Middle School Math (5164) - Algebra
Mrs. Johnson lets her students choose between two different word problems: Problem A: If you are digging for dinosaurs and need to fence off your dig site, what's the biggest site you can fence off with 40 ft. of fence? Problem B: What is the largest area you can create with 20 inches of rope? Mrs. Johnson finds a significant majority of her students chose to work Problem A. Which of the following is the most likely reason more students chose Problem A instead of Problem B? (Problem A requires a lower mathematical knowledge.) (Students who work Problem A get a greater reward from Mrs. Johnson than students who work Problem B.) (Problem B is less interesting than Problem A.) (Problem B is harder than Problem A.)
Problem B is less interesting than Problem A.
A student was given the equation 3 (x² + 4) - 2 (5x² + 1) and simplified it to equal -7x² + 2. See their work below. Which of the following is the first step with an error? Step 1: 3 (x² + 4) - 2 (5x² + 1) simplified to 3x² + 4 - 2 (5x² + 1) Step 2: 3x² + 4 - 2 (5x² + 1) simplified to 3x² + 4 - 10x² - 2 Step 3: 3x² + 4 - 10x² - 2 simplified to 3x² - 10x² + 4 - 2 Step 4: 3x² - 10x² + 4 - 2 simplified to -7x² + 2 (Step 1) (Step 2) (Step 3) (Step 4)
Step 1
A student's homework answer states that 2(3x - 8) + 3(4x + 5) = 13x - 8. Which of the following is the first step with an error? Step 1: 2(3x − 8) + 3(4x + 5) = 6x − 16 + 3(4x + 5) Step 2: 6x − 16 + 3(4x + 5) = 6x − 16 + 7x + 8 Step 3: 6x − 16 + 7x + 8 = 6x + 7x − 16 + 8 Step 4: 6x + 7x − 16 + 8 = 13x − 8 (Step 1) (Step 2) (Step 3) (Step 4)
Step 2
A teacher is checking a student's work and notices their conclusion that 3(x - 2) - (4x + 5) = -1x - 1. Looking at their work, where is the first step with a mistake? Step 1 3(x - 2) - (4x + 5) = 3x - 6 - (4x + 5) Step 2 3x - 6 - (4x + 5) = 3x - 6 - 4x + 5 Step 3 3x - 6 - 4x + 5 = 3x - 4x - 6 + 5 Step 4 3x - 4x - 6 + 5 = -1x - 1 (Step 1) (Step 2) (Step 3) (Step 4)
Step 2
The teacher notices an error in a student's work on the board. The student's conclusion was -5(3a + 4) - 7(2a + 3) = -29a +1 The student work is as follows. Which step is the first step with an error? Step 1: -5(3a + 4) - 7(2a + 3) = -15a - 20 - 7(2a + 3) Step 2: -15a - 20 - 7(2a + 3) = -15a - 20 - 14a + 21 Step 3: -15a - 20 - 14a + 21 = -15a - 14a - 20 + 21 Step 4: -15a - 14a - 20 + 21 = -29a + 1 (Step 1) (Step 2) (Step 3) (Step 4)
Step 2
A student simplifies the expression 4 - 3[3x - (-2 - 4y + 2x)]. In which step did the student commit the first error? Step 1: 4 - 3[3x + 2 + 4y - 2x] Step 2: 4 - 3[x + 2 + 4y] Step 3: 4 - 3x + 6 + 12y Step 4: 10 - 3x + 12y (Step 1) (Step 2) (Step 3) (Step 4)
Step 3
Which sequence of steps, when completed, will solve the equation -3y + 4 = -2? (Subtract 4 from each side and then divide both sides by -3.) (Subtract 4 from each side and then divide both sides by 3.) (Add 2 to both sides and then divide each side by -3.) (Divide both sides by -3 and then subtract 4.)
Subtract 4 from each side and then divide both sides by -3.
Maya had $30 and bought 3 chocolate bars, 2 sodas, and 5 bags of candy from the store. She wants to check that she received the correct amount of change from the cashier. If she creates an expression to determine the amount of change she should receive, which operation would she use last? (addition) (subtraction) (multiplication) (division)
Subtraction
Which of the following is not equivalent to T = 5m + 14 (5m - T = -14) (5m = T - 14) (T/5 - 14 = m) (m = (T - 14)/5)
T/5 - 14 = m
A first-year teacher taught his students to multiply binomials emphasizing only the FOIL method. Which of the following describes why learning other methods of binomial multiplication in addition to the FOIL method would best help students succeed when learning to multiply other polynomials? (The FOIL method works only for certain binomial multiplication problems, not for any binomial multiplication.) (The FOIL method is the most difficult method for students to learn.) (The FOIL method does not readily transfer to multiplying polynomials with more than two terms.) (Standardized test developers expect students to be able to solve problems in multiple ways.)
The FOIL method does not readily transfer to multiplying polynomials with more than two terms.
The profit from local fruit stands is based on the number of peaches (p), apples (a), nectarines (n), and employees (e). The profit from two fruit stands is represented by the two equations below: According to the equations, which of the following statements is true? (The employees are paid a higher hourly wage at the second fruit stand) (The peaches cost less at the second fruit stand) (The apples cost less at the first fruit stand) (The nectarines cost more at the first fruit stand)
The employees are paid a higher hourly wage at the second fruit stand
The function below models the height (in feet), h, of an object thrown into the air, where t represents the seconds that have passed since the object was launched. h(t) = -16t² + 80t + 38 What does the number 38 represent in this function? (the initial height of the object) (the maximum speed of the object) (the maximum height of the object) (the initial speed of the object)
The initial height of the object
A teacher gives her students the following comparison problems and asks the students to solve for the variables: x + 2 = 21 + 5 5 - y = 12 - 8 58 + 7 = n - 12 Which of the following math skills is the teacher assessing? (the meaning of the equal sign) (the order in which to combine like terms that include variables) (the correct use of multiplication and division when solving equations) (the correct use of the distributive property)
The meaning of the equal sign
A teacher wants to use algebra tiles like those represented in the following figure to help students understand the concept of completing the square. The teacher wants to identify a quadratic expression for which a visual representation using algebra tiles will be useful in demonstrating the concept of completing the square. Which of the following expressions best serves the teacher's purpose? (x^2 - 3x - 4) (x^2 + 6x + 11) (x^2 - 8x + 7) (x^2 + 9x + 16)
x^2 + 6x + 11
Solve 4x - 2y > 8 for y. (y < -4 + 2x) (y < -4 - 2x) (y > -4 + 2x) (y > 4 - 2x)
y < -4 + 2x
Which of the following inequalities represents the graph below? (y < -x² - 3x + 10) (y ≥ -x² - 3x + 10) (y ≤ -x² - 3x + 10) (y > -x² - 3x + 10)
y < -x² - 3x + 10
If 3y - 13x = 67, what is y in terms of x? (y = (-67 + 13x) x 3) (y = (-13x + 67)/3) (y = (67 + 13x)/3) (y = 3(13x + 67))
y = (67 + 13x)/3
Using the formula w = 3(y + t), if t is equal to 5, which of the following is equivalent to y? (y = (w + 15)/3) (y = (w/3) - 5) (y = 3w - 5) (y = (w/3) - (15t/3))
y = (w/3) - 5
A line passes through the point (4, 2) and is perpendicular to the line 3x-y=6. What is the equation of the line? (y = -3x + 14) (y = -1/3x + 10/3) (y = 1/3x + 4/3) (y=3x-10)
y = -1/3x + 10/3
