| {"question": "If $\\frac{x-1}{3}=k$ and $k=3$, what is the value of $x ?$", "options": ["(A)2", "(B)4", "(C)9", "(D)10"], "label": "D"} | |
| {"question": "For $i=\\sqrt{-1}$, what is the sum $(7+3 i)+(-8+9 i) ?$", "options": ["(A)$-1+12 i$", "(B)$-1-6 i$", "(C)$15+12 i$", "(D)$15-6 i$ 3"], "label": "A"} | |
| {"question": "On Saturday afternoon, Armand sent $m$ text messages each hour for 5 hours, and Tyrone sent $p$ text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?", "options": ["(A)$9 m p$", "(B)$20 m p$", "(C)$5 m+4 p$", "(D)$4 m+5 p$"], "label": "C"} | |
| {"question": "Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation $P=108-23 d$, where $P$ is the number of phones left and $d$ is the number of days she has worked that week. What is the meaning of the value 108 in this equation?", "options": ["(A)Kathy will complete the repairs within 108 days.", "(B)Kathy starts each week with 108 phones to fix.", "(C)Kathy repairs phones at a rate of 108 per hour.", "(D)Kathy repairs phones at a rate of 108 per day."], "label": "B"} | |
| {"question": "$$\\left(x^{2} y-3 y^{2}+5 x y^{2}\\right)-\\left(-x^{2} y+3 x y^{2}-3 y^{2}\\right)$$Which of the following is equivalent to the expression above?", "options": ["(A)$4 x^{2} y^{2}$", "(B)$8 x y^{2}-6 y^{2}$", "(C)$2 x^{2} y+2 x y^{2}$", "(D)$2 x^{2} y+8 x y^{2}-6 y^{2}$"], "label": "C"} | |
| {"question": "$$h=3 a+28.6$$A pediatrician uses the model above to estimate the height $h$ of a boy, in inches, in terms of the boy's age $a$, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy's height each year?", "options": ["(A)3", "(B)$\\quad 5.7$", "(C)9.5", "(D)14.3"], "label": "A"} | |
| {"question": "$$m=\\frac{\\left(\\frac{r}{1,200}\\right)\\left(1+\\frac{r}{1,200}\\right)^{N}}{\\left(1+\\frac{r}{1,200}\\right)^{N}-1} P$$The formula above gives the monthly payment $m$ needed to pay off a loan of $P$ dollars at $r$ percent annual interest over $N$ months. Which of the following gives $P$ in terms of $m, r$, and $N$ ?", "options": ["(A)$P=\\frac{\\left(\\frac{r}{1,200}\\right)\\left(1+\\frac{r}{1,200}\\right)^{N}}{\\left(1+\\frac{r}{1,200}\\right)^{N}-1} m$", "(B)$P=\\frac{\\left(1+\\frac{r}{1,200}\\right)^{N}-1}{\\left(\\frac{r}{1,200}\\right)\\left(1+\\frac{r}{1,200}\\right)^{N}} m$", "(C)$P=\\left(\\frac{r}{1,200}\\right) m$", "(D)$P=\\left(\\frac{1,200}{r}\\right) m$"], "label": "B"} | |
| {"question": "If $\\frac{a}{b}=2$, what is the value of $\\frac{4 b}{a} ?$", "options": ["(A)0", "(B)1", "(C)2", "(D)4"], "label": "C"} | |
| {"question": "$$\\begin{array}{r}3 x+4 y=-23 \\\\2 y-x=-19\\end{array}$$What is the solution $(x, y)$ to the system of equations above?", "options": ["(A)$(-5,-2)$", "(B)$(3,-8)$", "(C)$(4,-6)$", "(D)$(9,-6)$"], "label": "B"} | |
| {"question": "$$g(x)=a x^{2}+24$$For the function $g$ defined above, $a$ is a constant and $g(4)=8$. What is the value of $g(-4)$ ?", "options": ["(A)8", "(B)0", "(C)-1", "(D)-8"], "label": "A"} | |
| {"question": "$$\\begin{aligned}& b=2.35+0.25 x \\\\& c=1.75+0.40 x\\end{aligned}$$In the equations above, $b$ and $c$ represent the price per pound, in dollars, of beef and chicken, respectively, $x$ weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?", "options": ["(A)$\\$ 2.60$", "(B)$\\$ 2.85$", "(C)$\\$ 2.95$", "(D)$\\$ 3.35$"], "label": "D"} | |
| {"question": "A line in the $x y$-plane passes through the origin and has a slope of $\\frac{1}{7}$. Which of the following points lies on the line?", "options": ["(A)$(0,7)$", "(B)$(1,7)$", "(C)$(7,7)$", "(D)$(14,2)$"], "label": "D"} | |
| {"question": "If $x>3$, which of the following is equivalent to $\\frac{1}{\\frac{1}{x+2}+\\frac{1}{x+3}}$ ?", "options": ["(A)$\\frac{2 x+5}{x^{2}+5 x+6}$", "(B)$\\frac{x^{2}+5 x+6}{2 x+5}$", "(C)$2 x+5$", "(D)$x^{2}+5 x+6$"], "label": "B"} | |
| {"question": "If $3 x-y=12$, what is the value of $\\frac{8^{x}}{2^{y}} ?$", "options": ["(A)$2^{12}$", "(B)4", "(C)$8^{2}$", "(D)The value cannot be determined from the information given."], "label": "A"} | |
| {"question": "If $(a x+2)(b x+7)=15 x^{2}+c x+14$ for all values of $x$, and $a+b=8$, what are the two possible values for $c$ ?", "options": ["(A)3 and 5", "(B)6 and 35", "(C)10 and 21", "(D)31 and 41"], "label": "D"} | |
| {"question": "If $y=k x$, where $k$ is a constant, and $y=24$ when $x=6$, what is the value of $y$ when $x=5$ ?", "options": ["(A)6", "(B)15", "(C)20", "(D)23"], "label": "C"} | |
| {"question": "If $16+4 x$ is 10 more than 14 , what is the value of $8 x$ ?", "options": ["(A)2", "(B)6", "(C)16", "(D)80 5"], "label": "C"} | |
| {"question": "$$\\begin{aligned}1 \\text { decagram } & =10 \\text { grams } \\\\1,000 \\text { milligrams } & =1 \\text { gram }\\end{aligned}$$A hospital stores one type of medicine in 2-decagram containers. Based on the information given in the box above, how many 1-milligram doses are there in one 2-decagram container?", "options": ["(A)$\\quad 0.002$", "(B)$\\quad 200$", "(C)$\\quad 2,000$", "(D)20,000"], "label": "D"} | |
| {"question": "For what value of $n$ is $|n-1|+1$ equal to 0 ?", "options": ["(A)0", "(B)1", "(C)2", "(D)There is no such value of $n$."], "label": "D"} | |
| {"question": "Which of the following expresses the air temperature in terms of the speed of a sound wave?", "options": ["(A)$t=\\frac{a-1,052}{1.08}$", "(B)$t=\\frac{a+1,052}{1.08}$", "(C)$t=\\frac{1,052-a}{1.08}$", "(D)$t=\\frac{1.08}{a+1,052}$"], "label": "A"} | |
| {"question": "At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second?", "options": ["(A)$-46^{\\circ} \\mathrm{F}$", "(B)$-48^{\\circ} \\mathrm{F}$", "(C)$-49^{\\circ} \\mathrm{F}$", "(D)$-50^{\\circ} \\mathrm{F}$"], "label": "B"} | |
| {"question": "Which of the following numbers is NOT a solution of the inequality $3 x-5 \\geq 4 x-3$ ?", "options": ["(A)-1", "(B)-2", "(C)-3", "(D)-5"], "label": "A"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c|c|c|c|c|c|}\\cline { 3 - 5 }\\multicolumn{2}{c|}{} & \\multicolumn{3}{c|}{Course} & \\multicolumn{1}{c|}{} \\\\\\cline { 2 - 5 }\\multicolumn{2}{c|}{} & Algebra I & Geometry & $\\begin{array}{c}\\text { Algebra } \\\\ \\text { II }\\end{array}$ & \\multirow{2}{*}{Total} \\\\\\hline\\multirow{2}{*}{Gender} & Female & 35 & 53 & 62 & \\\\\\cline { 2 - 5 }& Male & 44 & 59 & 57 & 160 \\\\\\hline& Total & 79 & 112 & 119 & 310 \\\\\\hline\\end{tabular}\\end{center}A group of tenth-grade students responded to a survey that asked which math course they were currently enrolled in. The survey data were broken down as shown in the table above. Which of the following categories accounts for approximately 19 percent of all the survey respondents?", "options": ["(A)Females taking Geometry", "(B)Females taking Algebra II", "(C)Males taking Geometry", "(D)Males taking Algebra I"], "label": "C"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c|c|c|c|c|c|c|}\\hline\\multicolumn{7}{|c|}{Lengths of Fish (in inches)} \\\\\\hline8 & 9 & 9 & 9 & 10 & 10 & 11 \\\\\\hline11 & 12 & 12 & 12 & 12 & 13 & 13 \\\\\\hline13 & 14 & 14 & 15 & 15 & 16 & 24 \\\\\\hline\\end{tabular}\\end{center}The table above lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24 -inch measurement is removed from the data?", "options": ["(A)Mean", "(B)Median", "(C)Range", "(D)They will all change by the same amount."], "label": "C"} | |
| {"question": "$$\\begin{aligned}& y<-x+a \\\\& y>x+b\\end{aligned}$$In the $x y$-plane, if $(0,0)$ is a solution to the system of inequalities above, which of the following relationships between $a$ and $b$ must be true?", "options": ["(A)$a>b$", "(B)$b>a$", "(C)$|a|>|b|$", "(D)$a=-b$"], "label": "A"} | |
| {"question": "A food truck sells salads for $\\$ 6.50$ each and drinks for $\\$ 2.00$ each. The food truck's revenue from selling a total of 209 salads and drinks in one day was $\\$ 836.50$. How many salads were sold that day?", "options": ["(A)77", "(B)93", "(C)99", "(D)105"], "label": "B"} | |
| {"question": "Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was $p$ dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of $p$ ?", "options": ["(A)$0.88 p$", "(B)$\\frac{p}{0.88}$", "(C)$(0.8)(1.08) p$", "(D)$\\frac{p}{(0.8)(1.08)}$"], "label": "D"} | |
| {"question": "Dreams Recalled during One Week\\begin{center}\\begin{tabular}{|l|c|c|c|c|}\\hline& None & 1 to 4 & 5 or more & Total \\\\\\hline\\hlineGroup X & 15 & 28 & 57 & 100 \\\\\\hlineGroup Y & 21 & 11 & 68 & 100 \\\\\\hlineTotal & 36 & 39 & 125 & 200 \\\\\\hline\\end{tabular}\\end{center}The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y ?", "options": ["(A)$\\frac{68}{100}$", "(B)$\\frac{79}{100}$", "(C)$\\frac{79}{164}$", "(D)$\\frac{164}{200}$"], "label": "C"} | |
| {"question": "Which of the following is an equation of a circle in the $x y$-plane with center $(0,4)$ and a radius with endpoint $\\left(\\frac{4}{3}, 5\\right) ?$", "options": ["(A)$x^{2}+(y-4)^{2}=\\frac{25}{9}$", "(B)$x^{2}+(y+4)^{2}=\\frac{25}{9}$", "(C)$x^{2}+(y-4)^{2}=\\frac{5}{3}$", "(D)$x^{2}+(y+4)^{2}=\\frac{3}{5}$"], "label": "A"} | |
| {"question": "$$h=-4.9 t^{2}+25 t$$The equation above expresses the approximate height $h$, in meters, of a ball $t$ seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?", "options": ["(A)3.5", "(B)4.0", "(C)4.5", "(D)5.0"], "label": "D"} | |
