SAT: Algebra (200 questions)

Posljednje ažuriranje 4 months ago

201

SAT: Algebra (200 questions)

Posljednje ažuriranje 4 months ago

201

The function $h$ is defined by $h(x) = 4x + 28$. The graph of $y = h(x)$ in the xy-plane has an x-intercept at $(a, 0)$ and a y-intercept at $(0, b)$, where $a$ and $b$ are constants. What is the value of $a + b$?

If $4x - 28 = -24$, what is the value of $x - 7$?

$-24$

$-22$

$-6$

$-1$

For line $h$, the table shows three values of $x$ and their corresponding values of $y$. Line $k$ is the result of translating line $h$ down 5 units in the $xy$-plane. What is the $x$-intercept of line $k$?

$\left(-\dfrac{26}{3}, 0\right)$

$\left(-\dfrac{9}{2}, 0\right)$

$\left(-\dfrac{11}{3}, 0\right)$

$\left(-\dfrac{17}{6}, 0\right)$

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

An economist modeled the demand $Q$ for a certain product as a linear function of the selling price $P$. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?

16,250

16,500

16,750

17,500

The table shows two values of $x$ and their corresponding values of $y$.
$x$
$y$
$-12$
$-45$
$6$
$45$
The graph of the linear equation representing this relationship passes through the point $\left(\tfrac{1}{4},\,a\right)$. What is the value of $a$?

$x$	$y$
$-12$	$-45$
$6$	$45$

A certain apprentice has enrolled in 85 hours of training courses. The equation $10x + 15y = 85$ represents this situation, where $x$ is the number of on-site training courses and $y$ is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?

Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if $x$ represents the price, in dollars, of each shirt and $y$ represents the price, in dollars, of each pair of pants?

4x + 2y = 86, 3x + 5y = 166

4x + 3y = 86, 2x + 5y = 166

4x + 2y = 166, 3x + 5y = 86

4x + 3y = 166, 2x + 5y = 86

$d = 16 - \dfrac{x}{30}$
The equation shown gives the estimated amount of diesel $d$, in gallons, that remains in the gas tank of a truck after being driven $x$ miles, where $0 \le x \le 480$. What is the estimated amount of diesel, in gallons, that remains in the gas tank of the truck when $x = 300$?

$ax + by = 72$
$6x + 2by = 56$
In the given system of equations, $a$ and $b$ are constants. The graphs of these equations in the $xy$-plane intersect at the point $(4, y)$. What is the value of $a$?

$3$

$4$

$6$

$14$

A window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5 hours of repair is $400. Which function $f$ gives the total cost, in dollars, for $x$ hours of repair, where $x \ge 2$?

$f(x) = 60x + 100$

$f(x) = 60x + 220$

$f(x) = 80x$

$f(x) = 80x + 220$

$\dfrac{3}{2}y - \dfrac{1}{4}x = \dfrac{2}{3} - \dfrac{3}{2}y$
$\dfrac{1}{2}x + \dfrac{3}{2} = py + \dfrac{9}{2}$
In the given system of equations, $p$ is a constant. If the system has no solution, what is the value of $p$?

Line $\ell$ is defined by $3y + 12x = 5$. Line $n$ is perpendicular to line $\ell$ in the $xy$-plane. What is the slope of line $n$?

The graph of the equation $ax + ky = 6$ is a line in the $xy$-plane, where $a$ and $k$ are constants. If the line contains the points $(-2, -6)$ and $(0, -3)$, what is the value of $k$?

$-2$

$-1$

$2$

$3$

The total cost $f(x)$, in dollars, to lease a car for 36 months from a particular car dealership is given by $f(x) = 36x + 1{,}000$, where $x$ is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $\$400$?

$\$13{,}400$

$\$13{,}000$

$\$15{,}400$

$\$37{,}400$

A veterinarian recommends that each day a certain rabbit should eat 25 calories per pound of the rabbit’s weight, plus an additional 11 calories. Which equation represents this situation, where $c$ is the total number of calories the veterinarian recommends the rabbit should eat each day if the rabbit’s weight is $x$ pounds?

$c = 25x$

$c = 36x$

$c = 11x + 25$

$c = 25x + 11$

The system of equations above has solution $(x, y)$. What is the value of $x$?

$3$

Seven halves

$4$

$6$

$\dfrac{12x + 28}{4} - \dfrac{s}{13} = r(x - 8)$
In the given equation, $s$ and $r$ are constants, and $s > 0$. If the equation has infinitely many solutions, what is the value of $s$?

What system of linear equations is represented by the lines shown?

$8x + 4y = 32$
$-10x - 4y = -64$

$8x - 4y = 32$
$-10x + 4y = -64$

$4x - 10y = 32$
$-8x + 10y = -64$

$4x + 10y = 32$
$-8x - 10y = -64$

The function $f$ is defined by $f(x) = 25x + 30$. What is the value of $f(x)$ when $x = 2$?

110

Line $k$ is defined by $y = -\frac{17}{3}x + 5$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

$2(8x) + 4(7y) = 12$
$-2(8x) + 4(7y) = 12$
The solution to the given system of equations is $(x, y)$. What is the value of $8x + 7y$?

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?

Question: If $2x + 3 = 9$, what is the value of $6x - 1$?

The function $f$ is defined by $f(x) = 8x$. For what value of $x$ does $f(x) = 72$?

$f(x) = 4x + b$
For the linear function $f$, $b$ is a constant and $f(7) = 28$. What is the value of $b$?

The table gives the coordinates of two points on a line in the $xy$-plane.
$x$
$y$
$k$
$13$
$k + 7$
$-15$
The $y$-intercept of the line is $(k - 5, b)$, where $k$ and $b$ are constants. What is the value of $b$?

Gabriella deposits $35 in a savings account at the end of each week. At the beginning of the 1st week of a year there was $600 in that savings account. How much money, in dollars, will be in the account at the end of the 4th week of that year?

460

635

639

740

$3x = 36y - 45$
One of the two equations in a system of linear equations is given. The system has no solution. Which equation could be the second equation in this system?

$x = 4y$

$\dfrac{1}{3}x = 4y$

$x = 12y - 15$

$\dfrac{1}{3}x = 12y - 15$

ID: d1b66ae6
$-x + y = -3.5$
$x + 3y = 9.5$
If $(x, y)$ satisfies the system of equations above, what is the value of $y$?

A store sells two different-sized containers of a certain Greek yogurt. The store’s sales of this Greek yogurt totaled 1,277.94 dollars last month. The equation $5.48x + 7.30y = 1{,}277.94$ represents this situation, where $x$ is the number of smaller containers sold and $y$ is the number of larger containers sold. According to the equation, which of the following represents the price, in dollars, of each smaller container?

$5.48$

$7.30y$

$7.30$

$5.48x$

$7(2x - 3) = 63$
Which equation has the same solution as the given equation?

$2x - 3 = 9$

$2x - 3 = 56$

$2x - 21 = 63$

$2x - 21 = 70$

Line $k$ is defined by $y = 3x + 15$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

$-\dfrac{1}{3}$

$-\dfrac{1}{12}$

$-\dfrac{1}{18}$

$-\dfrac{1}{45}$

The point $(8, 2)$ in the xy-plane is a solution to which of the following systems of inequalities?

$x > 0$
$y > 0$

$x > 0$
$y < 0$

$x < 0$
$y > 0$

$x < 0$
$y < 0$

$5x = 15$
$-4x + y = -2$
The solution to the given system of equations is $(x, y)$. What is the value of $x + y$?

$-17$

$-13$

$13$

$17$

The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost $y$, in dollars, of renting the backhoe for $x$ days, where $x$ is a positive integer and $x \le 10$?

$y = 270x - 135$

$y = 270x + 135$

$y = 135x + 270$

$y = 135x + 135$

What value of $p$ satisfies the equation $5p + 180 = 250$?

250

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?

$h = 8s + 15$

$h = 15s + \dfrac{335}{8}$

$h = 8s + \dfrac{335}{15}$

$h = 15s + 8$

According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to four times the body weight of the bee, in grams. According to the model, what would be the head width, in millimeters, of a worker bumblebee that has a body weight of 0.5 grams?

The graph of a system of linear equations is shown. What is the solution $(x, y)$ to the system?

$(0, 3)$

$(1, 3)$

$(2, 3)$

$(3, 3)$

If $3x - 8 = 7$, what is the value of $3x + 8$?

