Math AEPA

33

1. A high school graduat recently sarted a new job. worked 20% more hours third week on the job than she did in the second week. She worked 30% more hours in the second week than she did in the first week, and she worked 10% fewer hours in the fist week than her regularly schedled weekly hours. If the graduate worked 46 hours in her 3rd week, approximately what are her regularly scheduled weekly wok hours?

5

10. On the first of Marc, some water is put into a water tank. For the next 32 days, 3 gallons of water is added to the tank each day. If, at the end of this period, there are 101 gallons of water in the tank, how many gallons were put in the tank of the first of March?

4

11. A photographer is trying to arrange four children in a row for a picture. Each child is wearing a different color sweater. If the child in the red sweater does not want to be placed on either end of the row and wants to be placed immediately to the right of the child in the blue sweater, in how may ways can the four children be arranged?

11.5

12. 19,5,16,12,k,11,3,20 If the mean of the list of numbers above is 12, what is the median of the list?

The respondents to the poll do not constitute a representtive sample of the whole population

22. A tv program asked its viewers to respond to the question, "Do you think the voting age should be raised to 21?" Of the 550 people who responded, 21% responded "yes," 72% responded "no," and 7% responded "unsure." Which of the following best explains why the results of this poll should not be used to make inferences about the entire population in the country?

y=2x-1

23. The inverse of which of the following functions is a function? y=2x-1 y=x^2 +x-4 y= lx-3l y= sqr 16-x^2

The x- intercept of the graph of g(x) is double the x-intercept of the graph of f(x)

24. Consider the graphs of the functions f(x)= ax+b and g(x)= hx+k, where a and b are negative integers and h= 1/2a and k=b. Which of the following describes a difference between the graphs of f(x) and g(x)?

(-infinity,2)U 2,-3)U(-3, infinity)

25. what is the domain of p(x)= x^2-5x-14 ----------- x^2-x-6

the inverse of [1 1 1 ] [ 1 -2 -2] [0 -2 1]

27. A rectangular box has length L, width W, and height H. The sum of its length, width and height is 75cm. its length is twice the sum of its width and height, and its height is 5cm less than twice its width. What are the dimesions of this box?

m<equal 2

29. The equation 2x^2-4x+m=0 has a real number solution if which of the following is true? m=>-2 m=>2 m=<-2 m=<2

$1500x .983 x983

3. A factory's energy costs in January are $1500. The factory owner estimates that the cost of energy will decrease by 1.7% per month over the next six months. Based on this estimate, what will the factory's energy cost be in March of the same year? Which of the following represents the solution to the problem above?

2015

30. The population in town A declined at a constant rate from 10,000 in the year 1990 to 9,040 in the year 1998. The population in town B increased at a constant rate from 4,000 in the year 1994 to 4,560 in the year 1998. If the rate of change of population in towns A and B remain the same, n approximately what year will the populations in the two towns be equal?

part of quad 3 and most of quad 4

31. Which of the following represents the solution set for the system of inequalities g(x)<=-2x and h(x)<= 8x-X^2?

s(t)=s_start 2^-t

32.Time (minutes) Speed( in knots) 0 20 1 10 2 5 3 2.5 4 1.25 Researchers are running an expriment to determine effects of the force of water on a boat. The experiment involves bringing the boat to a speed of 20 knots and then turning the motor off. The table above shows the speed of the boat at given times. If Start denotes the speed of the boat at the moment when the motor is turned off, which of the following functions describes the speed of the boat at any time t?

r=ln B(t)-ln500/t

33. The mass of a bacteria colony at time t is given by B(t)ke^rt where r is the rate of growth of the mass of bacteria. If the initial mass of the bacteria colony is 500 unites, which of the following represents the growth rate of the mass as a function of t and B(t)?

0,0 going up

34. The period of a pendulum, defined as the length of time the pendulum takes to make one complete swing, varies directly with the square root of the length of the pendulum. Which of the following graphs represents the length of a pendulum as a function of its period?

150

37. A citrus grower finds that when there are 100 oranges trees planted in his field, the yield per tree is 450 oranges. He estimates that the yield will decrease by 3 oranges per tree for each additional tree planted in the same field if the total yield of the citrus grower's field is given by a function of the form y(x)=ax^2+bx+45,000, where x denotes each additional tree planted, what is the value of b?

40mph

39. Each wheel on a vehicle has a radius of 20 inches. If the vehicle's wheels rotate at 340 revolutions per minute. What is the approximate speed of the vehicle in miles per hour?

4,210 degree

4. If z_1 and z_2 are complex numbers with z_1= -1+i sqr 3 and z_2=2i then which of the following is the polar representation of the product z_1z_2?

$22

40. A homeowner is planning to paint an 8ft by 22ft wall and wants to determine the cost of the project. She tests a 14 inch inch by 18 inch section of the wall and finds that 1 ounce of paint is needed for good coverage. If she uses paint that cost $28 per gallon, what will by the cost of the paint needed to give the entire wall a good coverge of paint?

6k parts/ million/ day

63. The daily amount of smog produced by cars in a city is given by s=3+4x^3/2, where s is the smong concentration in parts per million and x is the number of cars in the city. If the number of cars in the city increases at the rate of 20 per day, at wat rate will the smog concentration changes when there are 2500 in the city?

5/6

64.What is the area of the region bounded by the graphs of y=x^2, y=x and x=2

432

66. The number of journalist in a metropolitan region is increasing at a rate of 18t^2+60t journalists per year. If t=0 represents the present, what will be the increase in the total number of journalists in the region over the next 3 years?