| {"question": "Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina's observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?", "options": ["(A)115", "(B)120", "(C)124", "(D)173"], "label": "B"} | |
| {"question": "A square field measures 10 meters by 10 meters. Ten students each mark off a randomly selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. The students count the earthworms contained in the soil to a depth of 5 centimeters beneath the ground's surface in each region. The results are shown in the table below.\\begin{center}\\begin{tabular}{|c|c|c|c|}\\hlineRegion & $\\begin{array}{c}\\text { Number of } \\\\ \\text { earthworms }\\end{array}$ & Region & $\\begin{array}{c}\\text { Number of } \\\\ \\text { earthworms }\\end{array}$ \\\\\\hlineA & 107 & $\\mathrm{~F}$ & 141 \\\\\\hlineB & 147 & $\\mathrm{G}$ & 150 \\\\\\hlineC & 146 & $\\mathrm{H}$ & 154 \\\\\\hlineD & 135 & $\\mathrm{I}$ & 176 \\\\\\hlineE & 149 & $\\mathrm{~J}$ & 166 \\\\\\hline\\end{tabular}\\end{center}Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters beneath the ground's surface in the entire field?", "options": ["(A)$\\quad 150$", "(B)$\\quad 1,500$", "(C)15,000", "(D)150,000"], "label": "C"} | |
| {"question": "For a polynomial $p(x)$, the value of $p(3)$ is -2 .Which of the following must be true about $p(x)$ ?", "options": ["(A)$x-5$ is a factor of $p(x)$.", "(B)$x-2$ is a factor of $p(x)$.", "(C)$x+2$ is a factor of $p(x)$.", "(D)The remainder when $p(x)$ is divided by $x-3$ is -2 ."], "label": "D"} | |
| {"question": "$$2 z+1=z$$What value of $z$ satisfies the equation above?", "options": ["(A)-2", "(B)-1", "(C)$\\frac{1}{2}$", "(D)1"], "label": "B"} | |
| {"question": "A television with a price of $\\$ 300$ is to be purchased with an initial payment of $\\$ 60$ and weekly payments of $\\$ 30$. Which of the following equations can be used to find the number of weekly payments, $w$, required to complete the purchase, assuming there are no taxes or fees?", "options": ["(A)$300=30 w-60$", "(B)$300=30 w$", "(C)$300=30 w+60$", "(D)$300=60 w-30$"], "label": "C"} | |
| {"question": "Shipping Charges\\begin{center}\\begin{tabular}{|c|c|}\\hline$\\begin{array}{c}\\text { Merchandise weight } \\\\ \\text { (pounds) }\\end{array}$ & $\\begin{array}{c}\\text { Shipping } \\\\ \\text { charge }\\end{array}$ \\\\\\hline5 & $\\$ 16.94$ \\\\\\hline10 & $\\$ 21.89$ \\\\\\hline20 & $\\$ 31.79$ \\\\\\hline40 & $\\$ 51.59$ \\\\\\hline\\end{tabular}\\end{center}The table above shows shipping charges for an online retailer that sells sporting goods. There is a linear relationship between the shipping charge and the weight of the merchandise. Which function can be used to determine the total shipping charge $f(x)$, in dollars, for an order with a merchandise weight of $x$ pounds?", "options": ["(A)$f(x)=0.99 x$", "(B)$f(x)=0.99 x+11.99$", "(C)$f(x)=3.39 x$", "(D)$f(x)=3.39 x+16.94$"], "label": "B"} | |
| {"question": "$$\\sqrt{9 x^{2}}$$If $x>0$, which of the following is equivalent to the given expression?", "options": ["(A)$3 x$", "(B)$3 x^{2}$", "(C)$18 x$", "(D)$18 x^{4}$"], "label": "A"} | |
| {"question": "$$\\frac{x^{2}-1}{x-1}=-2$$What are all values of $x$ that satisfy the equation above?", "options": ["(A)-3", "(B)0", "(C)1", "(D)-3 and -1"], "label": "A"} | |
| {"question": "A circle in the $x y$-plane has center $(5,7)$ and radius 2. Which of the following is an equation of the circle?", "options": ["(A)$(x-5)^{2}+(y-7)^{2}=4$", "(B)$(x+5)^{2}+(y+7)^{2}=4$", "(C)$(x-5)^{2}+(y-7)^{2}=2$", "(D)$(x+5)^{2}+(y+7)^{2}=2$"], "label": "A"} | |
| {"question": "In the $x y$-plane, the graph of the function $f(x)=x^{2}+5 x+4$ has two $x$-intercepts. What is the distance between the $x$-intercepts?", "options": ["(A)1", "(B)2", "(C)3", "(D)4"], "label": "C"} | |
| {"question": "$$\\sqrt{4 x}=x-3$$What are all values of $x$ that satisfy the given equation?I. 1II. 9", "options": ["(A)I only", "(B)II only", "(C)I and II", "(D)Neither I nor II"], "label": "B"} | |
| {"question": "$$\\begin{aligned}& -3 x+y=6 \\\\& a x+2 y=4\\end{aligned}$$In the system of equations above, $a$ is a constant. For which of the following values of $a$ does the system have no solution?", "options": ["(A)-6", "(B)-3", "(C)3", "(D)6"], "label": "A"} | |
| {"question": "A helicopter, initially hovering 40 feet above the ground, begins to gain altitude at a rate of 21 feet per second. Which of the following functions represents the helicopter's altitude above the ground $y$, in feet, $t$ seconds after the helicopter begins to gain altitude?", "options": ["(A)$y=40+21$", "(B)$y=40+21 t$", "(C)$y=40-21 t$", "(D)$y=40 t+21$"], "label": "B"} | |
| {"question": "If $20-x=15$, what is the value of $3 x ?$", "options": ["(A)5", "(B)10", "(C)15", "(D)35"], "label": "C"} | |
| {"question": "$$f(x)=\\frac{x+3}{2}$$For the function $f$ defined above, what is the value of $f(-1)$ ?", "options": ["(A)-2", "(B)-1", "(C)1", "(D)2"], "label": "C"} | |
| {"question": "Which of the following is equivalent to $2 x\\left(x^{2}-3 x\\right)$ ?", "options": ["(A)$-4 x^{2}$", "(B)$3 x^{3}-x^{2}$", "(C)$2 x^{3}-3 x$", "(D)$2 x^{3}-6 x^{2}$"], "label": "D"} | |
| {"question": "A retail company has 50 large stores located in different areas throughout a state. A researcher for the company believes that employee job satisfaction varies greatly from store to store. Which of the following sampling methods is most appropriate to estimate the proportion of all employees of the company who are satisfied with their job?", "options": ["(A)Selecting one of the 50 stores at random and then surveying each employee at that store", "(B)Selecting 10 employees from each store at random and then surveying each employee selected", "(C)Surveying the 25 highest-paid employees and the 25 lowest-paid employees", "(D)Creating a website on which employees can express their opinions and then using the first 50 responses"], "label": "B"} | |
| {"question": "$$h(x)=2^{x}$$The function $h$ is defined above. What is $h(5)-h(3) ?$", "options": ["(A)2", "(B)4", "(C)24", "(D)28"], "label": "C"} | |
| {"question": "A researcher surveyed a random sample of students from a large university about how often they see movies. Using the sample data, the researcher estimated that $23 \\%$ of the students in the population saw a movie at least once per month. The margin of error for this estimation is $4 \\%$. Which of the following is the most appropriate conclusion about all students at the university, based on the given estimate and margin of error?", "options": ["(A)It is unlikely that less than $23 \\%$ of the students see a movie at least once per month.", "(B)At least 23\\%, but no more than $25 \\%$, of the students see a movie at least once per month.", "(C)The researcher is between $19 \\%$ and $27 \\%$ sure that most students see a movie at least once per month.", "(D)It is plausible that the percentage of students who see a movie at least once per month is between $19 \\%$ and $27 \\%$."], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c|c|c|c|c|c|c|}\\hlineList A & 1 & 2 & 3 & 4 & 5 & 6 \\\\\\hlineList B & 2 & 3 & 3 & 4 & 4 & 5 \\\\\\hline\\end{tabular}\\end{center}The table above shows two lists of numbers. Which of the following is a true statement comparing list $\\mathrm{A}$ and list B ?", "options": ["(A)The means are the same, and the standard deviations are different.", "(B)The means are the same, and the standard deviations are the same.", "(C)The means are different, and the standard deviations are different.", "(D)The means are different, and the standard deviations are the same."], "label": "A"} | |
| {"question": "A book was on sale for $40 \\%$ off its original price. If the sale price of the book was $\\$ 18.00$, what was the original price of the book? (Assume there is no sales tax.)", "options": ["(A)$\\$ 7.20$", "(B)$\\$ 10.80$", "(C)$\\$ 30.00$", "(D)$\\$ 45.00$"], "label": "C"} | |
| {"question": "A right circular cone has a volume of $24 \\pi$ cubic inches. If the height of the cone is 2 inches, what is the radius, in inches, of the base of the cone?", "options": ["(A)$2 \\sqrt{3}$", "(B)6", "(C)12", "(D)36"], "label": "B"} | |
| {"question": "In 2015 the populations of City $\\mathrm{X}$ and City $\\mathrm{Y}$ were equal. From 2010 to 2015, the population of City X increased by $20 \\%$ and the population of City $\\mathrm{Y}$ decreased by $10 \\%$. If the population of City $\\mathrm{X}$ was 120,000 in 2010, what was the population of City Y in 2010 ?", "options": ["(A)60,000", "(B)90,000", "(C)160,000", "(D)240,000"], "label": "C"} | |
| {"question": "The volume of a sphere is given by the formula $V=\\frac{4}{3} \\pi r^{3}$, where $r$ is the radius of the sphere. Which of the following gives the radius of the sphere in terms of the volume of the sphere?", "options": ["(A)$\\frac{4 \\pi}{3 V}$", "(B)$\\frac{3 V}{4 \\pi}$", "(C)$\\sqrt[3]{\\frac{4 \\pi}{3 V}}$", "(D)$\\sqrt[3]{\\frac{3 V}{4 \\pi}}$"], "label": "D"} | |
| {"question": "Survey Results\\begin{center}\\begin{tabular}{|l|c|}\\hlineAnswer & Percent \\\\\\hlineNever & $31.3 \\%$ \\\\\\hlineRarely & $24.3 \\%$ \\\\\\hlineOften & $13.5 \\%$ \\\\\\hlineAlways & $30.9 \\%$ \\\\\\hline\\end{tabular}\\end{center}The table above shows the results of a survey in which tablet users were asked how often they would watch video advertisements in order to access streaming content for free. Based on the table, which of the following is closest to the probability that a tablet user answered \"Always,\" given that the tablet user did not answer \"Never\"?", "options": ["(A)0.31", "(B)0.38", "(C)0.45", "(D)0.69"], "label": "C"} | |