$-1$

$5$

$13$

$23$

Line $p$ is defined by $4y + 8x = 6$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

If $3x - 27 = 24$, what is the value of $x - 9$?

Line $p$ is defined by $2y + 18x = 9$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

$-9$

$-\dfrac{1}{9}$

$\dfrac{1}{9}$

$9$

The graph in the $xy$-plane models the possible combinations of length $x$, in meters ($m$), and width $y$, in meters, for a rectangle with a perimeter of $36\ m$. Which statement is the best interpretation of the point $(8,10)$ in this context?

The length is $10\ m$ less than the perimeter, and the width is $8\ m$ less than the perimeter.

The length is $10\ m$, and the width is $8\ m$.

The length is $8\ m$, and the width is $10\ m$.

The length is $8\ m$ less than the perimeter, and the width is $10\ m$ less than the perimeter.

The function $f$ is defined by $f(x) = \dfrac{7}{10}x + 55$. What is the value of $f(20)$?

$8x - 7x + 130 = 260$
What value of $x$ is the solution to the given equation?

Adam’s school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, $w$, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of $w$ for which it would be faster for Adam to walk to school?

w - 5 < 20

w - 5 > 20

w + 5 < 20

w + 5 > 20

ID: 06fc1726
If $f$ is the function defined by $f(x) = \dfrac{2x - 1}{3}$, what is the value of $f(5)$?

$\dfrac{4}{3}$

$\dfrac{7}{3}$

$w + 7 = 357$
What value of $w$ is the solution to the given equation?

350

364

3,577

The function $f$ is defined by $f(x) = 4x + k(x - 1)$, where $k$ is a constant, and $f(5) = 32$. What is the value of $f(10)$?

$\dfrac{2}{5}x + \dfrac{7}{5}y = \dfrac{2}{7}$
$gx + ky = \dfrac{5}{2}$
In the given system of equations, $g$ and $k$ are constants. The system has infinitely many solutions. What is the value of $\dfrac{g}{k}$?

$2x - y > 883$
For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?
A.
$x$
$y$
440
0
441
$-2$
442
$-4$
B.
$x$
$y$
440
0
442
$-2$
441
$-4$
C.
$x$
$y$
442
0
440
$-2$
441
$-4$
D.
$x$
$y$
442
0
441
$-2$
440
$-4$

$d = 16t$
The given equation represents the distance $d$, in inches, where $t$ represents the number of seconds since an object started moving. Which of the following is the best interpretation of 16 in this context?

The object moved a total of 16 inches.

The object moved a total of $16t$ inches.

The object is moving at a rate of 16 inches per second.

The object is moving at a rate of $\dfrac{1}{16}$ inches per second.

$7x + 6y = 5$
$28x + 24y = 20$
For each real number $r$, which of the following points lies on the graph of each equation in the $xy$-plane for the given system?

$\left(r, -\dfrac{6r}{7} + \dfrac{5}{7}\right)$

$\left(r, \dfrac{7r}{6} + \dfrac{5}{6}\right)$

$\left(\dfrac{r}{4} + 5, -\dfrac{r}{4} + 20\right)$

$\left(-\dfrac{6r}{7} + \dfrac{5}{7}, r\right)$

ID: 51aabd93
$(p + 3) + 8 = 10$
What value of $p$ is the solution to the given equation?

$-1$

$5$

$15$

$21$

$f(x) = 39$
For the given linear function $f$, which table gives three values of $x$ and their corresponding values of $f(x)$?
A.
$x$
$f(x)$
0
0
1
0
2
0
B.
$x$
$f(x)$
0
39
1
39
2
39
C.
$x$
$f(x)$
0
0
1
39
2
78
D.
$x$
$f(x)$
0
39
1
0
2
-39

A manufacturing plant makes 10-inch, 9-inch, and 7-inch frying pans. During a certain day, the number of 10-inch frying pans that the manufacturing plant makes is 4 times the number $n$ of 9-inch frying pans it makes, and the number of 7-inch frying pans it makes is 10. During this day, the manufacturing plant makes 100 frying pans total. Which equation represents this situation?

$10(4n) + 9n + 7(10) = 100$

$10n + 9n + 7n = 100$

$4n + 10 = 100$

$5n + 10 = 100$

ID: b52e5b6f
A mixture consisting of only vitamin D and calcium has a total mass of 150 grams. The mass of vitamin D in the mixture is 50 grams. What is the mass, in grams, of calcium in the mixture?

200

150

100

The function $g$ is defined by $g(x) = 6x$. For what value of $x$ is $g(x) = 54$?

$4x + 5 = 165$
What is the solution to the given equation?

The graph of the linear function $f$ is shown, where $y = f(x)$. What is the x-intercept of the graph of $f$?

$(-12, 0)$

$(0, 0)$

$\left(\frac{1}{4}, 0\right)$

$(12, 0)$

A company that provides whale-watching tours takes groups of 21 people at a time. The company's revenue is 80 dollars per adult and 60 dollars per child. If the company's revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?

Line $k$ is defined by $y = \frac{17}{7}x + 4$. Line $j$ is parallel to line $k$ in the $xy$-plane. What is the slope of line $j$?

$\dfrac{7}{17}$

$\dfrac{17}{7}$

$4$

$17$

$-12x + 14y = 36$
$-6x + 7y = -18$
How many solutions does the given system of equations have?

Exactly one

Exactly two

Infinitely many

Zero

In August, a car dealer completed 15 more than 3 times the number of sales the car dealer completed in September. In August and September, the car dealer completed 363 sales. How many sales did the car dealer complete in September?

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0,3)$ and $(7,31)$. Which equation defines $f$, where $y = f(x)$?

$f(x) = 28x + 34$

$f(x) = 3x + 38$

$f(x) = 4x + 3$

$f(x) = 7x + 3$

$y = 12x - 20$
$y = 28$
What is the solution $(x, y)$ to the given system of equations?

$(4, 28)$

$(20, 28)$

$(28, 4)$

$(28, 20)$

The graph of the linear function $f$ is shown. What is the $y$-intercept of the graph of $y = f(x)$?

$(-5, 0)$

$(2, 0)$

$(0, 2)$

$(0, -5)$

The number $y$ is 84 less than the number $x$. Which equation represents the relationship between $x$ and $y$?

$y = x + 84$

$y = \dfrac{1}{84}x$

$y = 84x$

$y = x - 84$

The function $f$ is defined by $f(x) = 4x - 3$. What is the value of $f(10)$?

$-30$

$37$

$40$

$43$

The function $f$ is defined by the equation $f(x) = 7x + 2$. What is the value of $f(x)$ when $x = 4$?

ID: 0dd6227f
At how many points do the graphs of the equations $y = x + 20$ and $y = 8x$ intersect in the $xy$-plane?

For a snowstorm in a certain town, the minimum rate of snowfall recorded was 0.6 inches per hour, and the maximum rate of snowfall recorded was 1.8 inches per hour. Which inequality is true for all values of $s$, where $s$ represents a rate of snowfall, in inches per hour, recorded for this snowstorm?

$s \ge 2.4$

$s \ge 1.8$

$0 \le s \le 0.6$

$0.6 \le s \le 1.8$

During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where $s$ is the cruising speed, in miles per hour, during this portion of the flight?

$s \le 20$

$s \le 150$

$s \le 170$

$150 \le s \le 170$

John paid a total of $$165$ for a microscope by making a down payment of $$37$ plus $p$ monthly payments of $$16$ each. Which of the following equations represents this situation?

$16p - 37 = 165$

$37p - 16 = 165$

$16p + 37 = 165$

$37p + 16 = 165$

$y = 3x$
$2x + y = 12$
The solution to the given system of equations is $(x, y)$. What is the value of $5x$?

Valentina bought two containers of beads. In the first container 30% of the beads are red, and in the second container 70% of the beads are red. Together, the containers have at least 400 red beads. Which inequality shows this relationship, where $x$ is the total number of beads in the first container and $y$ is the total number of beads in the second container?

0.3x + 0.7y ≥ 400

0.7x + 0.3y ≤ 400

x/3 + y/7 ≤ 400

30x + 70y ≥ 400

$y = x + 4$
Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?
A.
$x$
$y$
0
4
1
5
2
6
B.
$x$
$y$
0
6
1
5
2
4
C.
$x$
$y$
0
2
1
1
2
0
D.
$x$
$y$
0
0
1
1
2
2

As part of a science project on evaporation, Amaya measured the height of a liquid in a container over a period of time. The function $f(x) = 33 - 0.18x$ gives the estimated height, in centimeters (cm), of the liquid in the container $x$ days after the start of the project. Which of the following is the best interpretation of 33 in this context?

