Math Test - No Calculator

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Questão 1

Which of the following expressions is equal to 0 for some value of x ?

A) |x − 1| − 1

B) |x + 1| + 1

C) |1 − x| + 1

D) |x − 1| + 1


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Questão 2

  In the function above, b is a constant. If f (6) = 7, what is the value of f (−2) ?


A) −5

B) −2

C) 1

D) 7


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Questão 3


If (x, y) is the solution to the system of equations above, what is the value of y ?

A) 2

B) 4

C) 12

D) 24

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Questão 4

If f (x) = −2x + 5, what is f (−3x) equal to?

A) −6x − 5

B) 6x + 5

C) 6x − 5

D) 6x2 − 15x

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Questão 5

3(2x +1)(4x + 1) Which of the following is equivalent to the expression above?

A) 45x

B) 24x2 + 3

C) 24x2 + 18x + 3

D) 18x2 + 6


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Questão 6

If     which of the following must also be true?



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Questão 7

While preparing to run a marathon, Amelia created a training schedule in which the distance of her longest run every week increased by a constant amount. If Amelia’s training schedule requires that her longest run in week 4 is a distance of 8 miles and her longest run in week 16 is a distance of 26 miles, which of the following best describes how the distance Amelia runs changes between week 4 and week 16 of her training schedule?

A) Amelia increases the distance of her longest run by 0.5 miles each week.

B) Amelia increases the distance of her longest run by 2 miles each week.

C) Amelia increases the distance of her longest run by 2 miles every 3 weeks.

D) Amelia increases the distance of her longest run by 1.5 miles each week.


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Questão 8

Which of the following equations represents a line that is parallel to the line with equation y = −3x + 4 ?

A) 6x + 2y = 15

B) 3x − y = 7

C) 2x − 3y = 6

D) x + 3y = 1


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Questão 9

If a = 2, what is the solution set of the equation above?

A)   {3,6}

B)   {2}

C)   {3}

D)   {6}


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Questão 10

If     what is the value of t?


A)  

B)   5

C)  

D)  


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Questão 11

x= 2y + 5

y= (2x - 3)(x + 9)

How many ordered pairs (x, y) satisfy the system of equations shown above?

A) 0

B) 1

C) 2

D) Infinitely many


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Questão 12

Ken and Paul each ordered a sandwich at a restaurant. The price of Ken’s sandwich was x dollars, and the price of Paul’s sandwich was $1 more than the price of Ken’s sandwich. If Ken and Paul split the cost of the sandwiches evenly and each paid a 20% tip, which of the following expressions represents the amount, in dollars, each of them paid? (Assume there is no sales tax.)

A) 0.2x + 0.2

B) 0.5x + 0.1

C) 1.2x + 0.6

D) 2.4x + 1.2


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Questão 13

The functions f and g, defined by f(x) = 8x2 - 2 and g(x) = - 8x2 + 2, are graphed in the xy-plane above. The graphs of f and g intersect at the points (k, 0) and (-k, 0). What is the value of k?

A)

B)

C) 1

D) 2


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Questão 14

If the expression above is rewritten in the form a + bi, where a and b are real numbers, what is the value of a? (Note: )

A)   2

B)  

C)   3

D)  


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Questão 15

In the quadratic equation above, k and p are constants. What are the solutions for x?

A) 

B) 

C) 

D) 


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Questão 16

Jim has a triangular shelf system that attaches to his showerhead. The total height of the system is 18 inches, and there are three parallel shelves as shown

above. What is the maximum height, in inches, of a shampoo bottle that can stand upright on the middle shelf?


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Questão 17

In the triangle above, the sine of x° is 0.6. What is the cosine of y° ?


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Questão 18

x3 - 5x2 + 2x - 10

For what real value of x is the equation above true?

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Questão 19

- 3x + 4y = 20

6x + 3y + 15

If (x, y) is the solution to the system of equations above, what is the value of x ?

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Questão 20

The mesosphere is the layer of Earth's atmosphere between 50 kilometers and 85 kilometers above Earth's surface. At a distance of 50 kilometers from Earth's surface, the temperature in the mesosphere is -5° Celsius, and at a distance of 80 kilometers from Earth's surface, the temperature in the mesosphere is -80° Celsius. For every additional 10 kilometers from Earth's surface, the temperature in the mesosphere decreases by k° Celsius, where k is a constant. What is the value of k ?

Math Test - Calculator

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Questão 21

The monthly membership fee for an online television and movie service is $9:80. The cost of viewing television shows online is included in the membership fee, but there is an additional fee of $1.50 to rent each movie online. For one month, Jill's membership and movie rental fees were $12.80. How many movies did Jill rent online that month?

A) 1

B) 2

C) 3

D) 4


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Questão 22

One of the requirements for becoming a court reporter is the ability to type 225 words per minute. Donald can currently type 180 words per minute, and believes that with practice he can increase his typing speed by 5 words per minute each month. Which of the following represents the number of words per minute that Donald believes he will be able to type m months from now?