The largest number that divides both p and q

68. A building contractor has a rectangle with sides of integer lengths p and q that is to be covered using the smllest number of identical squares tiles possible. The tiles are to be placed adjacent to one another and should not exceed the area of the rectangle. Which of the following represents the side length of the tile that should be used?

1/5N+1/4N+1/3N+N=150

70. Of the students in a high school, 1/5 freshmen, 1/4 sophomores, 1/3 jr, 150 students are sr. If N denotes the total number of students in the school, what is the correct statement?

(AnB)^cnB

72. If A and B are two finite sets in the universal set, what is equivalent to B-(AnB)?

RSTU is a parallelogram

73. In quadrilateral RSTU. angle TUS=28 degree. and RSU= 31 degree. To construct an indirect proof that quadrilateral RSTU is not a parallelogram, the first would be to assume that.

If a triangle is equilateral, then it is isosceles

74.If a tringle is not isosceles, then it is ot equilateral. If the statement above is true, then which of the following statemnt must also be true? C

Let a be a postive intger and let b be a negative integer

75. If a>b, then 1/a<1/b Which o the following would be a counterexample to the statement above?

Reflection

78. Students in an algebra class are comparing the graphs of f(x)=x+a and g(x)= -x-a. This topic of study is related to which of the following concepts from transformational geometry?

Given any two points, at least one line can be drawn through the points

79. In spherical geometry, lines are define as "great circles" that span the circumferece of a sphere. Which of the following statements from Euclidean geometry holds in spherical gemetry?

268=1x165+103

8. The Euclidean algorithm is used to find the greatest commn divisor of 2000 and 433. If the first step of the algorithm is expressed as 2000=4x 433+ 268, then which of the following could represent the third step of the algorithm?

A statement that follows readily from a theorem

80. Which of the following best describes a corollary?

10!/ 3! 7!

9. In how many ways may a person order an ice cream cone with scoops of three different flavors if there are ten flavors to choose from?

The ave. remains the same and the standard deviation decreases.

13. A list of various number has an average value of 24. If the number 24 is added to the list, which of the following describes the effect on the average and standard deviation of the original list?

1/4

16. six individual socks are drawn at random without replacement from a basket containing seven different pairs of socks. If the six socks drawn are all different from one another, what is the probability that the next sock drawn at random from the basket is also different from the rest?

1/4

17. A point (x,y) is randomly chosen such that 0 <=x<= 1 and 0<= y <= 1. what is the probability that y => 2x?

.25

18. Of all the cars sold at a car dealership, 80% are not convertibles, 40% are red, and 5% are red convertibles. Given that a car sold by a salesperson at this dealership is a convertible what is the probability that it is red?

.0668

19. The number of peanuts in a six- ounce bag of peanuts is normally distributed with a mean of 230 and a standard deviation of 20. What is the probability that a randomly selected six- ounce bag of peanuts has more than 260 peanuts in it?

scatter plot

21. For each subject in a study, researcher record vaules for random variables representing age, number of years of education, income level, and length of time with current employer. The researchers want to determine whether there is a correlation between anyof the two variables. Which of the following graphical representations would be most effective in enabling the researchers to make this determination?

4x^3-76x^2+360x in^3

45. A piece of cardboard measuring 18 inches by 20 inches is to be made into a box by cutting a squar out of each corner of the pience of carboard and then folding up the remaing flaps. If each square cut out of the corners has sides of length x inches what i the volume of the resulting box.

16ft

48. The cross section of the roof of a building shown above has a width of 40 feet and a slope of 4/5 feet. If the cross section of the roof represents an isosceles triangle, what is the height h of the roof?

The distributive propert and the commutative property

5. Prove that-1a=-a Proof: 1. -1a+a=-1a+1a 2. =(-1+1)a 3. = 0a 4. = a 5. = a+(-a) 6. = -a+a 7. -1a= -a

y=4/5x-17/5

50. A triangle RST has coordinates (0,2),(6,-4), and (-4,-12). Under a dilation centered at point R, with a scale factor of 1/2, triangle RST becomes triangles R` S` T`. Which of the following is the equation of the line joining pots S` and T`?

(-3,-1)

52. The graph of the parabola y=x^2- 1 is translated 3 units to the right and then reflected about the y-axis. What are the coordinates of the vertex of the parabola that results under this transformation?

4250.43 sq ft

53. To provide a swimming area for local residents, a town has enclosed a section of a pont with two sets of trings of buoys of length 86.32 ft and 100 ft. The strings of buoys form a triangluar region with the beach on the side of the pond. What is the area of the swimming pool?

12/5

54. Given that secO= 5/3 and 0<equal o <equal 3.14/2, what is the value of the expression tanO+ sin^2O/cosO?

2sqr3/3 3.14s

55.An equilateral triangle with side length s is inscribed in a circle. What is the circumference of the circle?

4

56. How many solutions does the equation 2cos^2x=1 have on the interval 0 <equal X <equal 2(3.14)?

10sin(x-3.14/2)

57. Which of the following functions has a graph that looks like thi graph of f(x) sifted 3.14/2 units to the right and has a period that is two times the period of f(x)?

h(t)=30cos(3.14t)+30

58. The wheels on an athlete's bicycle eah have a diameter of 60cm. At time t=0, a marker is placed at the top edge of the rear wheel of the bicycle. If the athlete rides the bicycle at a speed of 30(3.14) cm per second. Which of the following represents the height h of the marker at time t?

2

59. What is the value of lim K^2+ 2k/ k? k->

-20

62. What is the local minimum value of f(x)=2x^3-3x^2-12x?