The estimated height, in cm, of the liquid at the start of the project

The estimated height, in cm, of the liquid at the end of the project

The estimated change in the height, in cm, of the liquid each day

The estimated number of days for all of the liquid to evaporate

Lorenzo purchased a box of cereal and some strawberries at the grocery store. Lorenzo paid $2 for the box of cereal and $1.90 per pound for the strawberries. If Lorenzo paid a total of $9.60 for the box of cereal and the strawberries, which of the following equations can be used to find $p$, the number of pounds of strawberries Lorenzo purchased? (Assume there is no sales tax.)

$1.90p + 2 = 9.60$

$1.90p - 2 = 9.60$

$1.90 + 2p = 9.60$

$1.90 - 2p = 9.60$

$24.5x + 24.75y = 641$
Isabel ordered topsoil and crushed stone, which cost a total of $641, for her garden. The given equation represents the relationship between the number of cubic yards of topsoil, $x$, and the number of tons of crushed stone, $y$, Isabel ordered. How much more, in dollars, did a ton of crushed stone cost Isabel than a cubic yard of topsoil?

$48x - 64y = 48y + 24$
$ry = \frac{1}{8} - 12x$
In the given system of equations, $r$ is a constant. If the system has no solution, what is the value of $r$?

A chemist studying the impact of salt on a process mixes $x$ kilograms of a low-salt mixture, which is 2% salt by weight, with $y$ kilograms of a high-salt mixture, which is 96% salt by weight, to create 24 kilograms of a mixture that is 4% salt by weight. Which equation represents this situation?

$0.96x + 0.02y = (0.04)(24)$

$0.02x + 0.96y = (0.04)(24)$

$0.96x + 0.02y = 24$

$0.02x + 0.96y = 24$

The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for $t$ hours and intends to spend a maximum of $75 to rent the surfboard. Which inequality represents this situation?

$10t \le 75$

$10 + 25t \le 75$

$25t \le 75$

$25 + 10t \le 75$

A model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day in its first year of life. This model is defined by an equation in the form $f(x) = a + bx$, where $f(x)$ is the predicted weight, in pounds, of the animal $x$ days after it was born, and $a$ and $b$ are constants. What is the value of $a$?

$3a + 4b = 25$
A shipping company charged a customer $25 to ship some small boxes and some large boxes. The equation above represents the relationship between $a$, the number of small boxes, and $b$, the number of large boxes, the customer had shipped. If the customer had 3 small boxes shipped, how many large boxes were shipped?

ID: 24854644
What is the equation of the line that passes through the point $(0,5)$ and is parallel to the graph of $y = 7x + 4$ in the $xy$-plane?

$y = 5x$

$y = 7x + 5$

$y = 7x$

$y = 5x + 7$

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?

A company that creates and sells tape dispensers calculates its monthly profit, in dollars, by subtracting its fixed monthly costs, in dollars, from its monthly sales revenue, in dollars. The equation $15{,}000 = 2.00x - 4{,}500$ represents this situation for a month where $x$ tape dispensers are created and sold. Which statement is the best interpretation of $2.00x$ in this context?

The monthly sales revenue, in dollars, from selling $x$ tape dispensers

The monthly sales revenue, in dollars, from each tape dispenser sold

The monthly cost, in dollars, of creating each tape dispenser

The monthly cost, in dollars, of creating $x$ tape dispensers

A petting zoo sells two types of tickets. The standard ticket, for admission only, costs $5. The premium ticket, which includes admission and food to give to the animals, costs $12. One Saturday, the petting zoo sold a total of 250 tickets and collected a total of $2,300 from ticket sales. Which of the following systems of equations can be used to find the number of standard tickets, $s$, and premium tickets, $p$, sold on that Saturday?

$s + p = 250$

5s + 12p = 2,300

$s + p = 250$

12s + 5p = 2,300

5s + 12p = 250

$s + p = 2,300$

12s + 5p = 250

$s + p = 2,300$

In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0 feet. A restaurant owner recently resurfaced the restaurant’s parking lot and wants to determine the number of parking spaces, $n$, in the parking lot that could be placed perpendicular to a curb that is 135 feet long, based on the standard width of a parking space. Which of the following describes all the possible values of $n$?

18 ≤ n ≤ 135

7.5 ≤ n ≤ 9

15 ≤ n ≤ 135

15 ≤ n ≤ 18

Two customers purchased the same kind of bread and eggs at a store. The first customer paid 12.45 dollars for 1 loaf of bread and 2 dozen eggs. The second customer paid 19.42 dollars for 4 loaves of bread and 1 dozen eggs. What is the cost, in dollars, of 1 dozen eggs?

3.77

3.88

4.15

4.34

$x + y = 75$
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?

The number of minutes spent running each day

The number of minutes spent biking each day

The total number of minutes spent running and biking each day

The number of minutes spent biking for each minute spent running

$3x + 21 = 3x + k$
In the given equation, $k$ is a constant. The equation has infinitely many solutions. What is the value of $k$?

$g(x) = 11x + 4$
For the given linear function $g$, which table shows three values of $x$ and their corresponding values of $g(x)$?
A.
$x$
$g(x)$
$-1$
$7$
$0$
$11$
$1$
$15$
B.
$x$
$g(x)$
$-1$
$-4$
$0$
$0$
$1$
$4$
C.
$x$
$g(x)$
$-1$
$-7$
$0$
$4$
$1$
$15$
D.
$x$
$g(x)$
$-1$
$-11$
$0$
$0$
$1$
$11$

$3(2x - 6) - 11 = 4(x - 3) + 6$
If $x$ is the solution to the equation above, what is the value of $x - 3$?

$\dfrac{23}{2}$

$\dfrac{17}{2}$

$\dfrac{15}{2}$

$-\dfrac{15}{2}$

$y = 4$
$x = y + 6$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

A factory makes 9-inch, 7-inch, and 4-inch concrete screws. During a certain day, the number of 9-inch concrete screws that the factory makes is 5 times the number $n$ of 7-inch concrete screws, and the number of 4-inch concrete screws is 22. During this day, the factory makes 100 concrete screws total. Which equation represents this situation?

$9(5n) + 7n + 4(22) = 100$

$9n + 7n + 4n = 100$

$5n + 22 = 100$

$6n + 22 = 100$

The graph of a system of linear equations is shown. What is the solution $(x, y)$ to the system?

$(2, 3)$

$(3, 4)$

$(4, 5)$

$(5, 6)$

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?

A.
B.
C.
D.

$\dfrac{25}{4}m = 95$

$\dfrac{25}{4}m = 5$

$\dfrac{4}{25}m = 95$

$\dfrac{4}{25}m = 5$

A certain township consists of a 5-hectare industrial park and a 24-hectare neighborhood. The total number of trees in the township is 4,529. The equation $5x + 24y = 4{,}529$ represents this situation. Which of the following is the best interpretation of $x$ in this context?

The average number of trees per hectare in the industrial park

The average number of trees per hectare in the neighborhood

The total number of trees in the industrial park

The total number of trees in the neighborhood

The shaded region shown represents the solutions to an inequality. Which ordered pair $(x, y)$ is a solution to this inequality?

$(-5,-6)$

$(-2,5)$

$(1,4)$

$(6,-2)$

The equation $7g + 7b = 840$ represents the number of blue tiles, $b$, and the number of green tiles, $g$, an artist needs for an 840-square-inch tile project. The artist needs 71 blue tiles for the project. How many green tiles does he need?

The function $g$ is defined by $g(x) = -x + 8$.

What is the value of $g(0)$?

$-8$

$0$

$4$

$8$

A chemist combines water and acetic acid to make a mixture with a volume of $56$ milliliters (mL). The volume of acetic acid in the mixture is $10$ mL. What is the volume of water, in mL, in the mixture? (Assume that the volume of the mixture is the sum of the volumes of water and acetic acid before they were mixed.)

$y \le x$
$y \le -x$
Which of the following ordered pairs $(x, y)$ is a solution to the system of inequalities above?

$(1,0)$

$(-1,0)$

$(0,1)$

$(0,-1)$

Line $t$ in the $xy$-plane has a slope of $-\dfrac{1}{3}$ and passes through the point $(9,10)$. Which equation defines line $t$?

$y = 13x - \dfrac{1}{3}$

$y = 9x + 10$

$y = -\dfrac{x}{3} + 10$

$y = -\dfrac{x}{3} + 13$

$2n + 6 = 14$
A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years $n$ it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?

