Express the number in the statement in standard notation. 8. In 2002, the United States Postal Service served 1.77 Ã 106 new delivery points. a. 177,...

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Chapter 7 Test Multiple Choice Identify the choice that best completes the statement or answers the question. Simplify. Assume that no denominator is equal to zero.

Ê ˆÊ ˆ 1. ÁÁ a 5 b 5 ˜˜ ÁÁ a 5 b 3 ˜˜ Ë ¯Ë ¯ 25 15 a. a b b. a 25 b 8

c. d.

a 10 b 15 a 10 b 8

Ê ˆ3 2. ÁÁ 4g 3 h 4 ˜˜ Ë ¯ a. 12g 6 h 7

c. d.

64g 6 h 7 12g 9 h 12

c. d.

33 37

b.

3.

64g 9 h 12

3 10 37 a. 3 −3 b. 1 3

ÊÁ 5 ˆ˜ 2 Á 2a b ˜ Ë ¯ 4. 6 24b a 10 b 4 a. 6 b.

5.

a 10 12b 4

c. d.

a7 6b 4 a 10 6b 4

36m−4 n 6 4mn −2 p −4 a. b.

9n 4 p 4 m3 9n 8 m5 p 4

c. d.

9n 8 p 4 m5 9m5 n8p4

ID: A

Ê ˆÊ ˆ 6. ÁÁ −6hi 2 j 4 ˜˜ ÁÁ 3h 3 ij 3 ˜˜ Ë ¯Ë ¯ 4 3 7 a. 18h i j b.

−18h 4 i 3 j 7

d.

18h 3 i 2 j 12 −18h 3 i 2 j 12

c. d.

3.054 × 10 −4 305.4 × 10 −6

c.

Express the number in scientific notation. 7. 0.0003054 a. 30.54 × 10 −5 b. 0.3054 × 10−3

Express the number in the statement in standard notation. 8. In 2002, the United States Postal Service served 1.77 × 10 6 new delivery points. a. 177,000 c. 177,000,000 b. 17,700,000 d. 1,770,000 Evaluate. Express the result in scientific notation.

Ê ˆÊ ˆ 9. ÁÁ 7.5 × 10 3 ˜˜ ÁÁ 5 × 10 5 ˜˜ Ë ¯Ë ¯ 10 a. 0.375 × 10 b. 3.75 × 10 7

c. d.

37.5 × 10 8 3.75 × 10 9

c. d.

0.98 × 10 9 9.8 × 10 2

11. 10a 5 b 4 a. 20 b. 10

c. d.

9 5

12. 10a 3 b 2 + 13a 4 b 4 − 6a 4 b 6 a. 12 b. 8

c. d.

10 11

10.

49 × 10 3 5 × 10 −5 a. 9.8 × 10 8 b. 9.8 × 10 −2 Find the degree of the polynomial.

Find the sum or difference.

Ê ˆ 13. ÁÁ 5a − 3a 2 ˜˜ + (8 + 7a ) Ë ¯ 2 a. a + 12a + 8 b. −3a 2 + 12a + 8

c. d.

3a 2 + 12a + 8 −3a 2 + 12a − 8

Ê ˆ Ê ˆ 14. ÁÁ 11p − 6q 2 − q ˜˜ − ÁÁ q 2 − 5p + 7p 2 ˜˜ Ë ¯ Ë ¯ 2 2 a. 7p − 7q + 16p − q b. c. d.

−7p 2 − 7q 2 + 6p − q −7p 2 − 5q 2 + 16p − q −7p 2 − 7q 2 + 16p − q

Find the product.

Ê ˆ 15. −5r 3 ÁÁ 4r 2 − 2r − 5 ˜˜ Ë ¯ a. −20r 5 − 10r 4 − 25r 3 b. −20r 5 + 10r 4 + 25r 3 c. 20r 5 − 10r 4 − 25r 3 d. −20r 6 + 10r 3 + 25r 3 Ê ˆ 16. −2s 2 t 4 ÁÁ −6s 3 t 5 − 6st 4 − 4t ˜˜ Ë ¯ 6 20 2 16 a. 12s t + 12s t + 8s 2 t 4 b. 12s 5 t 9 + 12s 3 t 8 + 8s 2 t 5 c. 12s 5 t 9 + 12s 3 t 8 + 8t 5 d. −12s 5 t 9 − 12s 3 t 8 − 8s 2 t 5 Solve the equation. SHOW ALL WORK.

Ê ˆ 17. 4x (−x − 3) = 2 ÁÁ −2x 2 − 2˜˜ − 2 Ë ¯ 1 a. 2 4 b. 3

c. d.

2 3 3 4

Find the product. 18. (r − 8) (r + 5) a. r 2 − 40 b. r 2 + 13r − 40

c. d.

r−3 r 2 − 3r − 40

c. d.

36c 2 + 36 12c + 12

c. d.

16r 2 − 72r − 81 16r 2 − 81r + 81

19. (−6t − 4v) (−7t − 4v) a. 42t 2 + 16v 2 b. 42t 2 + 52tv + 16v 2 c. −13t − 8v d. 42t 2 − 52tv + 16v 2 2

20. (6c + 6) a. 36c 2 + 72c + 36 b. 36c 2 + 36c + 36 2

21. (4r − 9) a. 16r 2 − 72r + 81 b. 16r 2 + 81

Ê ˆÊ ˆ 22. ÁÁ 7m2 − 6m + 4 ˜˜ ÁÁ −4m2 − 2m − 7 ˜˜ Ë ¯Ë ¯ 2 a. 3m − 8m − 3 b. −28m4 + 10m3 − 53m2 + 34m − 28 c. −28m2 + 12m − 28 d. −28m4 − 38m3 − 77m2 − 50m − 28 Ê ˆ 23. (−6k + 4) ÁÁ −7k 2 + 2k − 7 ˜˜ Ë ¯ a. −7k 2 − 4k − 3 b. 42k 3 − 40k 2 + 50k − 28 c. −42k 3 − 40k 2 − 34k − 28 d. −7k 2 − 12k − 28

Find the product of each sum and difference. 24. (3l + 9) (3l − 9) a. 9l 2 + 27l − 81 b. 9l 2 − 81 Short Answer Express the area of the figure as a monomial. 25.

26.

c. d.

9l 2 + 81 6l

The measures of two sides of a triangle are given. If P is the perimeter, find the measure of the third side. 27. P = 9a + 2b

28. BONUS Find the area of the shaded region.