A line passes through the point (-1, 2) and is parallel to the line 2x + y=6. What is the equation of the line? (y = -2x + 4) (y = -2x) (y = 2x - 4) (y = 2x +2)
y = -2x
Which of the following is not an equation of the graph? (y = -2x + (x + 2)²) (y = -2(x - 3)(x + 5)) (y = -2x² - 4x + 30) (y = -2(x + 1)² + 32)
y = -2x + (x + 2)²
Which of the following pairs of equations result in parallel lines when graphed? (y = x + 5 and y = 4 - 2x) (y = -2x + 1 and y = x + 5) (y = -2x + 1 and y = 1/2x - 3) (y = -2x + 1 and y = 4 - 2x)
y = -2x + 1 and y = 4 - 2x
Which equation best represents the graph? (y = 1/2x² - 1) (y = -1/2x² + 1) (y = x² + 2x - 1) (y = -x² + 2x + 1)
y = 1/2x² - 1
In the graph below, line A is the graph of y - 3x = 2. Which of the following could be the equation of Line B? (y = 1/3x - 1) (y = -3x - 2) (y = -1/3x - 4) (y = 3x - 1)
y = 3x - 1
Which of the following equations is equivalent to the equation 9x - 4y = 12? (y = -9/4x - 3) (y = -9/4x + 3) (y = 9/4x - 3) (y = 9/4x + 3)
y = 9/4x - 3
If x + y = z, which of the following is also always true? (y = x - z) (y = z ÷ x and x ≠ 0) (y = x ÷ z and z ≠ 0) (y = z - x)
y = z - x
Which of the following inequalities represents the graph below? (y < x² + 2x - 3) (y ≥ x² + 2x - 3) (y ≤ x² + 2x - 3) (y > x² + 2x - 3)
y > x² + 2x - 3
Which of the following linear inequalities best represents the graph shown? (y < 3x - 5) (y ≤ 3x − 5) (y ≥ 3x − 5) (y > 3x − 5)
y ≥ 3x − 5
If x ÷ y = z and y ≠ 0, which of the following must also always be true? (y ÷ z = x) (z ÷ x = y) (x ⋅ z = y) (y ⋅ z = x)
y ⋅ z = x
Find the equation of the line perpendicular to y = - ¼ x +2 that goes through the point (3, -1). (y=-4x+11) (y=4x -13) (y= -¼ x - ¼) (y=4x-11)
y=4x -13
Find the line that is parallel to y-5x= 7 and passes through (-2, 3) (y=5x+13) (y = -1/5x - 2/5) (y= -5x +7) (y=5x+7)
y=5x+13
If x^2 - 3x - 54 = (x + k)(x + m) for all values of x, where k and m are constants, what is the value of |k - m|?
|k - m| = 15
John spends his summer working at a retail shop. As a result, he gets a 15 percent employee discount of everything sold in the store. He decides to buy 4 pairs of pants which retail for $30 and 5 shirts which retail for $20. What is the total price he must pay after his employee discount? ($195.50) ($230) ($187) ($220)
$187
The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500? ($500 - $0.75b = $2b) ($500 = $2b - $0.75b) ($500 = $2b + $0.75b) ($500 + $2b = $0.75b)
$500 = $2b - $0.75b
If y = 3x - 2 were graphed in the xy plane, which point would fall above the graph? (-1, -6) (-1, -1) (2, 1) (1, -1)
(-1, -1)
The given system is graphed below. y = x² - 5 y = 3x - 1 Which of the following points are the solutions to the system? ((0, -1)) ((0, -5)) ((-1, -4) and (4, 11)) ((-1, -4))
(-1, -4) and (4, 11)
Which ordered pair is a solution to the system of equations below? {x² - y² = 25 x² + y² + 18x + 65 = 0 ((-9, 4)) ((-7, -5)) ((-5, 0)) ((-9, 0))
(-5, 0)
The following system is graphed below. y = 2x² - 4x - 6 y = 4x - 6 Which of the following points are the solutions to the system? ((-1, 0), (1.5, 0), and (3, 0)) ((-1, 0) and (3, 0)) ((0, -6) and (4, 10)) ((1.5, 0))
(0, -6) and (4, 10)
Find the solution(s) to the following system: -2x + y = 2 y = -x^2 - x + 2 ((0, 2) and (-3, -4)) ((-2, 0) and (1, 0)) ((-1, 0)) ((1, 4))
(0, 2) and (-3, -4)
Find the solution(s) to the system: y = x² - 5x + 6 y = x - 2 ((2, 4)) ((-2, -4) and (-4, -6)) ((2, 0)) ((2, 0) and (4, 2))
(2, 0) and (4, 2)
What is the solution to the system of equations below? -4x + 3y = -5 y = x - 1 ((-2, -3)) ((2, 1)) ((1, 2)) ((-4, -5))
(2, 1)
Find the solution to the following system of equations: x - 2y = 5 5x - 3y = 18 ((1, -3)) ((-1, 3)) ((3, -1)) ((-3, 1))
(3, -1)
Mrs. Thompson presents the scenario to her class and asks them to use it to answer the following question: Kirsten wants to rent paddle boats for her group of friends. She will need 4 boats to fit all of her friends and the boat rental company charges $15 per hour for each boat. In addition to the hourly fee, there is a one-time membership fee of $40 to use the facilities, regardless of how many boats are rented. If Kirsten has budgeted $300 for this outing, how many hours will she and her friends enjoy on the lake? If h represents the number of hours, which of the following equations represents the scenario? (15h + 40 = 300) ((4 ⋅ 15h) + 40 = 300) ((4 ⋅ 15h) - 40 = 300) ((4 ⋅ 15h) + 40h = 300)
(4 ⋅ 15h) + 40 = 300
Three of the following expressions, when simplified, equal the same value. Which of the following equations, when simplified, is not equal to the other expressions? (15x + 8y - 3x - 7y) (1/2(20x + 6y) + 8(1/4x) - 2y) (-4y + 3x + x(5 + 4) + 5y) ((4x ⋅ 3x) + y)
(4x ⋅ 3x) + y
Factor completely: x² - x - 72 ((x + 8)(x - 9)) ((x + 4)(x - 18)) ((x - 8)(x + 9)) ((x + 6)(x - 12))
(x + 8)(x - 9)
Following an introductory lesson on multiplying two binomials, Ms. Davis wants to follow up with a quick problem at the end of class to assess student proficiency. The students will write their final answers on slips of paper and hand them to Ms. Davis as they exit the class. Which of the following expressions would be LEAST useful for assessing student proficiency in multiplying two binomials? ((x - 3)(x - 5)) ((x + 3)(x - 5)) ((x - 5)(x + 5)) ((x + 5)(x + 5))
(x - 5)(x + 5)
The graph of y = 2x² - 4x - 6 is shown below. For what x-values is 0 < 2x² - 4x - 6? ((-1, 3)) ((−∞, −1) ∪ (3, ∞)) ((−∞, −1] ∪ [3, ∞)) ((−∞, ∞))
(−∞, −1) ∪ (3, ∞)
Using the graph of y = x² + 3x - 4 below, find the interval(s) where 0 < x² + 3x - 4. ((-4, 1)) ((−∞, −4]) ((−∞, −4] and [1, ∞)) ((−∞, −4) and (1, ∞))
(−∞, −4) and (1, ∞)
Using the graph below, find the interval(s) where 0 ≥ -x² - 5x + 6. ((−∞, ∞)) ((−∞, −6] and [1, ∞)) ((-6, -1)) ((−∞, −1] and [6, ∞))
(−∞, −6] and [1, ∞)
What is the y-value of the solution to the system below? x = 7/2y + 1 2x - 4y = -1 (-5/2) (-1) (1) (9/2)
-1
Which of the following values of x is a solution to the set of inequalities below? -4 < 3x + 2 < 11 (-2) (-1) (5) (3)
-1
Three students found the correct solution to the equation -11n + 4n + 16 = 9, but they used different methods to find the solution. Which of the following student methods provide evidence of a mathematically valid strategy for finding the solution to the equation? Select ALL that apply. (-11n + 4n + 16 = 9 9n/9 = 9/9 n = 1) (-11n + 4n + 16 = 9 -7n + 16 + 7n - 9 = 9 + 7n - 9 7 = 7n 1 = n) (-11n + 4n + 16 = 9 -11n + 4n = 9 - 16 -7n/-7 = -7/-7 n = 1)
-11n + 4n + 16 = 9 -7n + 16 + 7n - 9 = 9 + 7n - 9 7 = 7n 1 = n, -11n + 4n + 16 = 9 -11n + 4n = 9 - 16 -7n/-7 = -7/-7 n = 1
Which of the following values of x is a solution to the set of inequalities below? -x - 2 < 4 or -x - 2 > 8 (-7) (-12) (-10) (-6)
-12
Which of the following values of x is a solution to the inequality below? 6 < -2x + 3 < 10 (-4) (0) (2) (-2)
-2
Which of the following equations is parallel to the line y = 5x - 2? (4 = 20y + 4x) (-20 = 4y - 20x) (-15 = 5y - 5x) (-10 = 5y + 5x)
-20 = 4y - 20x