The number of years it took the tree to double its height

The average number of feet that the tree grew per year

The height, in feet, of the tree when the tree was 1 year old

The average number of years it takes similar trees to grow 14 feet

$2x + 16 = a(x + 8)$
In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

In the $xy$-plane, line $t$ passes through the points $(0, 9)$ and $(1, 17)$. Which equation defines line $t$?

$y = \dfrac{1}{8}x + 9$

$y = x + \dfrac{1}{8}$

$y = x + 8$

$y = 8x + 9$

If $\dfrac{x}{8} = 5$, what is the value of $\dfrac{8}{x}$?

A machine makes large boxes or small boxes, one at a time, for a total of $700$ minutes each day. It takes the machine $10$ minutes to make a large box or $5$ minutes to make a small box. Which equation represents the possible number of large boxes, $x$, and small boxes, $y$, the machine can make each day?

$5x + 10y = 700$

$10x + 5y = 700$

$(x + y)(10 + 5) = 700$

$(10 + x)(5 + y) = 700$

The perimeter of an isosceles triangle is 83 inches. Each of the two congruent sides of the triangle has a length of 24 inches. What is the length, in inches, of the third side?

If $3x = 30$, what is the value of $3x - 12$?

$-2$

$18$

$22$

$42$

ID: 12ee1edc
$(b - 2)x = 8$
In the given equation, $b$ is a constant. If the equation has no solution, what is the value of $b$?

Line $r$ in the $xy$-plane has a slope of $4$ and passes through the point $(0,6)$. Which equation defines line $r$?

$y = -6x + 4$

$y = 6x + 4$

$y = 4x - 6$

$y = 4x + 6$

A total of 364 paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation $3x + 4y = 364$ represents this situation, where $x$ is the number of triangles constructed and $y$ is the number of rectangles constructed. What is the best interpretation of $(x, y) = (24, 73)$ in this context?

If 24 triangles were constructed, then 73 rectangles were constructed.

If 24 triangles were constructed, then 73 paper straws were used.

If 73 triangles were constructed, then 24 rectangles were constructed.

If 73 triangles were constructed, then 24 paper straws were used.

If the graph of $27x + 33y = 297$ is shifted down 5 units in the $xy$-plane, what is the y-intercept of the resulting graph?

$(0,4)$

$(0,6)$

$(0,14)$

$(0,28)$

The function $f$ is defined by $f(x) = 4x$. For what value of $x$ does $f(x) = 8$?

On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under $220$ miles. Rhett drove at an average speed of $35$ miles per hour (mph), and Jessica drove at an average speed of $40$ mph. Which of the following inequalities represents this situation, where $r$ is the number of hours Rhett drove and $j$ is the number of hours Jessica drove?

$35r + 40j \gt 220$

$35r + 40j \lt 220$

$40r + 35j \gt 220$

$40r + 35j \lt 220$

ID: ee2f611f
A local transit company sells a monthly pass for $95 that allows an unlimited number of trips of any length. Tickets for individual trips cost $1.50, $2.50, or $3.50, depending on the length of the trip. What is the minimum number of trips per month for which a monthly pass could cost less than purchasing individual tickets for trips?

The equation $y = 0.1x$ models the relationship between the number of different pieces of music a certain pianist practices, $y$, during an $x$-minute practice session. How many pieces did the pianist practice if the session lasted 30 minutes?

A bakery sells trays of cookies. Each tray contains at least 50 cookies but no more than 60. Which of the following could be the total number of cookies on 4 trays of cookies?

165

205

245

285

How many solutions does the equation $10(15x - 9) = -15(6 - 10x)$ have?

Exactly one

Exactly two

Infinitely many

Zero

$y = -2x$
$3x + y = 40$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

Hydrogen is placed inside a container and kept at a constant pressure. The graph shows the estimated volume $y$, in liters, of the hydrogen when its temperature is $x$ kelvins.What is the estimated volume, in liters, of the hydrogen when its temperature is 500 kelvins?

$0$

$\dfrac{7}{500}$

$7$

$\dfrac{500}{7}$

$x + y = 18$
$5y = x$
What is the solution $(x, y)$ to the given system of equations?

$(15,3)$

$(16,2)$

$(17,1)$

$(18,0)$

ID: 3f5375d9
The line graphed in the xy-plane below models the total cost, in dollars, for a cab ride, $y$, in a certain city during nonpeak hours based on the number of miles traveled, $x$.

Graph titled 'Total Cost for a Cab Ride' showing a line relating distance traveled in miles to total cost in dollars.

According to the graph, what is the cost for each additional mile traveled, in dollars, of a cab ride?

$2.00

$2.60

$3.00

$5.00

ID: fdee0fbf
In the xy-plane, line $k$ intersects the y-axis at the point $(0,-6)$ and passes through the point $(2,2)$. If the point $(20,w)$ lies on line $k$, what is the value of $w$?

$y \le x + 7$
$y \ge -2x - 1$
Which point $(x, y)$ is a solution to the given system of inequalities in the $xy$-plane?

$(-14,0)$

$(0,-14)$

$(0,14)$

$(14,0)$

A team of workers has been moving cargo off of a ship. The equation below models the approximate number of tons of cargo, $y$, that remains to be moved $x$ hours after the team started working.
$y = 120 - 25x$
The graph of this equation in the $xy$-plane is a line. What is the best interpretation of the x-intercept in this context?

The team will have moved all the cargo in about 4.8 hours.

The team has been moving about 4.8 tons of cargo per hour.

The team has been moving about 25 tons of cargo per hour.

The team started with 120 tons of cargo to move.

$y = 2x + 10$
$y = 2x - 1$
At how many points do the graphs of the given equations intersect in the $xy$-plane?

Zero

Exactly one

Exactly two

Infinitely many

ID: b2845d88
Which of the following is an equation of the graph shown in the xy-plane above?

y = -1/4 x - 1

y = -x - 4

y = -x - 1/4

y = -4x - 1

$4x - 6y = 10y + 2$
$ty = \dfrac{1}{2} + 2x$
In the given system of equations, $t$ is a constant. If the system has no solution, what is the value of $t$?

ID: d0e614a6
$\frac{3}{5}x + \frac{3}{4}y = 7$
Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?

$x$	$y$
1	$\frac{113}{20}$
2	$\frac{101}{20}$
4	$\frac{77}{20}$

$x$	$y$
1	$\frac{47}{5}$
2	$\frac{44}{5}$
4	$\frac{38}{5}$

$x$	$y$
1	$\frac{148}{15}$
2	$\frac{136}{15}$
4	$\frac{112}{15}$

$x$	$y$
1	$\frac{128}{15}$
2	$\frac{116}{15}$
4	$\frac{92}{15}$

In the $xy$-plane, line $k$ has a slope of $5$ and a $y$-intercept of $(0, -35)$. What is the $x$-coordinate of the $x$-intercept of line $k$?

A contract for a certain service requires a onetime activation cost of $35 and a monthly cost of $23. Which equation represents this situation, where $c$ is the total cost, in dollars, of this service contract for $t$ months?

$c = \dfrac{t}{23} + 35$

$c = \dfrac{t}{35} + 23$

$c = 23t + 35$

$c = 35t + 23$

An employee at a restaurant prepares sandwiches and salads. It takes the employee $1.5$ minutes to prepare a sandwich and $1.9$ minutes to prepare a salad. The employee spends a total of $46.1$ minutes preparing $x$ sandwiches and $y$ salads. Which equation represents this situation?

$1.9x + 1.5y = 46.1$

$1.5x + 1.9y = 46.1$

$x + y = 46.1$

$30.7x + 24.3y = 46.1$

$F(x) = \frac{9}{5}(x - 273.15) + 32$
The function $F$ gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of $x$ kelvins. If a temperature increased by $9.10$ kelvins, by how much did the temperature increase, in degrees Fahrenheit?

$16.38$

$48.38$

$475.29$

$507.29$

$\frac{4x}{5} = 20$
In the equation above, what is the value of $x$?

The pressure exerted on a scuba diver at sea level is $14.70$ pounds per square inch (psi). For each foot the scuba diver descends below sea level, the pressure exerted on the scuba diver increases by $0.44$ psi. What is the total pressure, in psi, exerted on the scuba diver at $105$ feet below sea level?