A) 5 + 180m

B) 225 + 5m

C) 180 + 5m

D) 180 - 5m


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Questão 23

If a 3-pound pizza is sliced in half and each half is sliced into thirds, what is the weight, in ounces, of each of the slices? (1 pound = 16 ounces)

A) 4

B) 6

C) 8

D) 16


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Questão 24

Nick surveyed a random sample of the freshman class of his high school to determine whether the Fall Festival should be held in October or November. Of the 90 students surveyed, 25.6% preferred October. Based on this information, about how many students in the entire 225-person class would be expected to prefer having the Fall Festival in October?

A) 50

B) 60

C) 75

D) 80


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Questão 25

The density of an object is equal to the mass of the object divided by the volume of the object. What is the volume, in milliliters, of an object with a mass of 24 grams and a density of 3 grams per milliliter?

A) 0.125

B) 8

C) 21

D) 72


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Questão 26

Last week Raul worked 11 more hours than Angelica. If they worked a combined total of 59 hours, how many hours did Angelica work last week?

A) 24

B) 35

C) 40

D) 48


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Questão 27

The table above represents the 50 movies that had the greatest ticket sales in 2012, categorized by movie type and Motion Picture Association of America (MPAA) rating. What proportion of the movies are comedies with a PG - 13 rating?

A)  

B)  

C)  

D)  


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Questão 28

Line l in the xy-plane contains points from each of Quadrants II, III, and IV, but no points from Quadrant I. Which of the following must be true?

A) The slope of line l is undefined.

B) The slope of line l is zero.

C) The slope of line l is positive.

D) The slope of line l is negative.


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Questão 29

The table above shows the number of registered voters in 2012, in thousands, in four geographic regions and five age groups. Based on the table, if a registered

voter who was 18 to 44 years old in 2012 is chosen at random, which of the following is closest to the probability that the registered voter was from the Midwest region?

A) 0.10

B) 0.25

C) 0.40

D) 0.75


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Questão 30

What is the life expectancy, in years, of the animal that has the longest gestation period?

A) 3

B) 4

C) 8

D) 10


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Questão 31

Of the labeled points, which represents the animal for which the ratio of life expectancy to gestation period is greatest?

A) A

B) B

C) C

D) D


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Questão 32

In the xy-plane, the graph of function f has x-intercepts at -3, -1, and 1. Which of the following could define f ?

A) f(x) = (x - 3)(x - 1)(x + 1)

B) f(x) = (x - 3)(x - 1)2

C) f(x) = (x - 1)(x + 1)(x + 3)

D) f(x) = (x + 1)2(x + 3)


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Questão 33

The population of mosquitoes in a swamp is estimated over the course of twenty weeks, as shown in the table.

Time (weeks) population
0 100
5 1,000
10 10,000
15 100,000
20 1,000,000


Which of the following best describes the relationship between time and the estimated population of mosquitoes during the twenty weeks?


A)  Increasing linear

B)  Decreasing linear

C)  Exponential growth

D)  Exponential decay


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Qestão 34


The expression above gives the amount of money, in dollars, generated in a year by a $1;000 deposit in a bank account that pays an annual interest rate of r%,compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of 5% than at an interest rate of 3% ?

A)  

B)  

C)  

D)  


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Questão 35

Which of the following scatterplots shows a relationship that is appropriately modeled with the equation y = axb, where a is positive and b is negative?

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Questão 36

For what number of days, x, will the total cost of buying the materials and renting the tools from Store B be less than or equal to the total cost of buying the materials and renting the tools from Store A ?

A)   x 6

B)   x 6

C)   x 7.3

D)   x 7.3


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Questão 37

If the relationship between the total cost, y, of buying the materials and renting the tools at Store C and the number of days, x, for which the tools are rented is graphed in the xy-plane, what does the slope of the line represent?

A) The total cost of the project

B) The total cost of the materials

C) The total daily cost of the project

D) The total daily rental costs of the tools


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Questão 38

Jim has identical drinking glasses each in the shape of a right circular cylinder with internal diameter of 3 inches. He pours milk from a gallon jug into each glass until it is full. If the height of milk in each glass is about 6 inches, what is the largest number of full milk glasses that he can pour from one gallon of milk? (Note: There are 231 cubic inches in 1 gallon.)

A) 2

B) 4

C) 5

D) 6


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Questão 39

If 3p - 2 1 , what is the least possible value of 3p + 2 ?

A) 5

B) 3

C) 2

D) 1


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Questão 40

The mass of living organisms in a lake is dened to be the biomass of the lake. If the biomass in a lake doubles each year, which of the following graphs could model the biomass in the lake as a function of time? (Note: In each graph below, O represents (0, 0).)