Which of the following values of x satisfies 3x²-6x-24 > 0? (-5) (1/3) (4) (-2)
-5
Which of the following is the solution set for ∣x + 4∣ < 1? (−5 ≤ x ≤ −3) (x < -3) (-5 < x < -3) (x > -3)
-5 < x < -3
Solve for x. 10x + 6 = 1/2(4x - 8) (-7/3) (-5/3) (-7/4) (-5/4)
-5/4
If f (x) = -x² + 3x - 2, find the value of f (4). (-6) (18) (2) (26)
-6
If 6(3x+4) = 2(x+2) - 8, what is the value of x? (-7/4) (-5/8) (-5/4) (7/4)
-7/4
Which of the following is equivalent to the expression below? 2x + 4y - 3x + 6 (-x² + 4y + 6) (5x + 4y + 6) (-x + 4y + 6) (9xy)
-x + 4y + 6
Which of the following is one solution to the inequality -6 < 2x - 4 < 8? (0) (-1) (6) (12)
0
Debbie is having a garage sale and prices her shirts, s, at $1.50 each and her pants, p, at $2.00 each. The amount she makes from selling clothes can be expressed as 1.5s + 2p. Which of the following represents the total amount she made from selling shirts? (2p) (1.5s) (2) (1.5)
1.5s
Solve the following equation. Write the solution as a fraction in simplest form. 3(4x - 5) + 8 = 9(2x - 1) (-1/3) (8/3) (3) (1/3)
1/3
Which of the following is equivalent to 1/2(4/3x² - 1/3)? (2/3x² - 2/3) (1/3(2x² - 1/2)) (1/6(x² - 1)) (8/3(x² - 2/3))
1/3(2x² - 1/2)
Marty gets an allowance of $5 each week from his parents. He also can earn extra money by doing additional chores outside of his usual household responsibilities for $1.50 per chore. He has been working on saving his money to buy a new game and thinks he will be close this week. If he would like to get at least $20 from his parents at the end of the week, what is the minimum number of additional chores Marty needs to complete? (10) (17) (14) (13)
10
Solve for a. 2a - 12 + a = 18 (2) (30) (10) (15)
10
The pictograph above displays data for sports equipment sold last Saturday at a certain sporting goods store. At this store, basketballs sell for $12, volleyballs sell for $15, and the total sales made last Saturday on the items shown in the pictograph was $212. If each soccer ball sold for d dollars, what is the value of d? ($9.25) ($23.13) ($10) ($36.50)
10
Mitchell started his weekly mathematics homework during study hall and finished 8 problems before returning home. At home, he found he took an average of 7 minutes to solve each of the remaining problems. Tawny finished only 2 problems at school but was able to solve one problem every 5 minutes at home. How many minutes did they each spend at home to finish their weekly assignment if they solved the same number of problems? (35) (140) (23) (105)
105
James has $10.95 in nickels, dimes, and pennies. He has an equal number of nickels and dimes. If he has x nickels, which of the following represents the number of pennies he has? (1095 - 15x) ((10.95 - 0.05x)/0.1) ((1095 - 15x)/0.01) (It is not possible to determine because there are 3 types of coins.)
1095 - 15x
Which of the following is equivalent to 5/6(12a³ + 4/15a)? (2a³ + 4/3a) (2a³ + 5/6a) (10a³ + 4/15a) (10a³ + 2/9a)
10a³ + 2/9a
Which of the following values of x is a solution to the inequality below? 10 < 2x/5 + 6 < 12 (11) (15) (29) (9)
11
Which of the following equations is perpendicular to the line y= x/3 + 2/3? (12 - 2y = 6x) (2 - 3y = -9x) (6 + 4y = 2x) (2 + 3y = x)
12 - 2y = 6x
Kate and Amelia both get summer jobs. Kate works 3 days a week for 4 hours each and Amelia works 2 days a week for 7 hours each. In addition, Kate makes $100 in tips each week and Amelia makes $75 in tips each week. Kate and Amelia make the same amount of money per week. If k represents the hourly wage Kate earns and a represents the hourly wage Amelia earns, which of the following equations accurately represent this situation? (k(12 + 100) = a(14 + 75)) (100k + 12 = 75a + 14) (12k + 100 = 14a + 75) (14k + 100 = 12a + 75)
12k + 100 = 14a + 75
Which of the following is an expanded version of the expression 3 (x + 7) (4x - 2)? (12x² + 78x + 42) (90x - 42) (12x² + 90x - 42) (12x² + 78x - 42)
12x² + 78x - 42
The cost to ski at a resort is T = 85 + 5h, where T is the total cost and h is the number of hours. If Carl has $150, how many hours can he ski? (13) (325) (30) (47)
13
Which of the following is an equation of the line in the xy-plane that passes through the points (-2, -2) and (7, 11)? (5x - 9y - 8 = 0) (9x - 5y + 8 = 0) (9x - 13y - 8 = 0) (13x - 9y + 8 = 0)
13x - 9y + 8 = 0
If 1/5x + 3 = 6, what is the value of x? (45) (15) (5) (20)
15
Which of the following is equivalent to 4/5 (20m² - 15/2m)? (4m² - 30m) (16m² - 6m) (24/5m² - 19/10m) (16m² - 7.5m)
16m² - 6m
Find the value of f (x) = 3x² - 2x + 1 when x = -2. (9) (-7) (17) (-15)
17
A computer store sells laptops that range from $300 to $4000 and currently has 40 laptops in stock. What is the maximum number of $4000 laptops the store could have if the current inventory for laptops totals $78,600? (18) (22) (15) (20)
18
Ally and Jenny are comparing their cell phone plans. Ally pays $30 per month for her phone line and $5 for every 1GB of data used. Jenny pays $20 per month for her phone line and $10 for every 1GB of data used. If Ally's and Jenny's monthly bills are the same this month, how many GB of data did they each use? (1) (2) (3) (4)
2
Two quadratics are shown in the tables below. How many solutions does this system of quadratics have? (0) (1) (2) (3)
2
Which of the following is a solution to the inequality below? -12 < 2 - 5x ≤ 7 (2.8) (-2) (-2.8) (2)
2
Use the system of equations below to answer the following question. x² + y² = 20 y = x² How many real solutions does the system have? (no real solution) (1 real solution) (2 real solutions) (infinitely many real solutions)
2 real solutions
Three of the following equations, when simplified, equal the same value. Which of the following equations, when simplified, is NOT equal to the other equations? (.25 X 100 - 40) (200 X 1/8 - 2(40 - 20)) (2(40 X .2) + 5[.4 X (1/4)]) ([20/(1/5)]-[5/(1/23)])
2(40 X .2) + 5[.4 X (1/4)]
Student council members are selling valentine cards as a fundraiser. They make $0.50 for each card they sell and want to sell 750 total. The graph shows the number of cards that have been sold thus far by each grade. How many more must be sold overall to meet their goal? (210 cards) (550 cards) (200 cards) (265 cards)
200 cards
Which of the following expressions is equivalent to 9x + 24 for all values of x? (5(45x + 8)) (28 + 1/5(45x-20)) (1/5(45x + 28 - 20)) (28 + 5(45x - 20))
28 + 1/5(45x-20)
Simplify the expression: 4(7x - 3) (28x - 12) (28x - 3) (28x + 12) (16x)
28x - 12
Which of the following equations is parallel to the line y = -3x + 7? (y + 7 = -4x) (2y - 4 = -6x) (-3y - 7 = x) (3y + 6 = x)
2y - 4 = -6x
Which of the following equations is perpendicular to the line y= -4x - 5? (3x + 5y = 1) (4y + x = 3) (2y - x/2 = 12) (8x + 2y = 7)
2y - x/2 = 12
A certain brand of paper plates can be purchased only in packages of 15 plates or in packages of 25 plates. Tanya purchased 8 packages of the paper plates, and there was a total of 150 plates in the packages. Of the packages Tanya purchased, how many were packages of 25 plates? (2) (3) (4) (6)