$60.90$

$31.50$

$14.70$

$0.44$

A truck can haul a maximum weight of $5{,}630$ pounds. During one trip, the truck will be used to haul a $190$-pound piece of equipment as well as several crates. Some of these crates weigh $25$ pounds each and the others weigh $62$ pounds each. Which inequality represents the possible combinations of the number of $25$-pound crates, $x$, and the number of $62$-pound crates, $y$, the truck can haul during one trip if only the piece of equipment and the crates are being hauled?

$25x + 62y \le 5{,}440$

$25x + 62y \ge 5{,}440$

$62x + 25y \le 5{,}630$

$62x + 25y \ge 5{,}630$

ID: 6e6a3241
$x + 5y = 5$
$2x - y = -4$
Which of the following graphs in the xy-plane could be used to solve the system of equations above?

Graph A

Graph B

Graph C

Graph D

$3(kx + 13) = \frac{48}{17}x + 36$
In the given equation, $k$ is a constant. The equation has no solution. What is the value of $k$?

The function $f$ is defined by $f(x) = 7x - 84$. What is the $x$-intercept of the graph of $y = f(x)$ in the $xy$-plane?

$(-12,0)$

$(-7,0)$

$(7,0)$

$(12,0)$

The table gives the average time $t$, in minutes, it takes Carly to travel a certain distance $d$, in kilometers. Which equation could represent this linear relationship?

$t = 4d$

$t = \dfrac{1}{25}d$

$t = 25d$

$t = \dfrac{1}{4}d$

The table shows four values of $x$ and their corresponding values of $f(x)$.
$x$
10
15
20
25
$f(x)$
82
137
192
247
There is a linear relationship between $x$ and $f(x)$ that is defined by the equation $f(x) = mx - 28$, where $m$ is a constant. What is the value of $m$?

Julissa needs at least 100 hours of flight time to get her private pilot certification. If Julissa already has 86 hours of flight time, what is the minimum number of additional hours of flight time Julissa needs to get her private pilot certification?

186

null The graph of the linear function $y = f(x) + 19$ is shown. If $c$ and $d$ are positive constants, which equation could define $f$?

If $c$ and $d$ are positive constants, which equation could define $f$?

$f(x) = -d - cx$

$f(x) = d - cx$

$f(x) = -d + cx$

$f(x) = d + cx$

$x = 10$
$y = x + 21$
The solution to the given system of equations is $(x, y)$. What is the value of $y$?

2.1

$y = -\dfrac{1}{9}x$
$y = \dfrac{1}{2}x$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

$-9$

$-7$

$0$

$2$

A salesperson’s total earnings consist of a base salary of $x$ dollars per year, plus commission earnings of $11\%$ of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least $3$ times and at most $4$ times the base salary. Which of the following inequalities represents all possible values of total sales $s$, in dollars, the salesperson can make this year in order to meet that goal?

$2x \le s \le 3x$

$\dfrac{2}{0.11}x \le s \le \dfrac{3}{0.11}x$

$3x \le s \le 4x$

$\dfrac{3}{0.11}x \le s \le \dfrac{4}{0.11}x$

For the linear function $f$, the table shows three values of $x$ and their corresponding values of $f(x)$. If $h(x) = f(x) - 13$, which equation defines $h$?

$h(x) = 5x - 4$

$h(x) = 5x + 7$

$h(x) = 5x + 9$

$h(x) = 5x + 20$

ID: 7392dfc1
Which of the following is equivalent to $4x + 6 = 12$?

$2x + 4 = 6$

$x + 3 = 3$

$3x + 2 = 4$

$2x + 3 = 6$

ID: 51568fb9
What is the slope of the graph of $10x - 5y = -12$ in the xy-plane?

$-2$

$-\dfrac{5}{6}$

$\dfrac{5}{6}$

$2$

In the $xy$-plane, line $p$ has a slope of $-\frac{5}{3}$ and an x-intercept of $(-6, 0)$. What is the y-coordinate of the y-intercept of line $p$?

One pound of grapes costs $2. At this rate, how many dollars will $c$ pounds of grapes cost?

$2c$

$2 + c$

$\dfrac{2}{c}$

$\dfrac{c}{2}$

The graph of the function $f$, where $y = f(x)$, gives the total cost $y$, in dollars, for a certain video game system and $x$ games. What is the best interpretation of the slope of the graph in this context?

Each game costs $25.

The video game system costs $100.

The video game system costs $25.

Each game costs $100.

A bus traveled on the highway and on local roads to complete a trip of $160$ miles. The trip took $4$ hours. The bus traveled at an average speed of $55$ miles per hour (mph) on the highway and an average speed of $25$ mph on local roads. If $x$ is the time, in hours, the bus traveled on the highway and $y$ is the time, in hours, it traveled on local roads, which system of equations represents this situation?

$55x + 25y = 4$
$x + y = 160$

$55x + 25y = 160$
$x + y = 4$

$25x + 55y = 4$
$x + y = 160$

$25x + 55y = 160$
$x + y = 4$

On a 210-mile trip, Cameron drove at an average speed of 60 miles per hour for the first $x$ hours. He then completed the trip, driving at an average speed of 50 miles per hour for the remaining $y$ hours. If $x = 1$, what is the value of $y$?

For the linear function $f$, the graph of $y = f(x)$ in the xy-plane has a slope of $2$ and has a y-intercept at $(0, -5)$. Which equation defines $f$?

$f(x) = \dfrac{1}{2}x - 5$

$f(x) = -\dfrac{1}{2}x - 5$

$f(x) = -2x - 5$

$f(x) = 2x - 5$

Ty set a goal to walk at least 24 kilometers every day to prepare for a multiday hike. On a certain day, Ty plans to walk at an average speed of 4 kilometers per hour. What is the minimum number of hours Ty must walk on that day to fulfill the daily goal?

What is the solution to the given system of equations?

(1, 2)

(1, 5)

(2, 3)

(2, 7)

A system of two linear equations is graphed in the xy-plane below.
Which of the following points is the solution to the system of equations?

(3,9)

(6,15)

(8,10)

(12,18)

$f(x) = 45x + 600$
The function $f$ gives the monthly fee $f(x)$, in dollars, a facility charges to keep $x$ crates in storage. What is the monthly fee, in dollars, the facility charges to keep 50 crates in storage?

The function $f$ is defined by $f(x) = 80 - 6x$. What is the value of $f(7)$?

If $46 = 16 + 2(x - 8)$, what is the value of $2(x - 8)$?

The functions $f$ and $g$ are defined as $f(x) = \frac{1}{4}x - 9$ and $g(x) = \frac{3}{4}x + 21$. If the function $h$ is defined as $h(x) = f(x) + g(x)$, what is the $x$-coordinate of the $x$-intercept of the graph of $y = h(x)$ in the $xy$-plane?

A principal used a total of 25 flags that were either blue or yellow for field day. The principal used 20 blue flags. How many yellow flags were used?

During a month, Morgan ran $r$ miles at 5 miles per hour and biked $b$ miles at 10 miles per hour. She ran and biked a total of 200 miles that month, and she biked for twice as many hours as she ran. What is the total number of miles that Morgan biked during the month?

100

120

160

$x + 3 = -2y + 5$
$x - 3 = 2y + 7$
The solution to the given system of equations is $(x, y)$. What is the value of $2x$?

$-2$

$6$

$12$

$24$

$8x = 88$
What value of $x$ is the solution to the given equation?

704

The combined original price for a mirror and a vase is $60. After a 25% discount to the mirror and a 45% discount to the vase are applied, the combined sale price for the two items is $39. Which system of equations gives the original price $m$, in dollars, of the mirror and the original price $v$, in dollars, of the vase?

$m + v = 60$
$0.55m + 0.75v = 39$

$m + v = 60$
$0.45m + 0.25v = 39$

$m + v = 60$
$0.75m + 0.55v = 39$

$m + v = 60$
$0.25m + 0.45v = 39$

The graph shown models the number of candy bars a certain machine wraps with a label in $x$ seconds. null

According to the graph, what is the estimated number of candy bars the machine wraps with a label per second?

$h(x) = x + b$
For the linear function $h$, $b$ is a constant and $h(0) = 45$. What is the value of $b$?

$4x + 5y = 100$
$5x + 4y = 62$
If the system of equations above has solution $(x, y)$, what is the value of $x + y$?

$2a + 8b = 198$
$2a + 4b = 98$
The solution to the given system of equations is $(a, b)$. What is the value of $b$?

The graph of the function $f$ is shown, where $y = f(x)$. What is the y-intercept of the graph?