| {"question": "$$y=-(x-3)^{2}+a$$In the equation above, $a$ is a constant. The graph of the equation in the $x y$-plane is a parabola. Which of the following is true about the parabola?", "options": ["(A)Its minimum occurs at $(-3, a)$.", "(B)Its minimum occurs at $(3, a)$.", "(C)Its maximum occurs at $(-3, a)$.", "(D)Its maximum occurs at $(3, a)$."], "label": "D"} | |
| {"question": "The maximum value of a data set consisting of 25 positive integers is 84 . A new data set consisting of 26 positive integers is created by including 96 in the original data set. Which of the following measures must be 12 greater for the new data set than for the original data set?", "options": ["(A)The mean", "(B)The median", "(C)The range", "(D)The standard deviation"], "label": "C"} | |
| {"question": "$$0.10 x+0.20 y=0.18(x+y)$$Clayton will mix $x$ milliliters of a $10 \\%$ by mass saline solution with $y$ milliliters of a $20 \\%$ by mass saline solution in order to create an $18 \\%$ by mass saline solution. The equation above represents this situation. If Clayton uses 100 milliliters of the $20 \\%$ by mass saline solution, how many milliliters of the $10 \\%$ by mass saline solution must he use?", "options": ["(A)5", "(B)25", "(C)50", "(D)100"], "label": "B"} | |
| {"question": "The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of people she had invited the previous year. If $f(n)$ is the number of people invited to the fund-raiser $n$ years after Eleanor began organizing the event, which of the following statements best describes the function $f$ ?", "options": ["(A)The function $f$ is a decreasing linear function.", "(B)The function $f$ is an increasing linear function.", "(C)The function $f$ is a decreasing exponential function.", "(D)The function $f$ is an increasing exponential function."], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c|c|c|c|}\\hline$x$ & $a$ & $3 a$ & $5 a$ \\\\\\hline$y$ & 0 & $-a$ & $-2 a$ \\\\\\hline\\end{tabular}\\end{center}Some values of $x$ and their corresponding values of $y$ are shown in the table above, where $a$ is a constant. If there is a linear relationship between $x$ and $y$, which of the following equations represents the relationship?", "options": ["(A)$x+2 y=a$", "(B)$x+2 y=5 a$", "(C)$2 x-y=-5 a$", "(D)$2 x-y=7 a$"], "label": "A"} | |
| {"question": "$$\\begin{aligned}& 2.4 x-1.5 y=0.3 \\\\& 1.6 x+0.5 y=-1.3\\end{aligned}$$The system of equations above is graphed in the $x y$-plane. What is the $x$-coordinate of the intersection point $(x, y)$ of the system?", "options": ["(A)-0.5", "(B)-0.25", "(C)0.8", "(D)1.75"], "label": "A"} | |
| {"question": "Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees' pollen grains per square centimeter that were deposited each year within layers of a lake's sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a $1 \\%$ annual increase in the number of grains per square centimeter thereafter. Which of the following functions models $P(t)$, the number of pollen grains per square centimeter $t$ years after the first year the grains were deposited?", "options": ["(A)$P(t)=310^{t}$", "(B)$P(t)=310^{1.01 t}$", "(C)$P(t)=310(0.99)^{t}$", "(D)$P(t)=310(1.01)^{t}$"], "label": "D"} | |
| {"question": "$$\\frac{2}{3}(9 x-6)-4=9 x-6$$Based on the equation above, what is the value of $3 x-2$ ?", "options": ["(A)-4", "(B)$-\\frac{4}{5}$", "(C)$-\\frac{2}{3}$", "(D)4"], "label": "A"} | |
| {"question": "$$H=1.88 L+32.01$$The formula above can be used to approximate the height $H$, in inches, of an adult male based on the length $L$, in inches, of his femur. What is the meaning of 1.88 in this context?", "options": ["(A)The approximate femur length, in inches, for a man with a height of 32.01 inches", "(B)The approximate increase in a man's femur length, in inches, for each increase of 32.01 inches in his height", "(C)The approximate increase in a man's femur length, in inches, for each one-inch increase in his height", "(D)The approximate increase in a man's height, in inches, for each one-inch increase in his femur length"], "label": "D"} | |
| {"question": "A painter will paint $n$ walls with the same size and shape in a building using a specific brand of paint. The painter's fee can be calculated by the expression $n K \\ell h$, where $n$ is the number of walls, $K$ is a constant with units of dollars per square foot, $\\ell$ is the length of each wall in feet, and $h$ is the height of each wall in feet. If the customer asks the painter to use a more expensive brand of paint, which of the factors in the expression would change?", "options": ["(A)$h$", "(B)$\\ell$", "(C)$K$", "(D)$n$"], "label": "C"} | |
| {"question": "If $3 r=18$, what is the value of $6 r+3$ ?", "options": ["(A)6", "(B)27", "(C)36", "(D)39"], "label": "D"} | |
| {"question": "Which of the following is equal to $a^{\\frac{2}{3}}$, for all values of $a$ ?", "options": ["(A)$\\sqrt{a^{\\frac{1}{3}}}$", "(B)$\\sqrt{a^{3}}$", "(C)$\\sqrt[3]{a^{\\frac{1}{2}}}$", "(D)$\\sqrt[3]{a^{2}}$"], "label": "D"} | |
| {"question": "The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and $x$ states joined between 1850 and 1900 , which of the following equations is true?", "options": ["(A)$30 x=2$", "(B)$2 x=30$", "(C)$\\frac{x}{2}=30$", "(D)$x+30=2$"], "label": "B"} | |
| {"question": "If $\\frac{5}{x}=\\frac{15}{x+20}$, what is the value of $\\frac{x}{5} ?$", "options": ["(A)10", "(B)5", "(C)2", "(D)$\\frac{1}{2}$"], "label": "C"} | |
| {"question": "$$\\begin{aligned}& 2 x-3 y=-14 \\\\& 3 x-2 y=-6\\end{aligned}$$If $(x, y)$ is a solution to the system of equations above, what is the value of $x-y$ ?", "options": ["(A)-20", "(B)$\\quad-8$", "(C)-4", "(D)8"], "label": "C"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c|c|}\\hline$x$ & $f(x)$ \\\\\\hline0 & 3 \\\\\\hline2 & 1 \\\\\\hline4 & 0 \\\\\\hline5 & -2 \\\\\\hline\\end{tabular}\\end{center}The function $f$ is defined by a polynomial. Some values of $x$ and $f(x)$ are shown in the table above. Which of the following must be a factor of $f(x)$ ?", "options": ["(A)$x-2$", "(B)$x-3$", "(C)$x-4$", "(D)$x-5$"], "label": "C"} | |
| {"question": "The line $y=k x+4$, where $k$ is a constant, is graphed in the $x y$-plane. If the line contains the point $(c, d)$, where $c \\neq 0$ and $d \\neq 0$, what is the slope of the line in terms of $c$ and $d$ ?", "options": ["(A)$\\frac{d-4}{c}$", "(B)$\\frac{c-4}{d}$", "(C)$\\frac{4-d}{c}$", "(D)$\\frac{4-c}{d}$"], "label": "A"} | |
| {"question": "$$\\begin{aligned}& k x-3 y=4 \\\\& 4 x-5 y=7\\end{aligned}$$In the system of equations above, $k$ is a constant and $x$ and $y$ are variables. For what value of $k$ will the system of equations have no solution?", "options": ["(A)$\\frac{12}{5}$", "(B)$\\frac{16}{7}$", "(C)$-\\frac{16}{7}$", "(D)$-\\frac{12}{5}$"], "label": "A"} | |
| {"question": "In the $x y$-plane, the parabola with equation $y=(x-11)^{2}$ intersects the line with equation $y=25$ at two points, $A$ and $B$. What is the length of $\\overline{A B}$ ?", "options": ["(A)10", "(B)12", "(C)14", "(D)16"], "label": "A"} | |
| {"question": "$$y=a(x-2)(x+4)$$In the quadratic equation above, $a$ is a nonzero constant. The graph of the equation in the $x y$-plane is a parabola with vertex $(c, d)$. Which of the following is equal to $d$ ?", "options": ["(A)$-9 a$", "(B)$-8 a$", "(C)$-5 a$", "(D)$-2 a$"], "label": "A"} | |
| {"question": "The equation $\\frac{24 x^{2}+25 x-47}{a x-2}=-8 x-3-\\frac{53}{a x-2}$ is true for all values of $x \\neq \\frac{2}{a}$, where $a$ is a constant.What is the value of $a$ ?", "options": ["(A)-16", "(B)-3", "(C)3", "(D)16"], "label": "B"} | |
| {"question": "What are the solutions to $3 x^{2}+12 x+6=0 ?$", "options": ["(A)$x=-2 \\pm \\sqrt{2}$", "(B)$x=-2 \\pm \\frac{\\sqrt{30}}{3}$", "(C)$x=-6 \\pm \\sqrt{2}$", "(D)$x=-6 \\pm 6 \\sqrt{2}$"], "label": "A"} | |
| {"question": "$$C=\\frac{5}{9}(F-32)$$The equation above shows how a temperature $F$, measured in degrees Fahrenheit, relates to a temperature $C$, measured in degrees Celsius. Based on the equation, which of the following must be true?I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $\\frac{5}{9}$ degree Celsius.II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.III. A temperature increase of $\\frac{5}{9}$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.", "options": ["(A)I only", "(B)II only", "(C)III only", "(D)I and II only"], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{|l||c|c||c|}\\cline { 2 - 4 }\\multicolumn{1}{c||}{} & \\multicolumn{2}{c||}{Age} & \\multirow{2}{c|}{Total} \\\\\\hlineGender & Under 40 & 40 or older \\\\\\hline\\hlineMale & 12 & 2 & 14 \\\\\\hlineFemale & 8 & 3 & 11 \\\\\\hline\\hlineTotal & 20 & 5 & 25 \\\\\\hline\\end{tabular}\\end{center}The table above shows the distribution of age and gender for 25 people who entered a contest. If the contest winner will be selected at random, what is the probability that the winner will be either a female under age 40 or a male age 40 or older?", "options": ["(A)$\\frac{4}{25}$", "(B)$\\frac{10}{25}$", "(C)$\\frac{11}{25}$", "(D)$\\frac{16}{25}$"], "label": "B"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c||c|c|c|c|}\\hline$n$ & 1 & 2 & 3 & 4 \\\\\\hline$f(n)$ & -2 & 1 & 4 & 7 \\\\\\hline\\end{tabular}\\end{center}The table above shows some values of the linear function $f$. Which of the following defines $f$ ?", "options": ["(A)$f(n)=n-3$", "(B)$f(n)=2 n-4$", "(C)$f(n)=3 n-5$", "(D)$f(n)=4 n-6$"], "label": "C"} | |