3
Functions f and g are defined as follows for all real values of x. f(x) = x^2 - 9 g(x) = 2^-x Which of the following values of x best approximates the solution to the equation f(x) = g(x)? (-9) (-3) (0) (3)
3
How many terms are in the expression 3x² + 6x + 3? (3) (2) (1) (4)
3
The graph of function f and a table of values for function g are given below. What is the value of f(g(2))? x -12 -3 0 2 4 g(x) 9 3 -7 -2 5 (3) (-5) (-2) (0)
3
Which of the following equations is perpendicular to the line y = -2x + 6? (3 = 2x - 4y) (6 = x/2 - 4y) (1 = x - 6y) (-6 = 8x + 4y)
3 = 2x - 4y
Which of the following expressions is equivalent to 19x + 36 for all values of x? (3(7x + 36) - 2x) (3(7x + 12) - 2x) (3(7x + 10) + 6) (3(7x - 2x + 12))
3(7x + 12) - 2x
Mrs. York is administering an exam consisting of 40 questions. The test is worth 100 points. Some of the questions are weighted 2 points and some are 4 points. How many 2-pt questions are on the test? (40) (30) (20) (10)
30
Estella and Manuel were hiking down from the top of a mountain toward the parking lot at the bottom. At 3:00 p.m. Estella was 1800 meters further down the mountain than Manuel. Estella hiked at a rate of 0.65 meters per second. Manuel hiked at a rate of 1.25 meters per second. At what time did Manuel catch up with Estella? (4:20) (3:30) (3:50) (4:00)
3:50
Elizabeth owns x books. Kierra owns 5 more books than Elizabeth and 8 fewer than Ana. Which of the following expressions represents the total number of books the three girls own? (3x - 3) (3x + 3) (3x + 13) (3x + 18)
3x + 18
Line m is graphed below. If line n is perpendicular to line m, which of the following could represent line n? (x - 3y = -3) (x + 3y = 6) (3x + y = 2) (3x - y = 1)
3x - y = 1
Susan is planning for volunteer day at the high school. Every person that signs up gets a free lunch for volunteering. This year, lunch includes 3 slices of pizza and a soda. If x = number of volunteers and one pizza has 8 slices, which equation can help her to determine the correct number of pizzas (n) to order? ((3x + 1)/8 = n) (3/8x = n) (3x/8 = n) (3/8 X x + 1 = n)
3x/8 = n
What is the first step in solving this equation? 3 (y + 4) - 2(3y - 1) = 10 (3y + 12 + 6y + 2 = 10) (3y + 4 − 6y − 1 = 10) (3y + 4 + 6y + 2 = 10) (3y + 12 − 6y + 2 = 10)
3y + 12 − 6y + 2 = 10
Last winter a local animal center hosted an adoption drive. The results of the number of cats adopted is in the table below by month. If 56 cats were adopted during this four month period, what does each cat picture represent? (4) (3) (2) (5)
4
Use the equation below to answer the question that follows. 4x + 8(x-3) = x+20 Which of the following is the correct value of x? (all real numbers) (4) (3) (6)
4
The pictograph shows the number of sales made by an ice cream store on a summer day. A bowl of ice cream is $3.00 and a cone costs $0.50 more than a bowl. If the total sales were $540.00 that day, how much is a sundae? ($3.50) ($4.50) ($4.00) ($4.25)
4.5
An airplane travels 7 times faster than a train. If the difference between the speed of the plane and the speed of the train is 420 m/h, how fast is the plane traveling? (294 m/h) (490 m/h) (70 m/h) (60 m/h)
490 m/h
Ms. Fisher's students are working on identifying like terms in algebraic expressions. When Ms. Fisher asks them how they know when terms are like terms, one student, Coleman, says, "Like terms have to have the same variable in them." Ms. Fisher wants to use a pair of terms to show Coleman that his description of like terms is incomplete and needs to be refined. Which of the following pairs of terms is best for Ms. Fisher to use for this purpose? (9m and 5) (8xy and xy) (5n^4 and 2n^4) (4h^2 and 7h^3)
4h^2 and 7h^3
Which of the following lines passes through the point (2, 3) and is parallel to 6x - 3y = 12? (4x - 2y = 2) (6x - 2y = 6) (x + 2y = 8) (2x - y = 4)
4x - 2y = 2
Which of the following equations is parallel to the line y = x/2 - 1/4? (2y + 4x = -8) (4y - 2x = 12) (4y - x = -1) (2y - 8x = -3)
4y - 2x = 12
The point with coordinates (-4, t) lies on line ℓ in the xy-plane, as shown in the following figure. What is the value of t? (4) (5) (9) (14)
5
The solutions to a linear inequality are represented on the following number line. Which of the following could be the inequality? (5(2x + 3) < 18x - 17) (5(2x + 3) ≤ 18x - 17) (5(2x + 3) > 18x - 17) (5(2x + 3) ≥ 18x - 17)
5(2x + 3) ≥ 18x - 17
Asher makes $240 every pay period plus 15% on all sales. He determines his paycheck using the expression 240 + .15x. Which of the following is equivalent to Asher's expression? (3(240 + .05x)) (5(48 + .03x)) (5(48 + .15x)) (3(48 + .05x))
5(48 + .03x)
Robbie is attending a baseball game, sitting in the outfield. A t-shirt cannon shoots a t-shirt into the air following the trajectory f(x) = -0.002x^2 + .12x + 2. If the ground slopes upward from the base of the t-shirt cannon at a rate of g(x) = 0.06x, how far from the cannon does Robbie need to stand in order to catch the t-shirt? (3 ft) (20 ft) (30 ft) (50 ft)
50 ft
On the way from school to the town library, Jenna rides her bike for 15 blocks and then walks the rest of the way at 13/21 block per minute. Micah follows the same route but walks the entire distance to the library at 6/7 block per minute. If they both walk for the same amount of time what is the total number of blocks between the school and the library? (54) (18) (63) (9)
54
Which of the following correctly simplifies the left side of the equation below? 3x - 4 + 6x + 5 - 4x - 2 = 16 ((3x - 4) + (6x + 5) - (4x + 2) = 16) (14x - 10 = 16) (13x - 11 = 16) (5x - 1 = 16)
5x - 1 = 16
Simplify the expression: 3x + 2(3x - 2) + 5 - 2(2x + 1) (5x + 4) (8x + 6) (13x + 11) (5x-1)
5x-1
Which of the following is equivalent to 8(8 + y + y) - 16y for all values of y? (48y) (48) (64) (64 - 8y)
64
Which of the following monomials is the greatest common factor that can be factored out of the polynomial below? 18x² + 12x (2x) (x) (6x) (6)
6x
Which of the following options shows a logical and correct first step to solving the algebraic equation given? 3(2x + 1) - 5(x + 4) = 11 (-2(3x + 5) = 11) (6x + 3 - 5x + 20 = 11) (6x + 3 - 5x - 20 = 11) (6x + 1 - 5x + 4 = 11)
6x + 3 - 5x - 20 = 11
Which equation, along with 3x + 2y = 4, creates a system of equations which has no solution? (6x + 4y = 8) (2x + 3y = 4) (6x + 4y = 12) (-2x + 3y = 6)
6x + 4y = 12
Which of the following values of x is a solution to the inequality below? -3 < -x/3 + 2 < 0 (0) (-4) (15) (7)
7
Samuel has an average base metabolic rate of 80 calories per hour and uses an additional 352 calories per day walking to and from school. Sabrina uses an extra 544 calories over her base metabolic rate while on her daily bike ride. Samuel and Sabrina typically burn the same total number of calories in each 24-hour day. Using these figures, what is Sabrina's average base metabolic rate in calories per hour? (72) (1728) (112) (2272)
72