$(0,-1)$

$(0,-4)$

$(0,1)$

$(0,4)$

The table shows three values of $x$ and their corresponding values of $y$. Which equation represents the linear relationship between $x$ and $y$?

$y = 5x + 6$

$y = 5x + 11$

$y = 6x + 5$

$y = 6x + 11$

The table shows four values of $x$ and their corresponding values of $y$. There is a linear relationship between $x$ and $y$. Which of the following equations represents this relationship?
$x$
$y$
$-6$
$65$
$-3$
$56$
$3$
$38$
$6$
$29$

$x$	$y$
$-6$	$65$
$-3$	$56$
$3$	$38$
$6$	$29$

$9x + 3y = 141$

$9x + 3y = 3$

$3x + 9y = 141$

$3x + 9y = 3$

A number $x$ is at most 2 less than 3 times the value of $y$. If the value of $y$ is $-4$, what is the greatest possible value of $x$?

Caleb used juice to make popsicles. The function $f(x) = -5x + 30$ approximates the volume, in fluid ounces, of juice Caleb had remaining after making $x$ popsicles. Which statement is the best interpretation of the y-intercept of the graph of $y = f(x)$ in the xy-plane in this context?

Caleb used approximately 5 fluid ounces of juice for each popsicle.

Caleb had approximately 5 fluid ounces of juice when he began to make the popsicles.

Caleb had approximately 30 fluid ounces of juice when he began to make the popsicles.

Caleb used approximately 30 fluid ounces of juice for each popsicle.

At a state fair, attendees can win tokens that are worth a different number of points depending on the shape. One attendee won $S$ square tokens and $C$ circle tokens worth a total of 1,120 points. The equation $80S + 90C = 1{,}120$ represents this situation. How many more points is a circle token worth than a square token?

950

According to data provided by the US Department of Energy, the average price per gallon of regular gasoline in the United States from September 1, 2014, to December 1, 2014, is modeled by the function $F$ defined below, where $F(x)$ is the average price per gallon $x$ months after September 1.
$F(x) = 2.74 - 0.19(x - 3)$
The constant 2.74 in this function estimates which of the following?

The average monthly decrease in the price per gallon

The difference in the average price per gallon from September 1, 2014, to December 1, 2014

The average price per gallon on September 1, 2014

The average price per gallon on December 1, 2014

In the xy-plane, the graph of $y = x + 3$ intersects the graph of $y = 2x - 6$ at the point $(a, b)$. What is the value of $a$?

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0, 2)$ and $(8, 34)$. Which equation defines $f$, where $y = f(x)$?

$f(x) = 2x + 42$

$f(x) = 32x + 36$

$f(x) = 4x + 2$

$f(x) = 8x + 2$

The table shows the linear relationship between the number of cars, $c$, on a commuter train and the maximum number of passengers and crew, $p$, that the train can carry.
Which equation represents the linear relationship between $c$ and $p$?

$55c - p = -9$

$55c - p = 9$

$55p - c = -9$

$55p - c = 9$

The y-intercept of the graph of $12x + 2y = 18$ in the $xy$-plane is $(0, y)$. What is the value of $y$?

Line j is shown in the xy-plane. Line k (not shown) is parallel to line j. What is the slope of line k?

In the xy-plane, line $\ell$ passes through the point $(0, 0)$ and is parallel to the line represented by the equation $y = 8x + 2$. If line $\ell$ also passes through the point $(3, d)$, what is the value of $d$?

The function $f$ is defined by the equation $f(x) = x + \frac{8}{11}$. What is the value of $f(x)$ when $x = \frac{3}{11}$?

Brian saves $\dfrac{2}{5}$ of the $215 he earns each week from his job. If Brian continues to save at this rate, how much money, in dollars, will Brian save in 9 weeks?

What is the slope of the graph of $y = \frac{1}{3}(29x + 10) + 5x$ in the $xy$-plane?

ID: d1f50dbe
One gallon of stain will cover 170 square feet of a surface. A yard has a total fence area of $w$ square feet. Which equation represents the total amount of stain $S$, in gallons, needed to stain the fence in this yard twice?

$S = \dfrac{w}{170}$

$S = 170w$

$S = 340w$

$S = \dfrac{w}{85}$

For the linear function $h$, the graph of $y = h(x)$ in the $xy$-plane passes through the points $(7, 21)$ and $(9, 25)$. Which equation defines $h$?

$h(x) = \tfrac{1}{2}x - \tfrac{7}{2}$

$h(x) = 2x + 7$

$h(x) = 7x + 21$

$h(x) = 9x + 25$

$f(x) = 8x + 4$
The function $f$ gives the estimated height, in feet, of a willow tree $x$ years after its height was first measured. Which statement is the best interpretation of $4$ in this context?

The tree will be measured each year for 4 years.

The tree is estimated to grow to a maximum height of 4 feet.

The estimated height of the tree increased by 4 feet each year.

The estimated height of the tree was 4 feet when it was first measured.

Tom scored 85, 78, and 98 on his first three exams in history class. Solving which inequality gives the score, $G$, on Tom’s fourth exam that will result in a mean score on all four exams of at least 90?

90 - (85 + 78 + 98) ≤ 4G

4G + 85 + 78 + 98 ≥ 360

(G + 85 + 78 + 98)/4 ≥ 90

(85 + 78 + 98)/4 ≥ 90 - 4G

ID: e1248a5c
In the system of equations below, $a$ and $c$ are constants.
If the system of equations has an infinite number of solutions $(x,y)$, what is the value of $a$?

$-\dfrac12$

$0$

One half

Three halves

Sean rents a tent at a cost of $11 per day plus a onetime insurance fee of $10. Which equation represents the total cost $c$, in dollars, to rent the tent with insurance for $d$ days?

$c = 11(d + 10)$

$c = 10(d + 11)$

$c = 11d + 10$

$c = 10d + 11$

SAT: Algebra (200 questions)

SAT: Algebra (200 questions)

The function $h$ is defined by $h(x) = 4x + 28$. The graph of $y = h(x)$ in the xy-plane has an x-intercept at $(a, 0)$ and a y-intercept at $(0, b)$, where $a$ and $b$ are constants. What is the value of $a + b$?

If $4x - 28 = -24$, what is the value of $x - 7$?

For line $h$, the table shows three values of $x$ and their corresponding values of $y$. Line $k$ is the result of translating line $h$ down 5 units in the $xy$-plane. What is the $x$-intercept of line $k$?

The table shows two values of $x$ and their corresponding values of $y$.$x$$y$$-12$$-45$$6$$45$The graph of the linear equation representing this relationship passes through the point $\left(\tfrac{1}{4},\,a\right)$. What is the value of $a$?

$ax + by = 72$$6x + 2by = 56$In the given system of equations, $a$ and $b$ are constants. The graphs of these equations in the $xy$-plane intersect at the point $(4, y)$. What is the value of $a$?

A window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5 hours of repair is $400. Which function $f$ gives the total cost, in dollars, for $x$ hours of repair, where $x \ge 2$?

$\dfrac{3}{2}y - \dfrac{1}{4}x = \dfrac{2}{3} - \dfrac{3}{2}y$$\dfrac{1}{2}x + \dfrac{3}{2} = py + \dfrac{9}{2}$In the given system of equations, $p$ is a constant. If the system has no solution, what is the value of $p$?

Line $\ell$ is defined by $3y + 12x = 5$. Line $n$ is perpendicular to line $\ell$ in the $xy$-plane. What is the slope of line $n$?

The graph of the equation $ax + ky = 6$ is a line in the $xy$-plane, where $a$ and $k$ are constants. If the line contains the points $(-2, -6)$ and $(0, -3)$, what is the value of $k$?

The total cost $f(x)$, in dollars, to lease a car for 36 months from a particular car dealership is given by $f(x) = 36x + 1{,}000$, where $x$ is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $\$400$?

The system of equations above has solution $(x, y)$. What is the value of $x$?

$\dfrac{12x + 28}{4} - \dfrac{s}{13} = r(x - 8)$In the given equation, $s$ and $r$ are constants, and $s > 0$. If the equation has infinitely many solutions, what is the value of $s$?

What system of linear equations is represented by the lines shown?

The function $f$ is defined by $f(x) = 25x + 30$. What is the value of $f(x)$ when $x = 2$?

Line $k$ is defined by $y = -\frac{17}{3}x + 5$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

$2(8x) + 4(7y) = 12$$-2(8x) + 4(7y) = 12$The solution to the given system of equations is $(x, y)$. What is the value of $8x + 7y$?