| {"question": "At Lincoln High School, approximately 7 percent of enrolled juniors and 5 percent of enrolled seniors were inducted into the National Honor Society last year. If there were 562 juniors and 602 seniors enrolled at Lincoln High School last year, which of the following is closest to the total number of juniors and seniors at Lincoln High School last year who were inducted into the National Honor Society?", "options": ["(A)140", "(B)69", "(C)39", "(D)30"], "label": "B"} | |
| {"question": "$$\\begin{aligned}& 3 x^{2}-5 x+2 \\\\& 5 x^{2}-2 x-6\\end{aligned}$$Which of the following is the sum of the two polynomials shown above?", "options": ["(A)$8 x^{2}-7 x-4$", "(B)$8 x^{2}+7 x-4$", "(C)$8 x^{4}-7 x^{2}-4$", "(D)$8 x^{4}+7 x^{2}-4$"], "label": "A"} | |
| {"question": "If $\\frac{3}{5} w=\\frac{4}{3}$, what is the value of $w ?$", "options": ["(A)$\\frac{9}{20}$", "(B)$\\frac{4}{5}$", "(C)$\\frac{5}{4}$", "(D)$\\frac{20}{9}$"], "label": "D"} | |
| {"question": "The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation $y=0.56 x+27.2$, where $x$ represents the number of years since 2000 , and $y$ represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation?", "options": ["(A)The total number of students at the school in 2000", "(B)The average number of students per classroom in 2000", "(C)The estimated increase in the average number of students per classroom each year", "(D)The estimated difference between the average number of students per classroom in 2010 and in 2000"], "label": "C"} | |
| {"question": "Nate walks 25 meters in 13.7 seconds. If he walks at this same rate, which of the following is closest to the distance he will walk in 4 minutes?", "options": ["(A)150 meters", "(B)450 meters", "(C)700 meters", "(D)1,400 meters"], "label": "B"} | |
| {"question": "What is the weight, in newtons, of an object on Mercury with a mass of 90 kilograms?", "options": ["(A)25", "(B)86", "(C)101", "(D)324"], "label": "D"} | |
| {"question": "An object on Earth has a weight of 150 newtons. On which planet would the same object have an approximate weight of 170 newtons?", "options": ["(A)Venus", "(B)Saturn", "(C)Uranus", "(D)Neptune"], "label": "B"} | |
| {"question": "$$h=-16 t^{2}+v t+k$$The equation above gives the height $h$, in feet, of a ball $t$ seconds after it is thrown straight up with an initial speed of $v$ feet per second from a height of $k$ feet. Which of the following gives $v$ in terms of $h, t$, and $k$ ?", "options": ["(A)$v=h+k-16 t$", "(B)$v=\\frac{h-k+16}{t}$", "(C)$v=\\frac{h+k}{t}-16 t$", "(D)$v=\\frac{h-k}{t}+16 t$"], "label": "D"} | |
| {"question": "In order to determine if treatment $\\mathrm{X}$ is successful in improving eyesight, a research study was conducted. From a large population of people with poor eyesight, 300 participants were selected at random. Half of the participants were randomly assigned to receive treatment $X$, and the other half did not receive treatment $X$. The resulting data showed that participants who received treatment $X$ had significantly improved eyesight as compared to those who did not receive treatment $X$. Based on the design and results of the study, which of the following is an appropriate conclusion?", "options": ["(A)Treatment $\\mathrm{X}$ is likely to improve the eyesight of people who have poor eyesight.", "(B)Treatment $\\mathrm{X}$ improves eyesight better than all other available treatments.", "(C)Treatment $X$ will improve the eyesight of anyone who takes it.", "(D)Treatment $\\mathrm{X}$ will cause a substantial improvement in eyesight."], "label": "A"} | |
| {"question": "How will the quantity of the product supplied to the market change if the price of the product is increased by $\\$ 10$ ?", "options": ["(A)The quantity supplied will decrease by 5 units.", "(B)The quantity supplied will increase by 5 units.", "(C)The quantity supplied will increase by 10 units.", "(D)The quantity supplied will increase by 50 units."], "label": "B"} | |
| {"question": "At what price will the quantity of the product supplied to the market equal the quantity of the product demanded by the market?", "options": ["(A)$\\$ 90$", "(B)$\\$ 120$", "(C)$\\$ 133$", "(D)$\\$ 155$"], "label": "B"} | |
| {"question": "Graphene, which is used in the manufacture of integrated circuits, is so thin that a sheet weighing one ounce can cover up to 7 football fields. If a football field has an area of approximately $1 \\frac{1}{3}$ acres, about how many acres could 48 ounces of graphene cover?", "options": ["(A)250", "(B)350", "(C)450", "(D)1,350"], "label": "C"} | |
| {"question": "Of the following four types of savings account plans, which option would yield exponential growth of the money in the account?", "options": ["(A)Each successive year, $2 \\%$ of the initial savings is added to the value of the account.", "(B)Each successive year, $1.5 \\%$ of the initial savings and $\\$ 100$ is added to the value of the account.", "(C)Each successive year, $1 \\%$ of the current value is added to the value of the account.", "(D)Each successive year, $\\$ 100$ is added to the value of the account."], "label": "C"} | |
| {"question": "The sum of three numbers is 855 . One of the numbers, $x$, is $50 \\%$ more than the sum of the other two numbers. What is the value of $x$ ?", "options": ["(A)570", "(B)513", "(C)214", "(D)155"], "label": "B"} | |
| {"question": "Mr. Kohl has a beaker containing $n$ milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class?", "options": ["(A)16", "(B)21", "(C)23", "(D)26"], "label": "D"} | |
| {"question": "In the $x y$-plane, the line determined by the points $(2, k)$ and $(k, 32)$ passes through the origin. Which of the following could be the value of $k$ ?", "options": ["(A)0", "(B)4", "(C)8", "(D)16"], "label": "C"} | |
| {"question": "A rectangle was altered by increasing its length by 10 percent and decreasing its width by $p$ percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of $p$ ?", "options": ["(A)12", "(B)15", "(C)20", "(D)22"], "label": "C"} | |
| {"question": "In planning maintenance for a city's infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 percent every 20 years. If the present population of the city is 50,000, which of the following expressions represents the engineer's estimate of the population of the city $t$ years from now?", "options": ["(A)$50,000(0.1)^{20 t}$", "(B)$50,000(0.1)^{\\frac{t}{20}}$", "(C)$50,000(0.9)^{20 t}$", "(D)$50,000(0.9)^{\\frac{t}{20}}$"], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{|l|c|c|}\\cline { 2 - 3 }\\multicolumn{1}{c|}{} & \\multicolumn{2}{c|}{Handedness} \\\\\\hlineGender & Left & Right \\\\\\hline\\hlineFemale & & \\\\\\hlineMale & & \\\\\\hline\\hlineTotal & 18 & 122 \\\\\\hline\\end{tabular}\\end{center}The incomplete table above summarizes the number of left-handed students and right-handed students by gender for the eighth-grade students atKeisel Middle School. There are 5 times as many right-handed female students as there are left-handed female students, and there are 9 times as many right-handed male students as there are left-handed male students. If there is a total of 18 left-handed students and 122 right-handed students in the school, which of the following is closest to the probability that a right-handed student selected at random is female? (Note: Assume that none of the eighth-grade students are both right-handed and left-handed.)", "options": ["(A)0.410", "(B)0.357", "(C)0.333", "(D)0.250"], "label": "A"} | |
| {"question": "$$\\begin{aligned}& 3 x+b=5 x-7 \\\\& 3 y+c=5 y-7\\end{aligned}$$In the equations above, $b$ and $c$ are constants.If $b$ is $c$ minus $\\frac{1}{2}$, which of the following is true?", "options": ["(A)$x$ is $y$ minus $\\frac{1}{4}$.", "(B)$x$ is $y$ minus $\\frac{1}{2}$.", "(C)$x$ is $y$ minus 1 .", "(D)$x$ is $y$ plus $\\frac{1}{2}$."], "label": "A"} | |
| {"question": "What are the solutions of the quadratic equation $4 x^{2}-8 x-12=0$ ?", "options": ["(A)$x=-1$ and $x=-3$", "(B)$x=-1$ and $x=3$", "(C)$x=1$ and $x=-3$", "(D)$x=1$ and $x=3$"], "label": "B"} | |
| {"question": "$$\\sqrt{k+2}-x=0$$In the equation above, $k$ is a constant. If $x=9$, what is the value of $k$ ?", "options": ["(A)1", "(B)7", "(C)16", "(D)79"], "label": "D"} | |
| {"question": "Which of the following is equivalent to the sum of the expressions $a^{2}-1$ and $a+1$ ?", "options": ["(A)$a^{2}+a$", "(B)$a^{3}-1$", "(C)$2 a^{2}$", "(D)$a^{3}$"], "label": "A"} | |
| {"question": "In air, the speed of sound $S$, in meters per second, is a linear function of the air temperature $T$, in degrees Celsius, and is given by $S(T)=0.6 T+331.4$. Which of the following statements is the best interpretation of the number 331.4 in this context?", "options": ["(A)The speed of sound, in meters per second, at $0^{\\circ} \\mathrm{C}$", "(B)The speed of sound, in meters per second, at $0.6^{\\circ} \\mathrm{C}$", "(C)The increase in the speed of sound, in meters per second, that corresponds to an increase of $1^{\\circ} \\mathrm{C}$", "(D)The increase in the speed of sound, in meters per second, that corresponds to an increase of $0.6^{\\circ} \\mathrm{C}$"], "label": "A"} | |