A couple is planning their wedding budget. The set cost of the venue, flowers, photographer, and DJ is $4,950, and the cost per person for food and drinks is $65. Therefore, t, the total cost of the couple's wedding, can be expressed by the equation t = 65p + 4,950, where p is the number of people that attend the wedding. If the couple has a budget of $10,000 to spend on the wedding, what is the maximum number of people that can attend? (76) (78) (77) (153)
77
Company F charges a one‑time fee of $85.00 to rent a truck plus $0.60 for every mile driven. Company G charges a one‑time fee of $61.00 to rent a truck plus $0.90 for every mile driven. For what number of miles is the cost to rent a truck the same at both companies?
80 miles
A student asks a teacher when would knowing the likelihood of a six being rolled on a dice be useful in real life. Which of the following examples would be the most appropriate response for the student? (a teacher averaging a student's grade for the semester) (a casino estimating the expected number of jackpot payouts over the next fiscal year) (a farmer measuring the length of the fields to determine area) (a builder cutting materials for a house)
A casino estimating the expected number of jackpot payouts over the next fiscal year
A student asks a teacher when calculating percentages of numbers will be useful in real life. Which of the following examples would be the most appropriate response for the student? (a parent going shopping at a store sale) (a builder cutting materials for a house) (a pharmacist measuring the correct amount of medication) (a architect designing a building)
A parent going shopping at a store sale
Which of the following sequences of steps will yield the valid solution for x to the equation -8 + 5x = 12? (Combine -8 and 5 to get -3x = 12, then divide by -3 on each side of the equation.) (Add 8 to each side of the equation, then divide by 5 on each side of the equation.) (Subtract 8 from each side of the equation, then divide by 5 on each side.) (Divide by 5 on both sides of the equation, then add 8 to each side.)
Add 8 to each side of the equation, then divide by 5 on each side of the equation.
Klaus is planning his annual garden. He wants to plant 2 carrot plants, 3 pepper plants, and 1 squash plant. If he knows the area that each plant requires to grow and wants to determine the total area his garden will require, which operation will he use last in his calculation? (subtraction) (division) (multiplication) (addition)
Addition
Student work is shown below. Step 1: 6x - 8 = 10x + 4 Step 2: -8 = 4x + 4 Step 3: -12 = 4x Step 4: -3 = x What property could be used to justify the student work from Step 1 to Step 2? (Multiplication property of equality) (Transitive property of equality) (Associative property of addition) (Addition property of equality)
Addition property of equality
Use the student work shown below to answer the question: Step 1: 3x + 2 = 16 - 4x Step 2: 7x + 2 = 16 Step 3: 7x = 14 Step 4: x = 2 Which property should the student use to justify step 3? (addition property of equality) (transitive property) (multiplication property of equality) (associative property of addition)
Addition property of equality
Using the student's work below, which property does the student still need to master? Step 1: 3x - 7 = 7x + 1 Step 2: 3x = 7x - 6 Step 3: 10x = -6 Step 4: x = -6/10 (addition property of equality) (multiplication property of equality) (transitive property) (associative property of addition)
Addition property of equality
Review the work below. Given 3(2x + 1) + 2(2x + 1) + 7 = 42 - 5x Step 1: 5(2x + 1) + 7 = 42 - 5x Step 2: 10x + 5 + 7 = 42 - 5x Step 3: 10x + 12 = 42 - 5x Step 4: 15x + 12 = 42 Step 5: 15x = 30 Step 6: x = 2 Which of the following justifies the simplification made from step 3 to step 4? (Additive property of equality) (Multiplicative inverse property) (Additive inverse property) (Multiplicative property of equality)
Additive property of equality
Jaya and Asha are selling baked goods at the bake sale. Jaya's profit can be found by using the equation P = 2b - 28, where P represents profit and b represents the amount of baked goods Jaya sells. Asha's profit can be found by using the equation P = 2.5b - 39, where P represents profit and b represents the amount of baked goods Asha sells. Which of the following conclusions can be made based on the two equations? (To make the same amount of profit, both girls need to sell 24 baked goods.) (Asha will make a higher profit.) (Asha is selling her baked goods for fifty cents more than Jaya.) (Jaya spent more on ingredients for the bake sale than Asha.)
Asha is selling her baked goods for fifty cents more than Jaya.
When solving an equation, Allie and Diane chose to take different approaches in their first steps. Which property ensures that they are both correct? Original equation: 5x + 3x − 2x = 4 Allie's approach: (5x + 3x) − 2x = 4 Diane's approach: 5x + (3x − 2x) = 4 (associative property of addition) (multiplication property of equality) (commutative property of addition) (addition property of equality)
Associative property of addition
Samuel solved the equation 3(2x + 4) = 4(2x + 4) + (3x + 6) below: Samuel arrived at an answer of -7/3. The correct answer is x = -2. Which operational property was misused in Samuel's work? (subtraction property of equality) (addition property of equality) (division property of equality) (multiplicative identity property)
Division property of equality
Mr. Sudu is a waiter. His total weekly earnings consist of a wage of $6 per hour plus approximately 15% in tips on his total sales for the week. One week Mr. Sudu worked 25 hours and had total sales of z dollars. Which of the following represents his total weekly earning in dollars, E, for that week? (E = 0.15z + 150) (E = 25 (0.15z + 6)) (E = 0.15 (z + 150)) (E = 6z + 25)
E = 0.15z + 150
Peter babysits in the evenings for neighborhood children. He charges a flat rate of $12 per evening plus $7 for each hour he sits. If E represents his total earnings for an evening of babysitting and t is the number of hours that Peter babysits that evening, which of the following equations represent the relationship between the amount of time he babysits and his total earnings? (E = 12t + 7) (E = 7t + 12) (E = 12(t - 1) + 7) (E = 1/7t + 12)
E = 7t + 12
Which of the following comparisons between equations and inequalities is NOT true? (An equation is a statement that two expressions are equal, while an inequality is a statement that two expressions are not equal.) (Equations are solved using inverse operations while inequalities cannot be solved with inverse operations.) (Equations typically have only one solution that makes the equation true, while inequalities typically have a solution set, or range of values, that make the inequality true.) (Equations contain only one possible symbol between each expression (=), while inequalities can contain four possible symbols between each expression (<, >, ≤, ≥).)