A)

B)

C)

D)


Question 41 and 42 refer to the following information

The bar graph above shows renewable energy consumption in quadrillions of British thermal units (Btu) in the United States, by energy source, for several energy sources in the years 2000 and 2010.


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Questão 41

In a scatterplot of this data, where renewable energy consumption in the year 2000 is plotted along the x-axis and renewable energy consumption in the year 2010 is plotted along the y-axis for each of the given energy sources, how many data points would be above the line y = x ?

A) 1

B) 2

C) 3

D) 4


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Questão 42

Of the following, which best approximates the percent decrease in consumption of wood power in the United States from 2000 to 2010 ?

A) 6%

B) 11%

C) 21%

D) 26%


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Questão 43

The tables below give the distribution of high temperatures in degrees Fahrenheit (°F) for City A and City B over the same 21 days in March.

Which of the following is true about the data shown for these 21 days?

A) The standard deviation of temperatures in City A is larger.

B) The standard deviation of temperatures in City B is larger.

C) The standard deviation of temperatures in City A is the same as that of City B.

D) The standard deviation of temperatures in these cities cannot be calculated with the data provided.


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Questão 44

In the circle above, segment AB is a diameter. If the length of arc   is 8, what is the length of the radius of the circle?

A) 2

B) 4

C) 8

D) 16


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Questão 45

f(x) = 2x3 + 6x2 + 4x

g(x) = x2 + 3x + 2

The polynomials f(x) and g(x) are defined above. Which of the following polynomials is divisible by 2x + 3?

A) h(x) = f(x) + g(x)

B) p(x) = f(x) + 3g(x)

C) r(x) = 2f(x) + 3g(x)

D) s(x) = 3f(x) + 2g(x)


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Questão 46

Let x and y be numbers such that -y < x < y. Which of the following must be true?

I. |x| < y

II. x > 0

III. y > 0

A) I only

B) I and II only

C) I and III only

D) I, II, and III


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Questão 47

The relative housing cost for a US city is defined to be the ratio , expressed as a percent.

The scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005. The line of best fit is also shown and has equation y = 0.0125x + 61. Which of the following best explains how the number 61 in the equation relates to the scatterplot?

A) In 2005, the lowest housing cost in the United States was about $61 per month.

B) In 2005, the lowest housing cost in the United States was about 61% of the highest housing cost.

C) In 2005, even in cities with low population densities, housing costs were never below 61% of the national average.

D) In 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.


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Questão 48

f(x) = (x + 6)(x - 4)

Which of the following is an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient?

A) f(x) = x2 - 24

B) f(x) = x2 + 2x - 24

C) f(x) = (x - 1)2 - 21

D) f(x) = (x + 1)22- 25

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Questão 49

If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m ?

A) m + 6

B) m + 7

C) 2m + 14

D) 3m + 21


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Questão 50

The function f(x) = x 3 - x2 - x - is graphed in the xy-plane above. If k is a constant such that the equation f(x) = k has three real solutions, which of the following could be the value of k ?

A)   2

B)   0

C) -2

D) -3


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Questão 51

A partially filled pool contains 600 gallons of water. A hose is turned on, and water ows into the pool at the rate of 8 gallons per minute. How many gallons of water will be in the pool after 70 minutes?


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Questão 52

The normal systolic blood pressure P, in millimeters of mercury, for an adult male x years old can be modeled by the equation   .   According to the model, for every increase of 1 year in age, by how many millimeters of mercury will the normal systolic blood pressure for an adult male increase?


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Questão 53

The pes, a Roman measure of length, is approximately equal to 11:65 inches. It is also equivalent to 16 smaller Roman units called digits. Based on these relationships, 75 Roman digits is equivalent to how many feet, to the nearest hundredth? (12 inches = 1 foot)

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Questão 54

In a study of bat migration habits, 240 male bats and 160 female bats have been tagged. If 100 more female bats are tagged, how many more male bats must be tagged so that     of the total number of bats in the study are male?


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Questão 55

The dynamic pressure q generated by a fluid moving with velocity v can be found using the formula above, where n is the constant density of the fluid. An aeronautical engineeruses the formula to find the dynamic pressure of a fluid moving with velocity v and the same fluid moving with velocity 1.5v. What is the ratio of the dynamic pressure of the faster fluid to the dynamic pressure of the slower fluid?


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Questão 56

In the figure above, the circle has center O and has radius 10. If the length of arc (shown in bold) is between 5 and 6, what is one possible >integer value of x ?


Questions 37 and 38 refer to the following information.

The stock price of one share in a certain company is worth $360 today. A stock analyst believes that the stock will lose 28 percent of its value each week for the next three weeks. The analyst uses the equation
V = 360(r)t to model the value, V , of the stock after t weeks.

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Questão 57

What value should the analyst use for r?


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Questão 58

To the nearest dollar, what does the analyst believe the value of the stock will be at the end of three weeks? (Note: Disregard the $ sign when gridding your

answer.)