| {"question": "$$\\begin{aligned}y & =x^{2} \\\\2 y+6 & =2(x+3)\\end{aligned}$$If $(x, y)$ is a solution of the system of equations above and $x>0$, what is the value of $x y$ ?", "options": ["(A)1", "(B)2", "(C)3", "(D)9"], "label": "A"} | |
| {"question": "If $a^{2}+b^{2}=z$ and $a b=y$, which of the following is equivalent to $4 z+8 y$ ?", "options": ["(A)$(a+2 b)^{2}$", "(B)$(2 a+2 b)^{2}$", "(C)$(4 a+4 b)^{2}$", "(D)$(4 a+8 b)^{2}$"], "label": "B"} | |
| {"question": "The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?", "options": ["(A)11", "(B)22", "(C)44", "(D)66"], "label": "C"} | |
| {"question": "Which of the following is equivalent to $9^{\\frac{3}{4}}$ ?", "options": ["(A)$\\sqrt[3]{9}$", "(B)$\\sqrt[4]{9}$", "(C)$\\sqrt{3}$", "(D)$3 \\sqrt{3}$"], "label": "D"} | |
| {"question": "At a restaurant, $n$ cups of tea are made by adding $t$ tea bags to hot water. If $t=n+2$, how many additional tea bags are needed to make each additional cup of tea?", "options": ["(A)None", "(B)One", "(C)Two", "(D)Three"], "label": "B"} | |
| {"question": "Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $\\$ 5$. Assuming gasoline costs $\\$ 4$ per gallon, which equation can Alan use to determine how many fewer average miles, $m$, he should drive each week?", "options": ["(A)$\\frac{25}{4} m=95$", "(B)$\\frac{25}{4} m=5$", "(C)$\\frac{4}{25} m=95$", "(D)$\\frac{4}{25} m=5$"], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c|c|}\\hline$x$ & $f(x)$ \\\\\\hline1 & 5 \\\\\\hline3 & 13 \\\\\\hline5 & 21 \\\\\\hline\\end{tabular}\\end{center}Some values of the linear function $f$ are shown in the table above. Which of the following defines $f$ ?", "options": ["(A)$f(x)=2 x+3$", "(B)$f(x)=3 x+2$", "(C)$f(x)=4 x+1$", "(D)$f(x)=5 x$"], "label": "C"} | |
| {"question": "To make a bakery's signature chocolate muffins, a baker needs 2.5 ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins?( 1 pound $=16$ ounces)", "options": ["(A)7.5", "(B)10", "(C)50.5", "(D)120"], "label": "A"} | |
| {"question": "If $3(c+d)=5$, what is the value of $c+d ?$", "options": ["(A)$\\frac{3}{5}$", "(B)$\\frac{5}{3}$", "(C)3", "(D)5"], "label": "B"} | |
| {"question": "The weight of an object on Venus is approximately $\\frac{9}{10}$ of its weight on Earth. The weight of an object on Jupiter is approximately $\\frac{23}{10}$ of its weight on Earth. If an object weighs 100 pounds on Earth, approximately how many more pounds does it weigh on Jupiter than it weighs on Venus?", "options": ["(A)90", "(B)111", "(C)140", "(D)230"], "label": "C"} | |
| {"question": "An online bookstore sells novels and magazines. Each novel sells for $\\$ 4$, and each magazine sells for $\\$ 1$. If Sadie purchased a total of 11 novels and magazines that have a combined selling price of $\\$ 20$, how many novels did she purchase?", "options": ["(A)2", "(B)3", "(C)4", "(D)5"], "label": "B"} | |
| {"question": "The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of $n$ businesses per year. There were $b$ businesses in the DBA at the beginning of this year. Which function best models the total number of businesses, $y$, the DBA plans to have as members $x$ years from now?", "options": ["(A)$y=n x+b$", "(B)$y=n x-b$", "(C)$y=b(n)^{x}$", "(D)$y=n(b)^{x}$"], "label": "A"} | |
| {"question": "Which of the following is an equivalent form of $(1.5 x-2.4)^{2}-\\left(5.2 x^{2}-6.4\\right) ?$", "options": ["(A)$-2.2 x^{2}+1.6$", "(B)$-2.2 x^{2}+11.2$", "(C)$-2.95 x^{2}-7.2 x+12.16$", "(D)$-2.95 x^{2}-7.2 x+0.64$"], "label": "C"} | |
| {"question": "The density $d$ of an object is found by dividing the mass $m$ of the object by its volume $V$. Which of the following equations gives the mass $m$ in terms of $d$ and $V$ ?", "options": ["(A)$m=d V$", "(B)$m=\\frac{d}{V}$", "(C)$m=\\frac{V}{d}$", "(D)$m=V+d$"], "label": "A"} | |
| {"question": "$$-2 x+3 y=6$$In the $x y$-plane, the graph of which of the following equations is perpendicular to the graph of the equation above?", "options": ["(A)$3 x+2 y=6$", "(B)$3 x+4 y=6$", "(C)$2 x+4 y=6$", "(D)$2 x+6 y=3$"], "label": "A"} | |
| {"question": "$$\\begin{array}{r}\\frac{1}{2} y=4 \\\\x-\\frac{1}{2} y=2\\end{array}$$The system of equations above has solution $(x, y)$. What is the value of $x$ ?", "options": ["(A)3", "(B)$\\frac{7}{2}$", "(C)4", "(D)6"], "label": "D"} | |
| {"question": "$$\\begin{gathered}y \\leq 3 x+1 \\\\x-y>1\\end{gathered}$$Which of the following ordered pairs $(x, y)$ satisfies the system of inequalities above?", "options": ["(A)$(-2,-1)$", "(B)$(-1,3)$", "(C)$(1,5)$", "(D)$(2,-1)$"], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{|l|c|c|c|}\\hline\\multirow{2}{*}{$\\begin{array}{c}\\text { Type of } \\\\\\text { surgeon }\\end{array}$} & \\multicolumn{2}{|c|}{$\\begin{array}{c}\\text { Major professional } \\\\\\text { activity }\\end{array}$} & \\multirow{2}{*}{Total} \\\\\\cline { 2 - 3 }& Teaching & Research \\\\\\hlineGeneral & 258 & 156 & 414 \\\\\\hlineOrthopedic & 119 & 74 & 193 \\\\\\hlineTotal & 377 & 230 & 607 \\\\\\hline\\end{tabular}\\end{center}In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated professional activity is research?", "options": ["(A)0.122", "(B)0.196", "(C)0.318", "(D)0.379"], "label": "A"} | |
| {"question": "A polling agency recently surveyed 1,000 adults who were selected at random from a large city and asked each of the adults, \"Are you satisfied with the quality of air in the city?\" Of those surveyed, 78 percent responded that they were satisfied with the quality of air in the city. Based on the results of the survey, which of the following statements must be true?I. Of all adults in the city, 78 percent are satisfied with the quality of air in the city.II. If another 1,000 adults selected at random from the city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.III. If 1,000 adults selected at random from a different city were surveyed, 78 percent of them would report they are satisfied with the quality of air in the city.", "options": ["(A)None", "(B)II only", "(C)I and II only", "(D)I and III only"], "label": "A"} | |
| {"question": "According to the information in the table, what is the approximate age of an American elm tree with a diameter of 12 inches?", "options": ["(A)24 years", "(B)36 years", "(C)40 years", "(D)48 years"], "label": "D"} | |
| {"question": "If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? $(1$ foot $=12$ inches $)$", "options": ["(A)1.0", "(B)1.2", "(C)1.3", "(D)1.4"], "label": "C"} | |
| {"question": "$$\\frac{a-b}{a}=c$$In the equation above, if $a$ is negative and $b$ is positive, which of the following must be true?", "options": ["(A)$c>1$", "(B)$c=1$", "(C)$c=-1$", "(D)$c<-1$"], "label": "A"} | |
| {"question": "In State X, Mr. Camp's eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth-grade class size in the state is 26. If the students in Mr. Camp's class are representative of students in the state's eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth-grade students in the state who have fewer than two siblings?", "options": ["(A)16,200", "(B)23,400", "(C)30,600", "(D)46,800 Questions 23 and 24 refer to the following information."], "label": "C"} | |
| {"question": "\\begin{center}\\begin{tabular}{|l|c|c|}\\hline\\multicolumn{3}{|c|}{Townsend Realty Group Investments} \\\\\\hlineProperty address & $\\begin{array}{c}\\text { Purchase price } \\\\ \\text { (dollars) }\\end{array}$ & $\\begin{array}{c}\\text { Monthly rental } \\\\ \\text { price } \\\\ \\text { (dollars) }\\end{array}$ \\\\\\hlineClearwater Lane & 128,000 & 950 \\\\\\hlineDriftwood Drive & 176,000 & 1,310 \\\\\\hlineEdgemont Street & 70,000 & 515 \\\\\\hlineGlenview Street & 140,000 & 1,040 \\\\\\hlineHamilton Circle & 450,000 & 3,365 \\\\\\hline\\end{tabular}\\end{center}The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations. 23The relationship between the monthly rental price $r$, in dollars, and the property's purchase price $p$, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?", "options": ["(A)$r(p)=2.5 p-870$", "(B)$r(p)=5 p+165$", "(C)$r(p)=6.5 p+440$", "(D)$r(p)=7.5 p-10$"], "label": "D"} | |
| {"question": "Townsend Realty purchased the Glenview Street property and received a $40 \\%$ discount off the original price along with an additional $20 \\%$ off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?", "options": ["(A)$\\$ 350,000$", "(B)$\\$ 291,700$", "(C)$\\$ 233,300$", "(D)$\\$ 175,000$"], "label": "B"} | |
| {"question": "A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, $p$ people chose the first picture in the set. If more than $20 \\%$ of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of $p$ ?", "options": ["(A)$p>0.20(300-36)$, where $p \\leq 150$", "(B)$p>0.20(300+36)$, where $p \\leq 150$", "(C)$p-36>0.20(300)$, where $p \\leq 150$", "(D)$p+36>0.20(300)$, where $p \\leq 150$"], "label": "D"} | |
| {"question": "The surface area of a cube is $6\\left(\\frac{a}{4}\\right)^{2}$, where $a$ is a positive constant. Which of the following gives the perimeter of one face of the cube?", "options": ["(A)$\\frac{a}{4}$", "(B)$a$", "(C)$4 a$", "(D)$6 a$"], "label": "B"} | |