Question: If $2x + 3 = 9$, what is the value of $6x - 1$?

The function $f$ is defined by $f(x) = 8x$. For what value of $x$ does $f(x) = 72$?

$f(x) = 4x + b$For the linear function $f$, $b$ is a constant and $f(7) = 28$. What is the value of $b$?

The table gives the coordinates of two points on a line in the $xy$-plane.$x$$y$$k$$13$$k + 7$$-15$The $y$-intercept of the line is $(k - 5, b)$, where $k$ and $b$ are constants. What is the value of $b$?

Gabriella deposits $35 in a savings account at the end of each week. At the beginning of the 1st week of a year there was $600 in that savings account. How much money, in dollars, will be in the account at the end of the 4th week of that year?

$3x = 36y - 45$One of the two equations in a system of linear equations is given. The system has no solution. Which equation could be the second equation in this system?

ID: d1b66ae6$-x + y = -3.5$$x + 3y = 9.5$If $(x, y)$ satisfies the system of equations above, what is the value of $y$?

$7(2x - 3) = 63$Which equation has the same solution as the given equation?

Line $k$ is defined by $y = 3x + 15$. Line $j$ is perpendicular to line $k$ in the $xy$-plane. What is the slope of line $j$?

The point $(8, 2)$ in the xy-plane is a solution to which of the following systems of inequalities?

$5x = 15$$-4x + y = -2$The solution to the given system of equations is $(x, y)$. What is the value of $x + y$?

The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost $y$, in dollars, of renting the backhoe for $x$ days, where $x$ is a positive integer and $x \le 10$?

What value of $p$ satisfies the equation $5p + 180 = 250$?

According to a model, the head width, in millimeters, of a worker bumblebee can be estimated by adding 0.6 to four times the body weight of the bee, in grams. According to the model, what would be the head width, in millimeters, of a worker bumblebee that has a body weight of 0.5 grams?

The graph of a system of linear equations is shown. What is the solution $(x, y)$ to the system?

If $3x - 8 = 7$, what is the value of $3x + 8$?

Line $p$ is defined by $4y + 8x = 6$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

If $3x - 27 = 24$, what is the value of $x - 9$?

Line $p$ is defined by $2y + 18x = 9$. Line $r$ is perpendicular to line $p$ in the $xy$-plane. What is the slope of line $r$?

The graph in the $xy$-plane models the possible combinations of length $x$, in meters ($m$), and width $y$, in meters, for a rectangle with a perimeter of $36\ m$. Which statement is the best interpretation of the point $(8,10)$ in this context?

The function $f$ is defined by $f(x) = \dfrac{7}{10}x + 55$. What is the value of $f(20)$?

$8x - 7x + 130 = 260$What value of $x$ is the solution to the given equation?

ID: 06fc1726If $f$ is the function defined by $f(x) = \dfrac{2x - 1}{3}$, what is the value of $f(5)$?

$w + 7 = 357$What value of $w$ is the solution to the given equation?

The function $f$ is defined by $f(x) = 4x + k(x - 1)$, where $k$ is a constant, and $f(5) = 32$. What is the value of $f(10)$?

$\dfrac{2}{5}x + \dfrac{7}{5}y = \dfrac{2}{7}$$gx + ky = \dfrac{5}{2}$In the given system of equations, $g$ and $k$ are constants. The system has infinitely many solutions. What is the value of $\dfrac{g}{k}$?

$2x - y > 883$For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?A.$x$$y$4400441$-2$442$-4$B.$x$$y$4400442$-2$441$-4$C.$x$$y$4420440$-2$441$-4$D.$x$$y$4420441$-2$440$-4$

$d = 16t$The given equation represents the distance $d$, in inches, where $t$ represents the number of seconds since an object started moving. Which of the following is the best interpretation of 16 in this context?

$7x + 6y = 5$$28x + 24y = 20$For each real number $r$, which of the following points lies on the graph of each equation in the $xy$-plane for the given system?

ID: 51aabd93$(p + 3) + 8 = 10$What value of $p$ is the solution to the given equation?

$f(x) = 39$For the given linear function $f$, which table gives three values of $x$ and their corresponding values of $f(x)$?A.$x$$f(x)$001020B.$x$$f(x)$039139239C.$x$$f(x)$00139278D.$x$$f(x)$039102-39

ID: b52e5b6fA mixture consisting of only vitamin D and calcium has a total mass of 150 grams. The mass of vitamin D in the mixture is 50 grams. What is the mass, in grams, of calcium in the mixture?

The function $g$ is defined by $g(x) = 6x$. For what value of $x$ is $g(x) = 54$?

$4x + 5 = 165$What is the solution to the given equation?

The graph of the linear function $f$ is shown, where $y = f(x)$. What is the x-intercept of the graph of $f$?

A company that provides whale-watching tours takes groups of 21 people at a time. The company's revenue is 80 dollars per adult and 60 dollars per child. If the company's revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?

Line $k$ is defined by $y = \frac{17}{7}x + 4$. Line $j$ is parallel to line $k$ in the $xy$-plane. What is the slope of line $j$?

$-12x + 14y = 36$$-6x + 7y = -18$How many solutions does the given system of equations have?

In August, a car dealer completed 15 more than 3 times the number of sales the car dealer completed in September. In August and September, the car dealer completed 363 sales. How many sales did the car dealer complete in September?

In the $xy$-plane, the graph of the linear function $f$ contains the points $(0,3)$ and $(7,31)$. Which equation defines $f$, where $y = f(x)$?

$y = 12x - 20$$y = 28$What is the solution $(x, y)$ to the given system of equations?

The graph of the linear function $f$ is shown. What is the $y$-intercept of the graph of $y = f(x)$?

The number $y$ is 84 less than the number $x$. Which equation represents the relationship between $x$ and $y$?

The function $f$ is defined by $f(x) = 4x - 3$. What is the value of $f(10)$?

The function $f$ is defined by the equation $f(x) = 7x + 2$. What is the value of $f(x)$ when $x = 4$?

ID: 0dd6227fAt how many points do the graphs of the equations $y = x + 20$ and $y = 8x$ intersect in the $xy$-plane?

During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where $s$ is the cruising speed, in miles per hour, during this portion of the flight?

John paid a total of $$165$ for a microscope by making a down payment of $$37$ plus $p$ monthly payments of $$16$ each. Which of the following equations represents this situation?

$y = 3x$$2x + y = 12$The solution to the given system of equations is $(x, y)$. What is the value of $5x$?

$y = x + 4$Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?A.$x$$y$041526B.$x$$y$061524C.$x$$y$021120D.$x$$y$001122

$48x - 64y = 48y + 24$$ry = \frac{1}{8} - 12x$In the given system of equations, $r$ is a constant. If the system has no solution, what is the value of $r$?

A chemist studying the impact of salt on a process mixes $x$ kilograms of a low-salt mixture, which is 2% salt by weight, with $y$ kilograms of a high-salt mixture, which is 96% salt by weight, to create 24 kilograms of a mixture that is 4% salt by weight. Which equation represents this situation?

The total cost, in dollars, to rent a surfboard consists of a $25 service fee and a $10 per hour rental fee. A person rents a surfboard for $t$ hours and intends to spend a maximum of $75 to rent the surfboard. Which inequality represents this situation?

ID: 24854644What is the equation of the line that passes through the point $(0,5)$ and is parallel to the graph of $y = 7x + 4$ in the $xy$-plane?

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?

Two customers purchased the same kind of bread and eggs at a store. The first customer paid 12.45 dollars for 1 loaf of bread and 2 dozen eggs. The second customer paid 19.42 dollars for 4 loaves of bread and 1 dozen eggs. What is the cost, in dollars, of 1 dozen eggs?

$x + y = 75$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?

$3x + 21 = 3x + k$In the given equation, $k$ is a constant. The equation has infinitely many solutions. What is the value of $k$?

$g(x) = 11x + 4$For the given linear function $g$, which table shows three values of $x$ and their corresponding values of $g(x)$?A.$x$$g(x)$$-1$$7$$0$$11$$1$$15$B.$x$$g(x)$$-1$$-4$$0$$0$$1$$4$C.$x$$g(x)$$-1$$-7$$0$$4$$1$$15$D.$x$$g(x)$$-1$$-11$$0$$0$$1$$11$

$3(2x - 6) - 11 = 4(x - 3) + 6$If $x$ is the solution to the equation above, what is the value of $x - 3$?