Equations are solved using inverse operations while inequalities cannot be solved with inverse operations.
Which of the graphs, shown, represents the system {y ≥ x² - 2 and y ≤ ∣x∣}? (Graph A) (Graph B) (Graph C) (Graph D)
Graph D
Which of the solution sets indicated in the graphs, shown, include all points on both boundaries? (Graph A) (Graph B) (Graph C) (Graph D)
Graph D
Which of the following scenarios is best modeled with the inequality 6 ≤ x? (Gloria had more than 6 pairs of shoes, x.) (Usman ran up to 6 miles, x.) (Hank ate at least 6 grapes, x.) (Rachel had $6, then spent $x on a coffee.)
Hank ate at least 6 grapes, x.
Mr. Romeo wants his students to understand that math is very important and used in the real world all the time. He wants them to understand that math is used outside of school on a regular basis. Which of the following is the best way to have students learn about this? (Have students do a hands-on project that uses math.) (Have students teach their younger siblings to use math to solve problems.) (Have students interview two adults about how they use math in their everyday life.) (Have students read a book about famous mathematicians.)
Have students interview two adults about how they use math in their everyday life.
A math teacher wants to introduce a lesson on the use of decimals and fractions. Which of the following strategies is most likely to increase the students' understanding of the concepts? (Highlight examples of decimal and fraction use from the students' lives.) (Repeat the lesson until students have committed the lesson to memory.) (Have students complete a pre-instructional worksheet on the topic.) (Have students write down what they think is the purpose of decimals and fractions.)
Highlight examples of decimal and fraction use from the students' lives.
Before teaching multiplying polynomials with any number of terms, Ms. Rodgers assesses her students' proficiency with multiplying two binomials. She asks her students to multiply (3x-2) by (2x + 3), show their work, state the answer, and explain their method. Which of the following student work does not demonstrate that the student is ready to move on to multiplying polynomials with any number of terms?
I used the FOIL method where I multiplied the first two terms, the outer two terms, the inner two terms, and the last two terms.
Jenna wants to rent a bike. Joe's Bike Rental rents bikes for a $10 deposit and $1.00 per hour. Bobbie's Bikes rents bikes for a $15 deposit and $0.50 per hour. Assuming that Jenna rides for h hours, which of the following statements must be true? (If h ≤ 15, Joe's is the best deal.) (Joe's is always the best deal.) (If h > 5, Bobbie's is the best deal.) (If h > 10, Bobbie's is the best deal.)
If h > 10, Bobbie's is the best deal.
Tom is looking for a family photographer. Sallie's Shots charges a $50 sitting fee plus $5.00 per picture purchased. Paul's Photos charges an $85 sitting fee but charges $2.50 per picture purchased. Assuming that Tom will purchase p pictures, which of the following statements is true? (Paul is always the best deal.) (If p>14, Paul has the better deal.) (Sallie is always the best deal.) (If p<14 Paul has the better deal.)
If p>14, Paul has the better deal.
A teacher prompted her students to write an example of an expression on their papers. One student wrote the following on their paper: 2x + 3 = 5 The student raises her hand and wants to know if her answer is correct. Of the following, which is the best teacher response to the student? (It is correct; expressions must contain an equal sign.) (It is incorrect; this is an equation because it contains an equal sign. There is an expression on either side of the equal sign, which could be possible correct answers.) (It is incorrect; expressions cannot contain variables.) (It is incorrect; expressions only contain one term. Any of the three terms by itself could be possible correct answers.)
It is incorrect; this is an equation because it contains an equal sign. There is an expression on either side of the equal sign, which could be possible correct answers.
Jordan was simplifying the expression: 3x^2 - 4 + 8x - 5x^2 + 6. She simplified it to 8x^2 + 8x + 10, and then raised her hand to have her teacher check her work. Of the following, what is the best response from the teacher to Jordan? (Jordan is not correct. Every term has a sign to the left of it. When she combined 3x^2 and -5x^2, she disregarded the sign of the 5x^2 term and got 8x^2 when she should have simplified it to -2x^2. She made the same mistake when adding the constants. She dropped the negative in front of the 4; -4 and 6 combine to 2.) (Jordan is not correct; 3x^2, 8x, and -5x^2 can all be combined to get 6x^3, and the constants -4 and 6 combine to 2, resulting in 6x^3 + 2.) (Jordan is not correct. 3x^2, -4, 8x, -5x^2, and 6 can all be combined to get 8x^3.) (Jordan is correct; she combined all the x^2 terms and all the x terms correctly to get 8x^2 + 8x + 10.)
Jordan is not correct. Every term has a sign to the left of it. When she combined 3x^2 and -5x^2, she disregarded the sign of the 5x^2 term and got 8x^2 when she should have simplified it to -2x^2. She made the same mistake when adding the constants. She dropped the negative in front of the 4; -4 and 6 combine to 2.
A model of an equation is shown. What is the value of M? (M = 3) (M = 4) (M = 2) (M = 5)
M = 3
Use the student work shown below to answer the question: Step 1: 5x + 4 = 3x - 2 Step 2: 2x + 4 = -2 Step 3: 2x = -6 Step 4: x = -3 Which property should the student use to justify step 4. (multiplication property of equality) (addition property of equality) (associative property of addition) (transitive property)
Multiplication property of equality
Mr. Silbaugh assesses his students' proficiency with multiplying binomials by asking his students to explain how they would find the product of (-x² + 4) and (3x + 1). Which of the following student explanations demonstrates that the student understands how to multiply binomials? (Multiply the terms in the first parentheses by the terms in the second parentheses.) (Regroup all terms using the associative property so all terms with x are together and all of the constants are together. Then, add like terms.) (Make a square and add like terms) (Multiply -x² in the first set of parentheses by both terms in the second set of parentheses, and then multiply 4 in the first set of parentheses by both terms in the second set of parentheses. Add like terms.)
Multiply -x² in the first set of parentheses by both terms in the second set of parentheses, and then multiply 4 in the first set of parentheses by both terms in the second set of parentheses. Add like terms.
Determine the solution(s) to the system. y = x² - 5x + 8 y = 2x - 4 ((3, 2)) ((3, 2) and (4, 4)) ((3, 4)) (There is no solution.)