| {"question": "The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?", "options": ["(A)20", "(B)24", "(C)32", "(D)36"], "label": "C"} | |
| {"question": "$$x^{2}+20 x+y^{2}+16 y=-20$$The equation above defines a circle in the $x y$-plane. What are the coordinates of the center of the circle?", "options": ["(A)$(-20,-16)$", "(B)$(-10,-8)$", "(C)$(10,8)$", "(D)$(20,16)$"], "label": "B"} | |
| {"question": "$$y=x^{2}-a$$In the equation above, $a$ is a positive constant and the graph of the equation in the $x y$-plane is a parabola. Which of the following is an equivalent form of the equation?", "options": ["(A)$y=(x+a)(x-a)$", "(B)$y=(x+\\sqrt{a})(x-\\sqrt{a})$", "(C)$y=\\left(x+\\frac{a}{2}\\right)\\left(x-\\frac{a}{2}\\right)$", "(D)$y=(x+a)^{2}$ DIRECTIONS"], "label": "B"} | |
| {"question": "$$x+y=75$$The equation above relates the number of minutes, $x$, Maria spends running each day and the number of minutes, $y$, she spends biking each day. In the equation, what does the number 75 represent?", "options": ["(A)The number of minutes spent running each day", "(B)The number of minutes spent biking each day", "(C)The total number of minutes spent running and biking each day", "(D)The number of minutes spent biking for each minute spent running"], "label": "C"} | |
| {"question": "Which of the following is equivalent to $3(x+5)-6$ ?", "options": ["(A)$3 x-3$", "(B)$3 x-1$", "(C)$3 x+9$", "(D)$15 x-6$"], "label": "C"} | |
| {"question": "$$\\begin{aligned}& x=y-3 \\\\& \\frac{x}{2}+2 y=6\\end{aligned}$$Which ordered pair $(x, y)$ satisfies the system of equations shown above?", "options": ["(A)$(-3,0)$", "(B)$(0,3)$", "(C)$(6,-3)$", "(D)$(36,-6)$"], "label": "B"} | |
| {"question": "Which of the following complex numbers is equal to $(5+12 i)-\\left(9 i^{2}-6 i\\right)$, for $i=\\sqrt{-1}$ ?", "options": ["(A)$-14-18 i$", "(B)$-4-6 i$", "(C)$4+6 i$", "(D)$14+18 i$"], "label": "D"} | |
| {"question": "If $f(x)=\\frac{x^{2}-6 x+3}{x-1}$, what is $f(-1)$ ?", "options": ["(A)-5", "(B)-2", "(C)2", "(D)5"], "label": "A"} | |
| {"question": "A company that makes wildlife videos purchases camera equipment for $\\$ 32,400$. The equipment depreciates in value at a constant rate for 12 years, after which it is considered to have no monetary value. How much is the camera equipment worth 4 years after it is purchased?", "options": ["(A)$\\$ 10,800$", "(B)$\\$ 16,200$", "(C)$\\$ 21,600$", "(D)$\\$ 29,700$"], "label": "C"} | |
| {"question": "$$x^{2}+6 x+4$$Which of the following is equivalent to the expression above?", "options": ["(A)$(x+3)^{2}+5$", "(B)$(x+3)^{2}-5$", "(C)$(x-3)^{2}+5$", "(D)$(x-3)^{2}-5$"], "label": "B"} | |
| {"question": "Ken is working this summer as part of a crew on a farm. He earned $\\$ 8$ per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $\\$ 10$ per hour for the rest of the week. Ken saves $90 \\%$ of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $\\$ 270$ for the week?", "options": ["(A)38", "(B)33", "(C)22", "(D)16"], "label": "C"} | |
| {"question": "Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $\\$ 640$ per week, and senior directors, who will be paid $\\$ 880$ per week. Her budget for paying the staff members is no more than $\\$ 9,700$ per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if $x$ is the number of junior directors and $y$ is the number of senior directors?", "options": ["(A)$640 x+880 y \\geq 9,700$ $x+y \\leq 10$ $x \\geq 3$ $y \\geq 1$", "(B)$640 x+880 y \\leq 9,700$ $x+y \\geq 10$ $x \\geq 3$ $y \\geq 1$", "(C)$640 x+880 y \\geq 9,700$ $x+y \\geq 10$ $x \\leq 3$ $y \\leq 1$", "(D)$640 x+880 y \\leq 9,700$ $x+y \\leq 10$ $x \\leq 3$ $y \\leq 1$"], "label": "B"} | |
| {"question": "$$a x^{3}+b x^{2}+c x+d=0$$In the equation above, $a, b, c$, and $d$ are constants. If the equation has roots $-1,-3$, and 5 , which of the following is a factor of $a x^{3}+b x^{2}+c x+d$ ?", "options": ["(A)$x-1$", "(B)$x+1$", "(C)$x-3$", "(D)$x+5$"], "label": "B"} | |
| {"question": "The function $f$ is defined by $f(x)=(x+3)(x+1)$. The graph of $f$ in the $x y$-plane is a parabola. Which of the following intervals contains the $x$-coordinate of the vertex of the graph of $f$ ?", "options": ["(A)$-4<x<-3$", "(B)$-3<x<1$", "(C)$1<x<3$", "(D)$3<x<4$"], "label": "B"} | |
| {"question": "Which of the following expressions is equivalent to $\\frac{x^{2}-2 x-5}{x-3} ?$", "options": ["(A)$x-5-\\frac{20}{x-3}$", "(B)$x-5-\\frac{10}{x-3}$", "(C)$x+1-\\frac{8}{x-3}$", "(D)$x+1-\\frac{2}{x-3}$"], "label": "D"} | |
| {"question": "A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width $x$, in inches, of the box?", "options": ["(A)$0<x \\leq 10$", "(B)$0<x \\leq 11 \\frac{2}{3}$", "(C)$0<x \\leq 17 \\frac{1}{2}$", "(D)$0<x \\leq 20$"], "label": "A"} | |
| {"question": "The expression $\\frac{1}{3} x^{2}-2$ can be rewritten as $\\frac{1}{3}(x-k)(x+k)$, where $k$ is a positive constant.What is the value of $k$ ?", "options": ["(A)2", "(B)6", "(C)$\\sqrt{2}$", "(D)$\\sqrt{6}$"], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{|c|c|c|c|}\\hline& $\\begin{array}{c}\\text { Fed only } \\\\ \\text { dry food }\\end{array}$ & $\\begin{array}{c}\\text { Fed both wet } \\\\ \\text { and dry food }\\end{array}$ & Total \\\\\\hlineCats & 5 & 11 & 16 \\\\\\hlineDogs & 2 & 23 & 25 \\\\\\hlineTotal & 7 & 34 & 41 \\\\\\hline\\end{tabular}\\end{center}The table above shows the kinds of foods that are fed to the cats and dogs currently boarded at a pet care facility. What fraction of the dogs are fed only dry food?", "options": ["(A)$\\frac{2}{41}$", "(B)$\\frac{2}{25}$", "(C)$\\frac{7}{41}$", "(D)$\\frac{2}{7}$"], "label": "B"} | |
| {"question": "$$\\left(x^{2}-3\\right)-\\left(-3 x^{2}+5\\right)$$Which of the following expressions is equivalent to the one above?", "options": ["(A)$4 x^{2}-8$", "(B)$4 x^{2}-2$", "(C)$-2 x^{2}-8$", "(D)$-2 x^{2}-2$"], "label": "A"} | |
| {"question": "A certain package requires 3 centimeters of tape to be closed securely. What is the maximum number of packages of this type that can be secured with 6 meters of tape? $(1$ meter $=100 \\mathrm{~cm})$", "options": ["(A)100", "(B)150", "(C)200", "(D)300"], "label": "C"} | |
| {"question": "A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, $95 \\%$ said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?", "options": ["(A)At least $95 \\%$ of people who go see movies will dislike this movie.", "(B)At least $95 \\%$ of people who read books will dislike this movie.", "(C)Most people who dislike this book will like this movie.", "(D)Most people who like this book will dislike this movie."], "label": "D"} | |
| {"question": "Which of the following ordered pairs $(x, y)$ satisfies the inequality $5 x-3 y<4$ ?I. $(1,1)$II. $(2,5)$III. $(3,2)$", "options": ["(A)I only", "(B)II only", "(C)I and II only", "(D)I and III only"], "label": "C"} | |
| {"question": "In the equation $(a x+3)^{2}=36, a$ is a constant. If $x=-3$ is one solution to the equation, what is a possible value of $a$ ?", "options": ["(A)-11", "(B)-5", "(C)-1", "(D)0"], "label": "C"} | |
| {"question": "$$9 a x+9 b-6=21$$Based on the equation above, what is the value of $a x+b ?$", "options": ["(A)3", "(B)6", "(C)8", "(D)12"], "label": "A"} | |
| {"question": "Lani spent $15 \\%$ of her 8-hour workday in meetings. How many minutes of her workday did she spend in meetings?", "options": ["(A)1.2", "(B)15", "(C)48", "(D)72"], "label": "D"} | |
| {"question": "A software company is selling a new game in a standard edition and a collector's edition. The box for the standard edition has a volume of 20 cubic inches, and the box for the collector's edition has a volume of 30 cubic inches. The company receives an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. Which of the following systems of equations can be used to determine the number of standard edition games, $s$, and collector's edition games, $c$, that were ordered?", "options": ["(A)$75-s=c$ $20 s+30 c=1,870$", "(B)$75-s=c$ $30 s+20 c=1,870$", "(C)$\\quad s-c=75$ $25(s+c)=1,870$", "(D)$\\quad s-c=75$ $30 s+20 c=1,870$"], "label": "A"} | |
| {"question": "A customer paid $\\$ 53.00$ for a jacket after a 6 percent sales tax was added. What was the price of the jacket before the sales tax was added?", "options": ["(A)$\\$ 47.60$", "(B)$\\$ 50.00$", "(C)$\\$ 52.60$", "(D)$\\$ 52.84$"], "label": "B"} | |
| {"question": "If 50 one-cent coins were stacked on top of each other in a column, the column would be approximately $3 \\frac{7}{8}$ inches tall. At this rate, which of the following is closest to the number of one-cent coins it would take to make an 8-inch-tall column?", "options": ["(A)75", "(B)100", "(C)200", "(D)390"], "label": "B"} | |
| {"question": "If $a-b=12$ and $\\frac{b}{2}=10$, what is the value of $a+b ?$", "options": ["(A)2", "(B)12", "(C)32", "(D)52"], "label": "D"} | |
| {"question": "$$y=19.99+1.50 x$$The equation above models the total cost $y$, in dollars, that a company charges a customer to rent a truck for one day and drive the truck $x$ miles. The total cost consists of a flat fee plus a charge per mile driven. When the equation is graphed in the $x y$-plane, what does the $y$-intercept of the graph represent in terms of the model?", "options": ["(A)A flat fee of $\\$ 19.99$", "(B)A charge per mile of $\\$ 1.50$", "(C)A charge per mile of $\\$ 19.99$", "(D)Total daily charges of $\\$ 21.49$"], "label": "A"} | |