$y = 4$$x = y + 6$The solution to the given system of equations is $(x, y)$. What is the value of $x$?

The graph of a system of linear equations is shown. What is the solution $(x, y)$ to the system?

The table shows two values of $x$ and their corresponding values of $y$.
$x$
$y$
$-12$
$-45$
$6$
$45$
The graph of the linear equation representing this relationship passes through the point $\left(\tfrac{1}{4},\,a\right)$. What is the value of $a$?

$ax + by = 72$
$6x + 2by = 56$
In the given system of equations, $a$ and $b$ are constants. The graphs of these equations in the $xy$-plane intersect at the point $(4, y)$. What is the value of $a$?

$\dfrac{3}{2}y - \dfrac{1}{4}x = \dfrac{2}{3} - \dfrac{3}{2}y$
$\dfrac{1}{2}x + \dfrac{3}{2} = py + \dfrac{9}{2}$
In the given system of equations, $p$ is a constant. If the system has no solution, what is the value of $p$?

$\dfrac{12x + 28}{4} - \dfrac{s}{13} = r(x - 8)$
In the given equation, $s$ and $r$ are constants, and $s > 0$. If the equation has infinitely many solutions, what is the value of $s$?

$2(8x) + 4(7y) = 12$
$-2(8x) + 4(7y) = 12$
The solution to the given system of equations is $(x, y)$. What is the value of $8x + 7y$?

$f(x) = 4x + b$
For the linear function $f$, $b$ is a constant and $f(7) = 28$. What is the value of $b$?

The table gives the coordinates of two points on a line in the $xy$-plane.
$x$
$y$
$k$
$13$
$k + 7$
$-15$
The $y$-intercept of the line is $(k - 5, b)$, where $k$ and $b$ are constants. What is the value of $b$?

$3x = 36y - 45$
One of the two equations in a system of linear equations is given. The system has no solution. Which equation could be the second equation in this system?

ID: d1b66ae6
$-x + y = -3.5$
$x + 3y = 9.5$
If $(x, y)$ satisfies the system of equations above, what is the value of $y$?

$7(2x - 3) = 63$
Which equation has the same solution as the given equation?

$5x = 15$
$-4x + y = -2$
The solution to the given system of equations is $(x, y)$. What is the value of $x + y$?

$8x - 7x + 130 = 260$
What value of $x$ is the solution to the given equation?

ID: 06fc1726
If $f$ is the function defined by $f(x) = \dfrac{2x - 1}{3}$, what is the value of $f(5)$?

$w + 7 = 357$
What value of $w$ is the solution to the given equation?

$\dfrac{2}{5}x + \dfrac{7}{5}y = \dfrac{2}{7}$
$gx + ky = \dfrac{5}{2}$
In the given system of equations, $g$ and $k$ are constants. The system has infinitely many solutions. What is the value of $\dfrac{g}{k}$?

$2x - y > 883$
For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?
A.
$x$
$y$
440
0
441
$-2$
442
$-4$
B.
$x$
$y$
440
0
442
$-2$
441
$-4$
C.
$x$
$y$
442
0
440
$-2$
441
$-4$
D.
$x$
$y$
442
0
441
$-2$
440
$-4$

$d = 16t$
The given equation represents the distance $d$, in inches, where $t$ represents the number of seconds since an object started moving. Which of the following is the best interpretation of 16 in this context?

$7x + 6y = 5$
$28x + 24y = 20$
For each real number $r$, which of the following points lies on the graph of each equation in the $xy$-plane for the given system?

ID: 51aabd93
$(p + 3) + 8 = 10$
What value of $p$ is the solution to the given equation?

$f(x) = 39$
For the given linear function $f$, which table gives three values of $x$ and their corresponding values of $f(x)$?
A.
$x$
$f(x)$
0
0
1
0
2
0
B.
$x$
$f(x)$
0
39
1
39
2
39
C.
$x$
$f(x)$
0
0
1
39
2
78
D.
$x$
$f(x)$
0
39
1
0
2
-39

ID: b52e5b6f
A mixture consisting of only vitamin D and calcium has a total mass of 150 grams. The mass of vitamin D in the mixture is 50 grams. What is the mass, in grams, of calcium in the mixture?

$4x + 5 = 165$
What is the solution to the given equation?

$-12x + 14y = 36$
$-6x + 7y = -18$
How many solutions does the given system of equations have?

$y = 12x - 20$
$y = 28$
What is the solution $(x, y)$ to the given system of equations?

ID: 0dd6227f
At how many points do the graphs of the equations $y = x + 20$ and $y = 8x$ intersect in the $xy$-plane?

$y = 3x$
$2x + y = 12$
The solution to the given system of equations is $(x, y)$. What is the value of $5x$?

$y = x + 4$
Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?
A.
$x$
$y$
0
4
1
5
2
6
B.
$x$
$y$
0
6
1
5
2
4
C.
$x$
$y$
0
2
1
1
2
0
D.
$x$
$y$
0
0
1
1
2
2

$48x - 64y = 48y + 24$
$ry = \frac{1}{8} - 12x$
In the given system of equations, $r$ is a constant. If the system has no solution, what is the value of $r$?

ID: 24854644
What is the equation of the line that passes through the point $(0,5)$ and is parallel to the graph of $y = 7x + 4$ in the $xy$-plane?

$x + y = 75$
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?

$3x + 21 = 3x + k$
In the given equation, $k$ is a constant. The equation has infinitely many solutions. What is the value of $k$?

$g(x) = 11x + 4$
For the given linear function $g$, which table shows three values of $x$ and their corresponding values of $g(x)$?
A.
$x$
$g(x)$
$-1$
$7$
$0$
$11$
$1$
$15$
B.
$x$
$g(x)$
$-1$
$-4$
$0$
$0$
$1$
$4$
C.
$x$
$g(x)$
$-1$
$-7$
$0$
$4$
$1$
$15$
D.
$x$
$g(x)$
$-1$
$-11$
$0$
$0$
$1$
$11$

$3(2x - 6) - 11 = 4(x - 3) + 6$
If $x$ is the solution to the equation above, what is the value of $x - 3$?

$y = 4$
$x = y + 6$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

The function $g$ is defined by $g(x) = -x + 8$.

What is the value of $g(0)$?

$y \le x$
$y \le -x$
Which of the following ordered pairs $(x, y)$ is a solution to the system of inequalities above?

$2n + 6 = 14$
A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years $n$ it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?

$2x + 16 = a(x + 8)$
In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

ID: 12ee1edc
$(b - 2)x = 8$
In the given equation, $b$ is a constant. If the equation has no solution, what is the value of $b$?

$y = -2x$
$3x + y = 40$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

$x + y = 18$
$5y = x$
What is the solution $(x, y)$ to the given system of equations?

ID: fdee0fbf
In the xy-plane, line $k$ intersects the y-axis at the point $(0,-6)$ and passes through the point $(2,2)$. If the point $(20,w)$ lies on line $k$, what is the value of $w$?

$y \le x + 7$
$y \ge -2x - 1$
Which point $(x, y)$ is a solution to the given system of inequalities in the $xy$-plane?

$y = 2x + 10$
$y = 2x - 1$
At how many points do the graphs of the given equations intersect in the $xy$-plane?

ID: b2845d88
Which of the following is an equation of the graph shown in the xy-plane above?

$4x - 6y = 10y + 2$
$ty = \dfrac{1}{2} + 2x$
In the given system of equations, $t$ is a constant. If the system has no solution, what is the value of $t$?

ID: d0e614a6
$\frac{3}{5}x + \frac{3}{4}y = 7$
Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?

$F(x) = \frac{9}{5}(x - 273.15) + 32$
The function $F$ gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of $x$ kelvins. If a temperature increased by $9.10$ kelvins, by how much did the temperature increase, in degrees Fahrenheit?

$\frac{4x}{5} = 20$
In the equation above, what is the value of $x$?

ID: 6e6a3241
$x + 5y = 5$
$2x - y = -4$
Which of the following graphs in the xy-plane could be used to solve the system of equations above?

$3(kx + 13) = \frac{48}{17}x + 36$
In the given equation, $k$ is a constant. The equation has no solution. What is the value of $k$?

The table shows four values of $x$ and their corresponding values of $f(x)$.
$x$
10
15
20
25
$f(x)$
82
137
192
247
There is a linear relationship between $x$ and $f(x)$ that is defined by the equation $f(x) = mx - 28$, where $m$ is a constant. What is the value of $m$?