55a

Real Test 2

Grades are available as of Test 2. Email your name and W number to nalexander@igc.org

4.4

1. The target zone for aerobic exercise is given by the following system of inequalities in which a represents one's age and p is one's pulse rate.

10 < a < 70

2a + 3p > 450

a + p < 190

Suppose a person is 9 years old with pulse rate 125 in beats per minute. Is this person inside the target zone?

a yes

b no

c nota

5.1

2. What is the degree of this polynomial ? f(x) = x⁸ - 4x .

a 1

b 8

c 6

d nota

3. Using the Leading Coefficient Test, we can say the polynomial of the previous problem:

a falls to the left, rises to the right

b rises to the left, falls to the right

c rises to the left, rises to the right

d falls to the left, falls to the right

e nota

4. What is f(1) of problem 2?

a -1

b -5

c - 3

d 1

e nota

5. Add. (4x⁴y - 8x⁶y² + 12x⁸y⁶) + (44x⁴y + 8x⁶y² - 13x⁸y⁶ )

a 48x⁴y + 8x⁶y² - 25x⁸y⁶

b 48x⁴y + 25x⁸y⁶

c 48x⁴y - x⁸y⁶

d nota

5.2

6. Multiply. 7t²(3t¹² - t¹⁶)

a 21t²⁴ - 7t³²

b 21t¹⁴ - 7t¹⁸

c nota

5.3

7 Factor completely. x⁹y⁶ + 12x⁷y⁵ + xy - 26x⁴y³

a xy(x⁸y⁵ + 12x⁶y³ + 1 - 26x³y²)

b xy(x⁸y⁵ + 12x⁶y⁴ - 26x³y²)

c xy(x⁸y⁵ + 12x⁶y⁴ + 1 - 26x³y²)

d nota

8. What is one factor of 5x³ + 4x² + 10x + 8 ? Hint: factor by grouping.

a (x² + 2)

b (x² - 2)

c (x² + 4)

d nota

9. Factor the greatest common factor from the expression:
4(4x + 3) - 3a(4x + 3). Note : This problem will help you understand the process for solving the previous one.

a (4 + 3a)(4x + 3)

b (4 - 3a)(4x + 3)

c (4 + 3a)(4x - 3)

d nota

10. Factor by grouping: x³ + 4x² + x + 4. What is one of the factors?

a (x² + 4)

b (x² + 1)

c (x + 2)

d nota

5.4

11. What is one of the factors of 8x³ + 48x² + 40x

a (x - 2)

b (x - 6)

c (x + 5)

d nota

5.5

12. What is one of the factors of 2x³ - 8x after it is completely factored??

a (x - 8)

b (x - 2)

c (x² - 4)

d nota

13. What is one of the factors of x³ + 27 after it is completely factored??

a (x + 6)

b (x - 3)

c (x² + 3x + 9)

d (x² - 3x + 9)

e nota

5.6

14. What is one of the factors of x³ + 5x² + 4x + 20 ?

a (x + 5)

b (x - 1)

c (x² + 1)

d (x² + 2)

e nota

15. What is one of the factors of 66,666x² - 66,666 after it is completely factored?

a (x - 66)

b 6

c (x - 66,666)

d (x + 1)

e nota

5.7

16.
Determine the x-intercepts of y = x² + 2x - 8 .

a (0,-4) and (0,2)

b (4,0) and (-2,0)

c (-4,0) and (2,0)

d (0,4) and (0,-2)

e nota

17. Solve by factoring: x³ - 2x² = x - 2 .

a x = 1, 2

b x = -1,2

c x = 1,-1, -2, 2

d x = 1,-1, 2

e nota

6.1

18. Simplify by factoring and canceling: (x³ - 2x² - x + 2)/(x - 2) .

a (x + 1)(x - 1)

b (x - 1)(x + 2)

c ( x - 1)(x - 2)

d nota

19.

a 3/7

b 7/3

c 3

d 9/7

e nota

6.2

20. Subtract. 7/(15x²) - 9/(24x)

a (56x - 45x²)/(120x)

b (56 - 45x²)/(120x²)

c (56 - 45x)/(120x²)

d nota

21. Add . 7 + 2/(x -1)

a 9/(x - 1)

b (7x - 4)/(x - 1)

c (7x - 5)/(x - 1)

d nota

6.3

22 Simplify : [5 - 2/x]/[1/5 + 6/x]

a [25 - 10x]/[1 + 30x]

b [25x - 10]/[1 + 30x]

c [25x - 10]/[x + 30]

d [25 - 10x]/[x + 30]

e nota

23. Simplify : [2 - 1/x - 1/x²]/[1 - 3/x + 2/x²] (Hint: Factor and cancel.)

a [2x + 1]/[x + 2]

b [2x + 1]/[x - 2]

c [2x - 1]/[x - 2]

d nota

6.6

24. Solve: 2/(x + 1) = 1/(x -1). (Hint: cross-multiply.) The answer for x is a value in the interval

a (5,10)

b (0, 5)

c (-5, 0)

d nota

25. Solve 6/x - x/3 = -1 (Hint: Multiply both sides by the LCD.) The values for the solution for x are in the intervals

a (-7, 0) or (0,4)

b (-4,0) or ( 0, 7)

c (-4, 0) or (0,2)

d nota

26. Clean-up costs for pollution removal in a river are given by
f(x) = 500x/(100 - x), in millions of dollars.
What is the percentage x cleaned if f(x) = 750 (million dollars)? The value for x is in the interval:

a (0,30)

b (30,50)

c (50,70)

d (70,90)

e nota

6.7

27.
Solve for x in the formula: B = xw/(x + w)

a (Bx - Bw)/w

b (Bx + Bw)/w

c Bw/(w + B)

d Bw/(w - B)

e nota

written problems

28. A pool can be filled by one pipe in 3 hours and by a second pipe in 6 hours. How long will it take using both pipes to fill the pool?

6.8

29. The cost C of an airplane varies directly as the number of miles M in the trip. Yo, a 3000 -mile trip costs $400. What is the cost of a 450-mile trip? Note this direct variation can also be thought of as a proportion problem:
(3000 miles)/($400) = (450 miles)/y. Thus, you can cross-multiply and solve for the cost y, i.e. solve: 3000/400 = 450/y.

7.1

30. Simplify these two problems:

31. Simplify this problem:

32. Simplify this problem:

33. 7.2. Simplify 27^2/3

EC spells Extra Credit

34. Add: 7 + 2/x

35. Solve for w in the formula: B = xw/(x + w)

36. Solve. 6/x - x/3 = 1

37. Solve. 1/(x + 1) = 2/(x -1)

38. Solve by factoring : x³ - 2x² - x + 2 = 0.