y + 3)
A. -3y^2 - 7y + 6 ***
B. 3y^2 - 11y + 6
C. 3y^2 - 7y - 6
D. 3y^2 + 11y + 6
Short Answer
22. Look at the given triangles.
a. Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplist form that shows the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle.
c. find the perimeter for each triangle when x = 3
*Your own answer*
23. Emma, Erin, and Eden completed the problem to the right.
a. Who completed the problem correctly?
b. What did the other two students do wrong in their answers?
*Your own answer*
1. The polynomial that the model represents is D. -x^2 + x - 2.
2. Simplifying the polynomial 3x^2 + 6 - 2x + 5x - 4x^2 + 9, we get A. -x^2 + 3x + 15.
3. Simplifying the polynomial 4x^2 + 8x - 11x + 6 - 5x^2 + 2, we get A. -x^2 - 3x + 8.
4. The coefficients in the polynomial 7x^2 - 4x + 6 are C. 7, -4, 6.
5. Simplifying the expression (m^2 - m - 4)+(m - 5), we get D. m^2 - 9.
6. Simplifying the expression (7x^2 - x - 2)-(-6x^3 + 3), we get A. 6x^3 + 7x^2 - x - 5.
7. The total earnings, when you earned 8t - 3 dollars on Monday and 6t + 5 dollars on Tuesday, is C. 14t + 2.
8. Simplifying the expression f^7 x f^1, we get A. f^8.
9. Simplifying the expression 64^10/64^5, we get D. 64^5.
10. Simplifying the expression x^11/x^4, we get A. x^7.
11. The expression that is true is A. 4^3 x 4^5 < 4^12.
12. The expression that is true is B. 3^3 x 3^6 > 3^8.
13. The value of the expression 2^3/2^3 is B. 1.
14. The value of the expression 3^3/3^6 is A. 1/27.
15. Multiplying (2.3 x 10^1)(7 x 10^6), we get B. 1.61 x 10^8.
16. Multiplying (1.7 x 10^-4)(5 x 10^-5), we get A. 8.5 x 10^-9.
17. Multiplying 8t^5 x 8t^5, we get B. 64t^10.
18. Simplifying -x(7x - 8), we get C. -7x^2 + 8x.
19. Simplifying 3k^2(-2k^2 - 4k + 7), we get B. -6k^4 - 12k^3 + 21k^2.
20. Simplifying (3k + 2)(k - 3), we get B. 3k^2 - 7k - 6.
21. Simplifying (-3y + 2)(y + 3), we get A. -3y^2 - 7y + 6.
22.
a. The expression in simplest form for the perimeter of each triangle would depend on the given information about the triangles.
b. The expression in simplest form to show the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle would also depend on the given information about the triangles.
c. To find the perimeter for each triangle when x = 3, substitute x = 3 into the expressions for the perimeter of each triangle.
23.
a. To determine who completed the problem correctly, the specific details of the problem and the answers provided by Emma, Erin, and Eden would need to be provided.
b. To determine what the other two students did wrong in their answers, the specific details of the problem and the answers provided by Emma, Erin, and Eden would need to be provided.
1. D. -x^2 + x - 2
2. A. -x^2 + 3x + 15
3. A. -x^2 - 3x + 8
4. D. 7, -4
5. D. m^2 - 9
6. A. 6x^3 + 7x^2 - x - 5
7. C. 14t + 2
8. A. f^8
9. D. 64^5
10. A. x^7
11. A. 4^3 x 4^5 < 4^12
12. B. 3^3 x 3^6 > 3^8
13. B. 1
14. A. 1/27
15. B. 1.61 x 10^8
16. A. 8.5 x 10^-9
17. A. 64t^25
18. C. -7x^2 + 8x
19. B. -6k^4 - 12k^3 + 21k^2
20. B. 3k^2 - 7k - 6
21. A. -3y^2 - 7y + 6
22. a. Triangle 1: 2x + 3, Triangle 2: 3x + 1
b. x + 2
c. Triangle 1: 8, Triangle 2: 7
23. a. Emma
b. Erin forgot to distribute the negative sign and Eden made an error when combining like terms.