(3, 2) and (4, 4)
Before purchasing a new car, Branden wants to know his monthly payments, m. He plans to make a down payment, d, and then pay off the rest of the car in 60 months. The total cost of the car plus interest is t. Which equation can Branden use to find his monthly payment? ((d-t)/60 = m) (60/(t-d) = m) ((t-d)/60 = m) (60/(d-t) = m)
(t-d)/60 = m
Which of the following is equivalent to x² - 6x - 15 = 0? ((x + 3)² = 24) ((x - 3)² = 6) ((x - 3)² = 15) ((x - 3)² = 24)
(x - 3)² = 24
Which of the following is not an appropriate first step when solving this equation? 6(y - 3) = 2(y - 3) + 8 (3(y - 3) = y - 3 + 4) (-2(y - 3) = 2(y - 3)) (6y - 18 = 2y - 6 + 8) (4(y - 3) = 8)
-2(y - 3) = 2(y - 3)
Solve for x. (10x + 2)/4 = 5x - 2 (1) (-4/5) (2/5) (-1)
1
Which four of the following lines are perpendicular to 5x - 2y = 7? Select all answers that apply. (5x + 2y = 7) (2/3x + 5/3y = 1/3) (5y = -2x + 10) (2x + 5y = 13) (y = -2/5x + 3) (-2y = -5x + 7)
2/3x + 5/3y = 1/3, 5y = -2x + 10, 2x + 5y = 13, y = -2/5x + 3
If 1/6x - 4 = 1, then x = (-18) (5/6) (30) (10)
30
John works in sales at a car dealership. His base salary is $550 per week and he makes $900 for each car he sells. His paycheck last week was more than $4000. What is the least number of cars he could have sold? (5) (4) (6) (3)
4
There are 110 cars that pass through the carpool lane daily. Some cars take 2 students and other cars take 3 students. If 255 students go through the carpool line, what fraction of the cars take 3 students? (1/3) (21/51) (3/5) (7/22)
7/22
A certain hill is 30 meters high and erodes at a rate of 1/5 meter per year. A nearby hill is 25 meters high and erodes at a rate of 2/15 meter per year. In how many years will the two hills be the same height if they continue to erode at these rates? (25) (15) (75) (5)
75
If f(x) = x² - 3x + 4, what is the value of f(-1)? (7) (2) (8) (0)
8
Which of the following are correct solutions to the inequality below? 2x + 5 ≥ 15 Select all answers that apply. (4) (2) (8) (5)
8, 5
Simplify the expression below: (32x + 12)/4 (8x + 12) (8x + 3) (32x + 3) (28x + 8)
8x + 3
A football team is selling raffle tickets as a fundraiser for equipment. They need at least $2000 for equipment and raffle tickets are $8.00 each. Which inequality represents the minimum number of tickets needed to be sold to reach their goal? (8x ≥ 2000) (8x ≤ 2000) (8x < 2000) (8x > 2000)
8x ≥ 2000
Which of the following is the solution to 4m + 8 ≤ 10m -4? (m ≥ 2/3) (m ≤ 2) (m ≥ 6/7) (m ≥ 2)
m ≥ 2
Solve P = 2(l + w) for w. (w = P/(2l)) (w = P - 2l) (w = (P - 2l)/2) (w = 2P - 4l)
w = (P - 2l)/2
A restaurant charges $7.00 for a bowl of noodles and $1.25 for each topping selected. Let D represent the total cost of a meal and let T represent the number of toppings selected. Which of the following is an equation for the total cost of a meal in dollars, D? (D = 7.00 - 1.25T) (D = 1.25 X 7.00T) (D = 1.25 + 7.00T) (D = 7.00 + 1.25T)
D = 7.00 + 1.25T
Which inequality and solution is represented by the graph below? (x - 4 < 3(x-2)) (x + 4 < 3(x-2)) (x + 4 < x - 2) (x - 4 < x - 2)
x + 4 < 3(x-2)
Which expression is true for the values of x given -10x + 3 > -5x - 7? (x > 2) (x > -2) (x < 2) (x < -2)
x < 2
Which of the following describes the possible values of x in the equation x < |⅓ - ⅔| ? (x < ⅓) (x < - ⅓ and x > ⅓) (x < - ⅓) (- ⅓ < x < ⅓)
x < ⅓
If -5y = 25 + 3x, what is x in terms of y? (x = (-5y - 25)/3) (x = (-5y + 25)/3) (x = -5/3y - 25) (x = 3(-5y - 25))
x = (-5y - 25)/3
If 3y = 2x - 18, what is x in terms of y? (x = 2(3y - 18)) (x = 2(3y + 18)) (x = (3y + 18)/2) (x = (3y - 18)/2)
x = (3y + 18)/2
What is x in terms of y for the equation: 74 - 6x = 9y (x = (9y -74) ÷ -6) (x = 6(9y -74)) (x = (9y -74) ÷ 6) (x = -6(9y -74))
x = (9y -74) ÷ -6
Which of the following is the solution to the equation 2x² + x - 28 = 0? (x = -4 and x = -3.5) (x = -4 and x = 3.5) (x = 3.5 and x = 4) (x = -3.5 and x = 4)
x = -4 and x = 3.5
What are the solutions to x² - 2x = 24? (x = -4, x = 6) (x = -2, x = 12) (x = -6, x = 4) (x = 0, x = 2)
x = -4, x = 6
If 2x + 8y = -24, what is x in terms of y? (x = (8y + 24)/2) (x = 4y - 12) (x = -1/4y - 3) (x = -4y - 12)
x = -4y - 12
Which of the following is the solution set for the system {y = 2x − 8 and y + 2 = x + 6}? (x = -6, y = -2) (x = 4, y = 0) (x = 12, y = 16) (x = -8, y = -4)
x = 12, y = 16
What are the roots of the equation y = x² - 15x + 14? (x = 14 and x = 1) (x = -14 and x = -1) (x = 7 and x = 2) (x = -15 and x = 14)
x = 14 and x = 1
Which of the following are the solutions to the equation x² - 11x + 24 = 0? (x = -8 and x = 3) (x = -8 and x = -3) (x = 3 and x = 8) (x = -3 and x = 8)
x = 3 and x = 8
Which of the following is an equivalent form of the equation a = x - y? (x = a/y) (x = a - y) (x = ay) (x = a + y)
x = a + y
Which of the following inequalities is equivalent to 6x + 1 > 4x - 5? (x > -2) (x > 2) (x > -3) (x > 3)
x > -3
Solve the inequality: 9x - 8 > 24 - 7x (x > 2) (x > 16) (x < 2) (x < -16)
x > 2
Which of the following is a solution for x in the inequality: -3(-2x - 2) > 21 + 3x (x < 5) (x < 9) (x > 5) (x > 9)
x > 5
Find the line parallel to the line x=-4 that goes through (2, 6). (x=2) (x=6) (y=-4x+14) (y=6)
x=2
A teacher demonstrates two ways to multiply the binomials (-2x + 4) and (x - 5), as shown below. The teacher then asks the students to explain why both methods produce the same results. Which student responses show an understanding of why the two processes are equivalent? Select all that apply. Select all answers that apply. (The first way is just multiplying and the second way is like finding an area. Since areas are found by multiplying the side lengths, the two methods are equivalent.) (Both methods multiply each term of the first binomial by each term of the second binomial and the results are simplified by combining like terms.) (The two methods do the same thing because the answers are the same no matter which method is used.) (In both methods -2x is multiplied by x and by -5, and 4 is multiplied by x and -5, then the results are added.)
Both methods multiply each term of the first binomial by each term of the second binomial and the results are simplified by combining like terms., In both methods -2x is multiplied by x and by -5, and 4 is multiplied by x and -5, then the results are added.
The formula for converting Fahrenheit to Celsius is C = 5/9(F - 32). Which of the following equations is not equivalent to this formula? (9/5C = F - 32) (C/(F - 32) = 5/9) (9/5C + 32 = F) (C - 5/9 = F - 32)
C - 5/9 = F - 32
A travel lacrosse league requires a $200 deposit and then charges $75 a month during the season. If m is the number of months, which equation represents the cost, C, of a season? (C = 200 - 75m) (C = 125 + 75m) (C = 75 + 200m) (C = 200 + 75m)
C = 200 + 75m
When working on solving an equation, Josef rearranged the terms on each side of the equation so: Original equation: -2 + 3x = 4 - 5x New equation: 3x - 2 = -5x + 4 Which property did Josef use to allow him to make this change? (addition property of equality) (commutative property of addition) (associative property of addition) (transitive property)
Commutative property of addition
Two customers are paying for a house plant that costs $6.25. Customer 1 provides the cashier with 17 quarters, 24 dimes, and 22 pennies. Customer 2 pays with 18 quarters, 5 dimes, and 19 nickels. Which of the following statements is true? (Customer 1 will receive $0.62 in change after purchasing the plant.) (Customer 2 gave the cashier more money than Customer 1.) (Customer 2 will receive $0.30 in change after purchasing the plant.) (Customer 1 does not have adequate money to pay for the house plant.)