| {"question": "Based on Current's formula, what is $w$ in terms of $A$ ?", "options": ["(A)$w=30 A-4$", "(B)$w=30 A+4$", "(C)$w=30(A-4)$", "(D)$w=30(A+4)$"], "label": "A"} | |
| {"question": "If Mosteller's and Current's formulas give the same estimate for $A$, which of the following expressions is equivalent to $\\sqrt{h w}$ ?", "options": ["(A)$\\frac{4+w}{2}$", "(B)$\\frac{4+w}{1,800}$", "(C)$2(4+w)$", "(D)$\\frac{(4+w)^{2}}{2}$"], "label": "C"} | |
| {"question": "Percent of Residents Who Earned a Bachelor's Degree or Higher\\begin{center}\\begin{tabular}{|c|c|}\\hlineState & Percent of residents \\\\\\hlineState A & $21.9 \\%$ \\\\\\hlineState B & $27.9 \\%$ \\\\\\hlineState C & $25.9 \\%$ \\\\\\hlineState D & $19.5 \\%$ \\\\\\hlineState E & $30.1 \\%$ \\\\\\hlineState F & $36.4 \\%$ \\\\\\hlineState G & $35.5 \\%$ \\\\\\hline\\end{tabular}\\end{center}A survey was given to residents of all 50 states asking if they had earned a bachelor's degree or higher.The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor's degree or higher for all 50 states was $26.95 \\%$. What is the difference between the median percent of residents who earned a bachelor's degree or higher for these 7 states and the median for all 50 states?", "options": ["(A)$0.05 \\%$", "(B)$0.95 \\%$", "(C)$1.22 \\%$", "(D)$7.45 \\%$"], "label": "B"} | |
| {"question": "A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of $75 \\mathrm{~cm}^{2}$, and the height of the can is $10 \\mathrm{~cm}$. If $110 \\mathrm{~cm}^{3}$ of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?", "options": ["(A)$7.5 \\mathrm{~cm}^{3}$", "(B)$185 \\mathrm{~cm}^{3}$", "(C)$640 \\mathrm{~cm}^{3}$", "(D)$750 \\mathrm{~cm}^{3}$"], "label": "C"} | |
| {"question": "$$h(t)=-16 t^{2}+110 t+72$$The function above models the height $h$, in feet, of an object above ground $t$ seconds after being launched straight up in the air. What does the number 72 represent in the function?", "options": ["(A)The initial height, in feet, of the object", "(B)The maximum height, in feet, of the object", "(C)The initial speed, in feet per second, of the object", "(D)The maximum speed, in feet per second, of the object"], "label": "A"} | |
| {"question": "If $x$ food calories is equivalent to $k$ kilojoules, of the following, which best represents the relationship between $x$ and $k$ ?", "options": ["(A)$k=0.24 x$", "(B)$k=4.2 x$", "(C)$x=4.2 k$", "(D)$x k=4.2$"], "label": "B"} | |
| {"question": "If the 180 food calories in a granola bar come entirely from $p$ grams of protein, $f$ grams of fat, and $c$ grams of carbohydrate, which of the following expresses $f$ in terms of $p$ and $c$ ?", "options": ["(A)$f=20+\\frac{4}{9}(p+c)$", "(B)$f=20-\\frac{4}{9}(p+c)$", "(C)$f=20-\\frac{4}{9}(p-c)$", "(D)$f=20+\\frac{9}{4}(p+c)$"], "label": "B"} | |
| {"question": "The world's population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion people in the world in 1975. Which of the following functions represents the world's population $P$, in billions of people, $t$ years since $1975 ?(1$ billion $=1,000,000,000)$", "options": ["(A)$P(t)=4(1.019)^{t}$", "(B)$P(t)=4(1.9)^{t}$", "(C)$P(t)=1.19 t+4$", "(D)$P(t)=1.019 t+4$"], "label": "A"} | |
| {"question": "A circle in the $x y$-plane has equation$(x+3)^{2}+(y-1)^{2}=25$. Which of the following points does NOT lie in the interior of the circle?", "options": ["(A)$(-7,3)$", "(B)$(-3,1)$", "(C)$(0,0)$", "(D)$(3,2)$"], "label": "D"} | |
| {"question": "\\begin{center}\\begin{tabular}{c|c}Year & $\\begin{array}{c}\\text { Subscriptions } \\\\ \\text { sold }\\end{array}$ \\\\\\hline2012 & 5,600 \\\\2013 & 5,880 \\\\\\end{tabular}\\end{center}The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014 . How many subscriptions did the manager expect would be sold in 2014 ?", "options": ["(A)6,020", "(B)6,027", "(C)6,440", "(D)6,468 DIRECTIONS"], "label": "B"} | |
| {"question": "$$3 x+x+x+x-3-2=7+x+x$$In the equation above, what is the value of $x$ ?", "options": ["(A)$-\\frac{5}{7}$", "(B)1", "(C)$\\frac{12}{7}$", "(D)3"], "label": "D"} | |
| {"question": "The formula below is often used by project managers to compute $E$, the estimated time to complete a job, where $O$ is the shortest completion time, $P$ is the longest completion time, and $M$ is the most likely completion time.$$E=\\frac{O+4 M+P}{6}$$Which of the following correctly gives $P$ in terms of $E, O$, and $M$ ?", "options": ["(A)$P=6 E-O-4 M$", "(B)$P=-6 E+O+4 M$", "(C)$P=\\frac{O+4 M+E}{6}$", "(D)$P=\\frac{O+4 M-E}{6}$"], "label": "A"} | |
| {"question": "The width of a rectangular dance floor is $w$ feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of $w$ ?", "options": ["(A)$2 w+6$", "(B)$4 w+12$", "(C)$w^{2}+6$", "(D)$w^{2}+6 w$"], "label": "B"} | |
| {"question": "$$\\begin{aligned}y & >2 x-1 \\\\2 x & >5\\end{aligned}$$Which of the following consists of the $y$-coordinates of all the points that satisfy the system of inequalities above?", "options": ["(A)$y>6$", "(B)$y>4$", "(C)$y>\\frac{5}{2}$", "(D)$y>\\frac{3}{2}$"], "label": "B"} | |
| {"question": "$$\\sqrt{2 x+6}+4=x+3$$What is the solution set of the equation above?", "options": ["(A)$\\{-1\\}$", "(B)$\\{5\\}$", "(C)$\\{-1,5\\}$", "(D)$\\{0,-1,5\\}$"], "label": "B"} | |
| {"question": "$$\\begin{aligned}& f(x)=x^{3}-9 x \\\\& g(x)=x^{2}-2 x-3\\end{aligned}$$Which of the following expressions is equivalent to$\\frac{f(x)}{g(x)}$, for $x>3 ?$", "options": ["(A)$\\frac{1}{x+1}$", "(B)$\\frac{x+3}{x+1}$", "(C)$\\frac{x(x-3)}{x+1}$", "(D)$\\frac{x(x+3)}{x+1}$"], "label": "D"} | |
| {"question": "A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?", "options": ["(A)30", "(B)20", "(C)19", "(D)18 11"], "label": "C"} | |
| {"question": "If $\\frac{2 a}{b}=\\frac{1}{2}$, what is the value of $\\frac{b}{a} ?$", "options": ["(A)$\\frac{1}{8}$", "(B)$\\frac{1}{4}$", "(C)2", "(D)4"], "label": "D"} | |
| {"question": "Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions $f$ best models the production, in millions of barrels, $t$ years after the year 2000 ?", "options": ["(A)$f(t)=\\frac{21}{130} t+4$", "(B)$f(t)=\\frac{19}{130} t+4$", "(C)$f(t)=-\\frac{21}{130} t+4$", "(D)$f(t)=-\\frac{19}{130} t+4$"], "label": "C"} | |
| {"question": "$$\\begin{aligned}& y=x^{2}+3 x-7 \\\\& y-5 x+8=0\\end{aligned}$$How many solutions are there to the system of equations above?", "options": ["(A)There are exactly 4 solutions.", "(B)There are exactly 2 solutions.", "(C)There is exactly 1 solution.", "(D)There are no solutions."], "label": "C"} | |
| {"question": "$$\\begin{aligned}& g(x)=2 x-1 \\\\& h(x)=1-g(x)\\end{aligned}$$The functions $g$ and $h$ are defined above. What is the value of $h(0)$ ?", "options": ["(A)-2", "(B)0", "(C)1", "(D)2"], "label": "D"} | |
| {"question": "One pound of grapes costs $\\$ 2$. At this rate, how many dollars will $c$ pounds of grapes cost?", "options": ["(A)$2 c$", "(B)$2+c$", "(C)$\\frac{2}{c}$", "(D)$\\frac{c}{2}$"], "label": "A"} | |
| {"question": "In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of 10,000 cars of the same model will have a manufacturing defect?", "options": ["(A)150", "(B)200", "(C)250", "(D)300"], "label": "A"} | |
| {"question": "Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost $\\$ 75$ each, and tickets to sit on the lawn during the concert cost $\\$ 40$ each. Organizers of the concert announced that 350 tickets had been sold and that $\\$ 19,250$ had been raised through ticket sales alone. Which of the following systems of equations could be used to find the number of tickets for bench seats, $B$, and the number of tickets for lawn seats, $L$, that were sold for the concert?", "options": ["(A)$(75 B)(40 L)=1,950$ $B+L=350$", "(B)$40 B+75 L=19,250$ $B+L=350$", "(C)$75 B+40 L=350$ $B+L=19,250$", "(D)$75 B+40 L=19,250$ $B+L=350$"], "label": "D"} | |
| {"question": "In the $x y$-plane, the graph of which of the following equations is a line with a slope of 3 ?", "options": ["(A)$y=\\frac{1}{3} x$", "(B)$y=x-3$", "(C)$y=3 x+2$", "(D)$y=6 x+3$"], "label": "C"} | |
| {"question": "$$x+1=\\frac{2}{x+1}$$In the equation above, which of the following is a possible value of $x+1$ ?", "options": ["(A)$1-\\sqrt{2}$", "(B)$\\sqrt{2}$", "(C)2", "(D)4"], "label": "B"} | |
| {"question": "Roberto is an insurance agent who sells two types of policies: a $\\$ 50,000$ policy and a $\\$ 100,000$ policy. Last month, his goal was to sell at least 57 insurance policies. While he did not meet his goal, the total value of the policies he sold was over $\\$ 3,000,000$. Which of the following systems of inequalities describes $x$, the possible number of $\\$ 50,000$ policies, and $y$, the possible number of $\\$ 100,000$ policies, that Roberto sold last month?", "options": ["(A)$x+y<57$ $50,000 x+100,000 y<3,000,000$", "(B)$x+y>57$ $50,000 x+100,000 y>3,000,000$", "(C)$x+y<57$ $50,000 x+100,000 y>3,000,000$", "(D)$x+y>57$ $50,000 x+100,000 y<3,000,000$"], "label": "C"} | |
| {"question": "$$\\begin{aligned}& 2 x-y=8 \\\\& x+2 y=4\\end{aligned}$$For the system of equations above, what is the value of $x+y$ ?", "options": ["(A)-1", "(B)4", "(C)5", "(D)20"], "label": "B"} | |
| {"question": "Which of the following is equivalent to $2\\left(x^{2}-x\\right)+3\\left(x^{2}-x\\right) ?$", "options": ["(A)$5 x^{2}-5 x$", "(B)$5 x^{2}+5 x$", "(C)$5 x$", "(D)$5 x^{2}$"], "label": "A"} | |
