Homework SourseExample 1showing work Simplify 462 a 4 b 8 c 8 d 2 work 4 1
Example 1:(showing work)
Simplify 4-6*2
a. -4
b. -8
c. 8
d. 2
work: 4 - 12
-8
answer = b
Example 2 (explanation)
State the property illustrated in the following
7+2=2+7
a. associative property
b. distributive property
c. substitution property
d. commutative property
This is the commutative property for addition since the order has changed around the + sign.
answer = d
You may use graph paper, the Reference Information Sheet, a ruler, and a calculator in answering the questions. Use scratch paper to work out your answers to each problem.
Notes:
(1)Figures are drawn as accurately as possible except when it is stated that a figure is not drawn to scale. All figures lie in a plane unless otherwise noted.
(2)All numbers used are real numbers. All algebraic expressions represent real numbers unless otherwise stated.
Simplify #1 through 9.
1. 3 + 42 - 5
a. 6
b. 14
c. 45
d. 67
2. 30 – 23 (3)
a. 6
b. 17
c. 55
d. 72
3. (43)5
a. 4-2
b. 43
c. 48
d. 415
4. (43)(44)
49
a. 416
b. 42
c. ¼2
d. 1/4
5. a(x – 5) – a(x + 2)
a. -7a
b. ax – 3a
c. ax – 7a
d. 2ax – 3a
6. 16x3 – 8x2 + 4x4
2x
a. 8x2 – 4x + 2x3
b. 8x2 – 4 + 2x3
c. 8x3 – 4x + 2x3
d. 8x2 – 4x + 2x
7. (3x3 + 2x2 + 10) + (3x3 + 2x2 + 10x)
a. 6x3 + 4x2 + 20x
b. 6x3 + 4x2 + 10x + 10
c. 9x3 + 4x2 + 100x
d. 9x3 + 4x2 + 10x + 10
8. (x + 5)(2x – 6)
a. 2x2 - 30
b. 2x2 – 6x
c. 2x2 + 7x – 6
d. 2x2 + 4x – 30
9. x2 – 9
x2 + 2x - 15
a. x + 3
x + 5
b. 3
2x + 5
c. x – 1
x – 6
d. 9
15 – 2x
Factor #10 through 14 completely.
10. x2 + 2x - 15
a. (x – 5)(x + 3)
b. (x – 5)(x - 3)
c. (x + 5)(x + 3)
d. (x + 5)(x - 3)
11. 2x2 - 50
a. 2(x + 5)2
b. 2(x - 5)2
c. (x + 5)(x – 5)
d. 2(x + 5)(x – 5)
12. x2 - x + 7
a. (x + 7)(x – 1)
b. (x + 1)(x + 7)
c. (x – 7)(x + 1)
d. cannot be factored
13. 9x2 – 9x
a. 9(x-1)
b. 9(x + 1)(x – 1)
c. 9x(x- 1)
d. x(3x + 1)(3x – 1)
14. Which expression is equivalent to (2x – 5) – (3x – 8)?
a. –x-13
b. –x+3
c. 2x-16
d. 5x-3
15. Evaluate 4² + 8 – 3(8 – 2) + 11 .
a. 237
b. 137
c. 17
d. 42
16. Simplify (-3a2 + 8a – 2) – (-4a2 – 2a + 6)
a. a2 + 10a - 8
b. 12a4 - 16a2 - 12
c. -7a2 + 6a + 4
d. a2 + 6a - 8
17. Divide (16x6 – 12x4+ 4x2) by 4x2.
a. 4x3 - 3x2 + 1
b. 4x4 - 3x2
c. 4x4 - 3x2 + 1
d. 12x4 - 8x2 + 0
18. Simplify (a3b)2.
a. a3b2
b. a6b
c. a6b2
d. a9b2
19. Subtract (6a2 + 3a) – (4a2 - 2a) .
a. 2a2 + a
b. 2a2+ 5a
c. 3
d. 3a3
20. Factor y2 – 400.
a. (y – 20)2
b. (y – 20)(y+20)
c. (y + 20)2
d. cannot be factored
21. Multiply (a+b)(a-b).
a. a2 + 2ab + b2
b. a2 + b2
c. a2 – b2
d. a2 – 2ab + b2
22. The perimeter of a rectangle is (2x – 7) inches and its width is (x2 – 5) inches. Find an expression for the perimeter of the rectangle.
a. 2x3 + 35
b. x2 - 2x + 2
c. x2 + 2x – 12
d. 2x2 + 4x – 24
23. Mrs. Reed is decorating wreaths. She needs 24 inches of gold ribbon and 45 inches of white ribbon to tie around each wreath. The white ribbon is sold by the foot. About how many feet of white ribbon will Mrs. Reed need to make 18 wreaths?
a. 30 ft.
b. 50 ft.
c. 70 ft.
d. 90 ft.
24. Sarah’s parents are filling their swimming pool. Her pool holds 22,000 gallons. It takes 16 hours to fill. What unit would you use to represent the rate that water is flowing into the pool?
a. Hours
b. Gallons
c. gallons per hour
d. gallons per minute
25. What is (2.5 X 102)(6.3 X 105) in scientific notation?
a. 1.575 X 107
b. 1.575 X 106
c. 1.575 X 1010
d. 1.575 X 108
Solution
SOLUTION
1. 3+42-5
= 45-5=40
2. 30-23*3
= 30-69= -39
3. 43*5
= 215
5.a(x-5)-a(x+2)
= a(x-5-x-2)
=- 7a
option a
6. (16x3-8x2+4x4)/2x
=4x4/2x+ 16x3/2x -8x2/2x
=2x3 + 8x2 - 4x
=8x2 - 4x+ 2x3
option a
7. (3x3+2x2+10)+(3x3+2x2+10x)
= 6x3+4x2+10x+10
option b.
8. (x + 5)(2x – 6)
= x*2x-6x+5*2x-5*6
= 2x2-6x+10x-30
=2x2+4x-30
option d.