Customer 1 will receive $0.62 in change after purchasing the plant.
Ms. Adams tells her students that the x in the equation 3(2x + 5) = 39 is called a variable. She then asks her students to write down what they think the word "variable" means in this context. One student wrote, "The variable is a letter that stands for something we don't know." Which of the following revisions to the student's definition most improves the precision of the definition as it relates to this use of the word "variable" in this context? (The variable is a letter that stands for any number that is unknown.) (The variable is a letter that stands for a number that is unknown in the equation.) (The variable is a letter that stands for an unknown number that can take on different values.) (The variable is a letter that stands for the unknown number that will make the equation true.)
The variable is a letter that stands for the unknown number that will make the equation true.
After solving a system of two linear equations, a student's work resulted in the equation 4 = 4. Assuming no mistakes were made, what can the student conclude about the given system? (There are no solutions.) (There are infinitely many solutions.) (There is no way of knowing if there are any solutions to the system.) (There are 4 solutions.)
There are infinitely many solutions.
Jamie deposits $245 into her health club account at the beginning of the year. Each time she visits, $7 is deducted from her account. Which equation represents V, the value in her account after x visits? (V = 245x - 7) (V = 245 - 7x) (V = 7x - 245) (V = 245 + 7x)
V = 245 - 7x
Mrs. Goertz's class is having a discussion about how to solve the system of equations below: 3x + 2y = 4 4x - 2y = -18 Hyein raises her hand and says that the best way to solve this system would be to graph each equation and find the point where the lines intersect. Of the following, which is the best response for Mrs. Goertz to give Hyein?
While the system could be solved by graphing, this is not the easiest method because neither equation is in slope-intercept form. The easiest method for this system is elimination.
For the bake sale, students sold c dozen cupcakes. It cost $0.98 to make a batch of 12 cupcakes and they charged $0.50 per cupcake. Which expression, in terms of c, represents the profit, p, made from the cupcake sales? Assume the students sold all cupcakes made. ([(12)(c) - 0.98]/0.5 = p) ([(12)(0.5) - 0.98]/c = p) ([(12)(c) - 0.98]0.5 = p) ([(12)(0.5) - 0.98]c = p)
[(12)(0.5) - 0.98]c = p
The table shows Jenna's scores in her math class. Quiz 1 Quiz 2 Unit Test 1 Quiz 3 Unit Test 2 Midterm 86% 81% 85% 91% 87% 88% The tests count twice as much as the quizzes, and the midterm counts three times as much as the quizzes. To find her average score in the class at midterm, Jenna uses the following expression: (86 + 81 + 85 + 85 + 91 + 87 + 87 + 88 + 88 + 88) X (1/10) Which of the following is another way to find her average score at midterm? ([86 + 81 + 2(85) + 91 + 2(87) + 3(88)] X 10) (10 ÷ (86 + 81 + 85 + 85 + 91 + 87 + 87 + 88 + 88 + 88) (86 + 81 + 85 + 85 + 91 + 87 + 87 + 88 + 88 + 88 ÷ 10) ([86 + 81 + 91 + 2(85 + 87) + 3(88)] ÷ 10)
[86 + 81 + 91 + 2(85 + 87) + 3(88)] ÷ 10
The formula for the perimeter of an isosceles triangle is P = 2a + b. Solve for a. (a = (P - b)/2) (a = 2(P - b)) (a = P/(2 + b)) (a = (b - P)/2)
a = (P - b)/2
Which of the following equations can be used to define multiplication? (a ⋅b = c if a = c − b and b ≠ 0) (a ⋅b = c if a = c ⋅ b and b ≠ 0) (a ⋅b = c if a = c ÷ b and b ≠ 0) (a ⋅b = c if a = c + b and b ≠ 0)
a ⋅b = c if a = c ÷ b and b ≠ 0
The graph of a quadratic of the form y = ax² + c is graphed below. If a and c are both integers, what are the values of a and c? (a=2, c=-2) (a= -1, c=2) (a=2, c=2) (a= -2, c =2)
a= -2, c =2
The graph of a quadratic of the form y = ax² + c is graphed below. If a and c are both integers, what are the values of a and c? (a=-1, c=-2) (a=-3, c=-2) (a=1, c=-2) (a=3, c=-2)
a=3, c=-2
The formula for the area of a triangle is A = 1/2bh. Solve for b. (b = A/(2h)) (b = h/(2A)) (b = 2Ah) (b = (2A)/h)
b = (2A)/h
Which of the following is a solution for b in the inequality: -2b + 4 ≤ 7 - b (b ≤ 3) (b ≤ -3) (b ≥ -3) (b ≥ 3)
b ≥ -3
The number of tennis shoes, t, in a dorm is 12 more than 5 times the number of dress shoes. Which of the following represents the number of dress shoes in the dorm in terms of t? (d = 5t + 12) (d = (t - 12)/5) (d = (t/5) - 12) (d = 5t - 12)
d = (t - 12)/5
Which graph below is the most narrow? (f(x) = 1/2(x - 2)²) (f(x) = -(x + 4)² - 1) (f(x) = -3x² + 5) (f(x) = 12/5(x + 3)²)
f(x) = -3x² + 5
Which of the following is an equivalent form of the equation P = (h+v)/3? (h = 3P - v) (h = P/3 - v) (h = 3(P - v)) (h = (P - v)/3)
h = 3P - v
The formula for the volume of a cylinder is V = πr²h. Solve the formula for h. (h = Vπr²) (h = V/(πr²)) (h = V - πr²) (h = (πr²)/V)
h = V/(πr²)
Using the formula V = i/R, if R is equal to 12, which of the following is equivalent to i? (i = V/12) (i = 12RV) (i = 12/V) (i = 12V)
i = 12V
Which of the inequalities below is the solution to 3k + 4 ≥ 5k + 6? (k ≥ -1) (k ≤ -1) (k ≥ 1) (k ≤ 1)
k ≤ -1
If h and k are nonzero real numbers, which of the following expressions is equivalent to (h^-3/k^-2)^5? (h^2/k^3) (k^3/h^2) (h^15/k^10) (k^10/h^15)
k^10/h^15
The formula for the surface area of a rectangular prism is represented by A = 2lw + 2lh + 2wh. Solve the formula for l. (l = A - (2wh)/(2w - 2h)) (l = A/(2w + 2h + 2wh)) (l = (2w + 2h)/(A - 2wh)) (l = (A - 2wh)/(2w + 2h))
l = (A - 2wh)/(2w + 2h)
A toy store is running a promotion where they charge $75 for a yearly membership and $9.45 for each toy purchased throughout the year, including tax. Anyone that signs up for the promotion gets their first toy free. How much money, m, does someone spend after buying t toys and a yearly membership? (m = 9.45t + 75) (m = 75 + 9.45(t - 1)) (m = 9.45t) (m = 9.45(t - 1))
m = 75 + 9.45(t - 1)
Using the formula v = u + at, if a is equal to 6, which of the following is equivalent to t? (t = 1/6(v - u)) (t = 6/(u - v)) (t = 6(v - u)) (t = (v - 6)/u)
t = 1/6(v - u)