| {"question": "Which of the following statements is true about the graph of the equation $2 y-3 x=-4$ in the $x y$-plane?", "options": ["(A)It has a negative slope and a positive $y$-intercept.", "(B)It has a negative slope and a negative $y$-intercept.", "(C)It has a positive slope and a positive $y$-intercept.", "(D)It has a positive slope and a negative $y$-intercept."], "label": "D"} | |
| {"question": "The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height $h$, in feet, of the front of the roller-coaster car $s$ seconds after it starts up the hill?", "options": ["(A)$h=8 s+15$", "(B)$h=15 s+\\frac{335}{8}$", "(C)$h=8 s+\\frac{335}{15}$", "(D)$h=15 s+8$"], "label": "A"} | |
| {"question": "$$C=75 h+125$$The equation above gives the amount $C$, in dollars, an electrician charges for a job that takes $h$ hours. Ms. Sanchez and Mr. Roland each hired this electrician. The electrician worked 2 hours longer on Ms. Sanchez's job than on Mr. Roland's job. How much more did the electrician charge Ms. Sanchez than Mr. Roland?", "options": ["(A)$\\$ 75$", "(B)$\\$ 125$", "(C)$\\$ 150$", "(D)$\\$ 275$"], "label": "C"} | |
| {"question": "If $\\frac{8}{x}=160$, what is the value of $x ?$", "options": ["(A)1,280", "(B)80", "(C)20", "(D)0.05"], "label": "D"} | |
| {"question": "$$2 a x-15=3(x+5)+5(x-1)$$In the equation above, $a$ is a constant. If no value of $x$ satisfies the equation, what is the value of $a$ ?", "options": ["(A)1", "(B)2", "(C)4", "(D)8"], "label": "C"} | |
| {"question": "$$(a x+3)\\left(5 x^{2}-b x+4\\right)=20 x^{3}-9 x^{2}-2 x+12$$The equation above is true for all $x$, where $a$ and $b$ are constants. What is the value of $a b$ ?", "options": ["(A)18", "(B)20", "(C)24", "(D)40"], "label": "C"} | |
| {"question": "$$\\frac{x}{x-3}=\\frac{2 x}{2}$$Which of the following represents all the possible values of $x$ that satisfy the equation above?", "options": ["(A)0 and 2", "(B)0 and 4", "(C)-4 and 4", "(D)4"], "label": "B"} | |
| {"question": "$$\\frac{1}{2 x+1}+5$$Which of the following is equivalent to the expression above for $x>0$ ?", "options": ["(A)$\\frac{2 x+5}{2 x+1}$", "(B)$\\frac{2 x+6}{2 x+1}$", "(C)$\\frac{10 x+5}{2 x+1}$", "(D)$\\frac{10 x+6}{2 x+1}$"], "label": "D"} | |
| {"question": "What is the set of all solutions to the equation $\\sqrt{x+2}=-x ?$", "options": ["(A)$\\{-1,2\\}$", "(B)$\\{-1\\}$", "(C)$\\{2\\}$", "(D)There are no solutions to the given equation."], "label": "B"} | |
| {"question": "What value of $x$ satisfies the equation $3 x+3=27$ ?", "options": ["(A)3", "(B)8", "(C)10", "(D)27"], "label": "B"} | |
| {"question": "If $\\frac{2 n}{5}=10$, what is the value of $2 n-1 ?$", "options": ["(A)24", "(B)49", "(C)50", "(D)99"], "label": "B"} | |
| {"question": "$$\\sqrt{x^{2}}=x$$Which of the following values of $x$ is NOT a solution to the equation above?", "options": ["(A)-4", "(B)0", "(C)1", "(D)3"], "label": "A"} | |
| {"question": "Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey about potential changes to next year's schedule. Of students selected for the survey, $\\frac{1}{4}$ were freshmen and $\\frac{1}{3}$ were sophomores. Half of the remaining selected students were juniors. If336 students were selected for the survey, how many were seniors?", "options": ["(A)240", "(B)140", "(C)120", "(D)70"], "label": "D"} | |
| {"question": "Plant A is currently 20 centimeters tall, and Plant B is currently 12 centimeters tall. The ratio of the heights of Plant A to Plant B is equal to the ratio of the heights of Plant $\\mathrm{C}$ to Plant D. If Plant $\\mathrm{C}$ is 54 centimeters tall, what is the height of Plant $\\mathrm{D}$, in centimeters?", "options": ["(A)32.4", "(B)44.0", "(C)62.0", "(D)90.0"], "label": "A"} | |
| {"question": "Biologists found a new species of pale shrimp at the world's deepest undersea vent, the Beebe Vent Field. The vent is 3.1 miles below the sea's surface.Approximately how many kilometers below the sea's surface is the vent? ( 1 kilometer $\\approx 0.6214$ miles)", "options": ["(A)2", "(B)3", "(C)4", "(D)5"], "label": "D"} | |
| {"question": "A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?", "options": ["(A)2", "(B)4", "(C)5", "(D)6"], "label": "C"} | |
| {"question": "A company purchased a machine valued at $\\$ 120,000$. The value of the machine depreciates by the same amount each year so that after 10 years the value will be $\\$ 30,000$. Which of the following equations gives the value, $v$, of the machine, in dollars, $t$ years after it was purchased for $0 \\leq t \\leq 10 ?$", "options": ["(A)$v=30,000-9,000 t$", "(B)$v=120,000-9,000 t$", "(C)$v=120,000+9,000 t$", "(D)$v=120,000-30,000 t$"], "label": "B"} | |
| {"question": "Line $m$ in the $x y$-plane contains the points $(2,4)$ and $(0,1)$. Which of the following is an equation of line $m$ ?", "options": ["(A)$y=2 x+3$", "(B)$y=2 x+4$", "(C)$y=\\frac{3}{2} x+3$", "(D)$y=\\frac{3}{2} x+1$"], "label": "D"} | |
| {"question": "$$(4 x+4)(a x-1)-x^{2}+4$$In the expression above, $a$ is a constant. If the expression is equivalent to $b x$, where $b$ is a constant, what is the value of $b$ ?", "options": ["(A)-5", "(B)-3", "(C)0", "(D)12"], "label": "B"} | |
| {"question": "If $2 w+4 t=14$ and $4 w+5 t=25$, what is the value of $2 w+3 t ?$", "options": ["(A)6", "(B)10", "(C)13", "(D)17"], "label": "C"} | |
| {"question": "If $p$ percent of an adult's daily allowance of potassium is provided by $x$ servings of Crunchy Grain cereal per day, which of the following expresses $p$ in terms of $x$ ?", "options": ["(A)$p=0.5 x$", "(B)$p=5 x$", "(C)$p=(0.05)^{x}$", "(D)$p=(1.05)^{x}$"], "label": "B"} | |
| {"question": "On Tuesday, Jennifer will mix Crunchy Grain cereal with Super Grain cereal for her breakfast. Super Grain cereal provides 240 calories per cup. If the total number of calories in one cup of Jennifer's mixture is 270, how much Super Grain cereal is in one cup of the mixture?", "options": ["(A)$\\frac{1}{8} \\operatorname{cup}$", "(B)$\\frac{1}{4} \\operatorname{cup}$", "(C)$\\frac{1}{3} \\operatorname{cup}$", "(D)$\\frac{1}{2} \\operatorname{cup}$"], "label": "B"} | |
| {"question": "The graph of the exponential function $h$ in the $x y$-plane, where $y=h(x)$, has a $y$-intercept of $d$, where $d$ is a positive constant. Which of the following could define the function $h$ ?", "options": ["(A)$h(x)=-3(d)^{x}$", "(B)$h(x)=3(x) d$", "(C)$h(x)=d(-x)^{3}$", "(D)$h(x)=d(3)^{x}$"], "label": "D"} | |
| {"question": "The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation for the data were found. The horse with the lowest reported weight was found to actually weigh 10 pounds less than its reported weight. What value remains unchanged if the four values are reported using the corrected weight?", "options": ["(A)Mean", "(B)Median", "(C)Range", "(D)Standard deviation"], "label": "B"} | |
| {"question": "Near the end of a US cable news show, the host invited viewers to respond to a poll on the show's website that asked, \"Do you support the new federal policy discussed during the show?\" At the end of the show, the host reported that $28 \\%$ responded \"Yes,\" and $70 \\%$ responded \"No.\" Which of the following best explains why the results are unlikely to represent the sentiments of the population of the United States?", "options": ["(A)The percentages do not add up to $100 \\%$, so any possible conclusions from the poll are invalid.", "(B)Those who responded to the poll were not a random sample of the population of the United States.", "(C)There were not $50 \\%$ \"Yes\" responses and $50 \\%$ \"No\" responses.", "(D)The show did not allow viewers enough time to respond to the poll."], "label": "B"} | |
| {"question": "If $f(x)=5 x^{2}-3$ and $f(x+a)=5 x^{2}+30 x+42$, what is the value of $a$ ?", "options": ["(A)-30", "(B)$\\quad-3$", "(C)3", "(D)30"], "label": "C"} | |
| {"question": "If $\\sin x^{\\circ}=a$, which of the following must be true for all values of $x$ ?", "options": ["(A)$\\cos x^{\\circ}=a$", "(B)$\\sin \\left(90^{\\circ}-x^{\\circ}\\right)=a$", "(C)$\\cos \\left(90^{\\circ}-x^{\\circ}\\right)=a$", "(D)$\\sin \\left(x^{2}\\right)^{\\circ}=a^{2}$"], "label": "C"} | |
| {"question": "$$h(x)=-16 x^{2}+100 x+10$$The quadratic function above models the height above the ground $h$, in feet, of a projectile $x$ seconds after it had been launched vertically. If $y=h(x)$ is graphed in the $x y$-plane, which of the following represents the real-life meaning of the positive $x$-intercept of the graph?", "options": ["(A)The initial height of the projectile", "(B)The maximum height of the projectile", "(C)The time at which the projectile reaches its maximum height", "(D)The time at which the projectile hits the ground"], "label": "D"} | |
| {"question": "In the $x y$-plane, the graph of the polynomial function $f$ crosses the $x$-axis at exactly two points, $(a, 0)$ and $(b, 0)$, where $a$ and $b$ are both positive. Which of the following could define $f$ ?", "options": ["(A)$f(x)=(x-a)(x-b)$", "(B)$f(x)=(x+a)(x+b)$", "(C)$f(x)=(x-a)(x+b)$", "(D)$f(x)=x(x-a)(x-b)$"], "label": "A"} | |
| {"question": "If $y=3 x^{2}+6 x+2$ is graphed in the $x y$-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?", "options": ["(A)$y$-coordinate of the vertex", "(B)$x$-intercept $(\\mathrm{s})$", "(C)$y$-intercept", "(D)$x$-intercept of the line of symmetry"], "label": "C"} | |