Algebra I
Which trinomial is factored?
NOT C.,A
Which is the graph of the step function f(x)?
b.
What is the value of h(2)?
C. 0
What is the square root of r64?
D. r32
Which r-value represents the weakest correlation?
C. 0.11
Which could be the function?
C. f(x) = (x - 4)2
6k + 10.5 = 3k + 12
A. k = 0.5
Which is the graph of f(x) = 0.5(4)x?
A.
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?
B. 4
Which graph represents the function f(x) = |x + 3|?
B.
Which are the solutions of x2 = -11x + 4?
A.
Which is the graph of F(x)=(3 2/3)X?
D.
What is the solution to the system of equations? y = 1.5x - 4 y = -x
D. (1.6, -1.6)
What are the factors of m2 - 12m + 20?
NOT A. m - 5 and m - 4
What is the value of the function when x = 2?
NOT C,B
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
C. 4
Which value is in the domain of f(x)?
C. 4
Which function is represented by the graph?
B.
What is the vertex of the graph of g(x) = |x - 8| + 6?
B. (8, 6)
Which polynomial is prime?
B. 3x3 - 2x2 + 3x - 4
What are the zeros of the quadratic function f(x) = 2x2 - 10x - 3?
C
Which graph represents exponential decay?
C.
What is the missing term in the factorization of 2x2 + 5x + 3?
1
Which terms could have a greatest common factor of 5m2n2? Check all that apply.
5m4n3 15m2n2
What is the value of y in the solution to the system of equations? 1/3x +1/4 y = 1 2x - 3y = -30
D. 8
What is the sum of the polynomials? (7x3 - 4x2) + (2x3 - 4x2)
D. 9x3 - 8x2
What is the solution to the system of equations? 2x - y = 7 y = 2x + 3
C. no solution
What is the value of n in the equation 1/2(n - 4) - 3 = 3 - (2n + 3)? n= ?
2
Which expression represents the total perimeter of her sandwich, and if x = 1.2, what is the approximate length of the crust?
B. 8x2 + 34; 45.52 centimeters
What is the initial value of the exponential function shown on the graph?
D. 4
What value of x is in the solution set of 2x - 3 > 11 - 5x?
D. 4
Consider the equation 3p - 7 + p = 13. What is the resulting equation after the first step in the solution?
D. 4p - 7 = 13
The roots of the function f(x) = x2 - 2x - 3 are shown. What is the missing number? x = -1 and x =
3
The graph of which function has an axis of symmetry at x = 3?
D.
What is the value of the discriminant for the quadratic equation 0 = x + 2 + x2? Discriminant = b2 - 4ac
B. -7
Which function has zeros at x = 10 and x = 2?
NOT D. f(x) = 5x2 + 60x + 100
The first few steps in solving the quadratic equation 8x2 + 80x = −5 by completing the square are shown. 8x2 + 80x = −5 8(x2 + 10x) = −5 8(x2 + 10x + 25) = −5 + ______ Which number is missing in the last step?
D. 200
Solve the inequality. 2(4x - 3) ≥ -3(3x) + 5x?
A. x ≥ 0.5
Which equation represents y, the profit earned by the concession stand for x hot dogs sold?
C. y = 2x - 48
Which shows the four-term polynomial and factored form of x2 + 6x - 27?
C. x2 + 9x - 3x - 27 = (x + 9)(x - 3)
Marta is solving the equation S = 2Πrh + 2Πr2 for h. Which should be the result?
A. S/2pieR- r = h
Which function best models the data?
NOT B, C
What is the solution to the system of equations?
(7, 13/3)
The graph shows that f(x) = 3x is translated horizontally and vertically to create the function g(x) = 3x - h + k. What is the value of h?
2
The numbers that should be placed in the boxes, from left to right, are _____.
6 && 3
Which are the solutions of the quadratic equation? x2 = -5x - 3
B.
Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 4 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W -0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
B. 160 minutes
Which unit tiles are needed to complete the factorization?
B. 2 positive unit tiles
For which year would this model most likely be sufficient to make a prediction of the population?
B. 2005
To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied? First equation: 4x − 3y = 34 Second equation: 3x + 2y = 17
A. The first equation should be multiplied by 2 and the second equation by 3.
Based on the graph of the regression model, which is true?
A. The number of weeds is decreasing by a multiplicative rate.
The system of equations is solved using the linear combination method. What does 0 = −12 mean regarding the solution to the system?
A. There are no solutions to the system because the equations represent parallel lines.
How does the word count of an essay relate to its score in the contest?
A. Word count tends to decrease as the score decreases.
The graph of f(x) = 6(0.25)x and its reflection across the y-axis, g(x), are shown. What is the domain of g(x)?
A. all real numbers
Which simplified expression represents the area of the parallelogram?
B. 2x3 - 6x2 - 14x + 24 square centimeters
Fuji apples cost $3.00 per pound, and Golden Delicious apples cost $2.00 per pound. A childcare center purchases 30 pounds of a combination of the two types of apples for a total of $80. Which value could replace x in the table?
B. 3(30 - g)
Which describes all of the values for which the graph is positive and decreasing?
A. all real values of x where x < −1
What are the domain, range, and asymptote of h(x) = (1.4)x + 5?
A. domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
The table represents the function f(x). Which function of t has the same slope and y-intercept as f(x)?
A. f(t) = 2/3t + 4
Which function of t has the same slope and y-intercept as f(x)?
A. f(t) =2/3 t + 4
Which exponential function has an initial value of 2?
A. f(x) = 2(3x)
The graph shows the function f(x) = |x - h| + k. What is the value of k?
A. k = -2.5
Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x + 3)2 + 4?
A. left 3, up 4
Which describes the translation of f(x) to g(x)?
A. translation of four units up
A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?
A. y = -4x + 5
The population of a town grows exponentially. After 1 year, the population is 34,560. After 2 years, the population is 37,325. Which equation can be used to predict, y, the number of people living in the town after x years? (Round population values to the nearest whole number.)
A. y = 32,000(1.08)x
Line GH passes through points (2, 5) and (6, 9). Which equation represents line GH?
A. y = x + 3
Given the function f(x) = −5x2 − x + 20, find f(3).
A. −28
The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis. Which is an equivalent equation solved for the slope, m?
B.
Which graph shows exponential growth?
B.
Which number line represents the solution set for the inequality -1/2x ≥ 4?
B.
Which number line represents the solutions to |x - 5| = 1?
B.
Which table represents exponential growth?
B.
What is the solution to the system of equations? y = 2/3x + 3 x = -2
B. ( -2, 5/3)
What is the solution to the system of equations? y = -3x - 2 5x + 2y = 15
B. (-19, 55)
What is the solution to this system of linear equations? 12q + 3r = 15 -4q - 4r = -44
B. (-2, 13)
Over which interval is the graph of the parent absolute value function decreasing?
B. (-∞, 0)
What is the solution to this system of linear equations? 7x - 2y = -6 8x + y = 3
B. (0, 3)
What is the y-intercept of the quadratic function f(x) = (x - 6)(x - 2)?
B. (0,12)
Which is the best approximate solution of the system of linear equations y = 1.5x - 1 and y = 1?
B. (1.33, 1)
The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?
B. (3, -2)
The step function f(x) is graphed. What is the value of f(−1)?
B. -1
A quadratic equation has exactly one real number solution. Which is the value of its discriminant?
B. 0
Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. The table shows the amount of each solution. What is the value of x, the concentration of the unknown ethanol solution?
B. 0.04
Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment. Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?
B. 0.15(40) + 0.6(x - 40) = 0.25(x)
The system of equations below has no solution. Which equation could represent a linear combination of the system?
B. 0=26
Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?
B. 1/4 cup
Jeremy rides a Ferris wheel. The graph shows h, Jeremy's height above the ground at any time during the ride. Which inequality represents the heights shown on the graph?
B. 10 ≤ h ≤ 50
Mr. Ishimoto ordered x new math books and y new workbooks for his class. The total weight of the box of books cannot be more than 50 pounds. If each math book weighs 3.2 pounds and each workbook weighs 0.8 pounds, which inequality represents the maximum number of each type of book that can be shipped in a single box?
B. 3.2x + 0.8y ≤ 50
It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
B. 5/8 + 5r = 1
Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour. Which equation can be used to find t, the time it takes for Milla and Luka to meet?
B. 5t + 4t = 3
Which equation is true?
B. 9x2 - 25 = (3x - 5)(3x + 5)
Which change can be made to correct the chart?
B. The expression 6x should be 6x2.
Which statement about the function is true?
B. The function is negative for all real values of x where -6 < x < -2.
Which best describes the graph of the function f(x) = 4(1.5)x?
B. The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test?
B. The test contains 10 three-point questions and 14 five-point questions.
What are the domain, range, and asymptote of h(x) = 6x - 4?
B. domain: {x | x is a real number}; range: {y | y > -4}; asymptote: y = -4
The graph of which function is decreasing over the interval (-4, ∞)?
B. f(x) = -(x + 4)2 + 4
Which exponential function is represented by the graph?
B. f(x) = 1/2(2)x
Which quadratic function is represented by the table?
B. f(x) = 3x2 - 2x + 5
Which best explains or justifies Step 2?
B. factoring the binomial
The graph of g(x) is the result of translating the graph of f(x) = (1/2) three units to the left. What is the equation of g(x)?
B. g(x) = (1/2)x+3
Which function represents a reflection of f(x) = 5(0.8)x across the x-axis?
B. g(x) = -5(0.8)x
The graph shows the function f(x) = |x - h| + k. What is the value of h?
B. h = -1.5
What is the correlation between age and weight as shown in the table?
B. positive
y + 3 = -y + 9
B. y = 3
Which linear inequality is represented by the graph?
B. y > 3x + 2
Which linear inequality is represented by the graph?
B. y ≤ 1/3x - 4
Which linear inequality is represented by the graph?
B. y ≥ 1/3x − 1
What is the range of f(x)?
B. { f(x)| -∞ < f(x) ≤ 4}
Brenton's weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)?
B. {h| 0 ≤ h ≤ 60}
To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?
B. |x - 645| = 20; maximum guess: 665 beans
What is the value of x when h(x) = −3?
B. −1
Sanjay begins to correctly graph the function f(x) = (x + 1)2 - 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay's?
C.
The piecewise function f(x) has opposite expressions. f(x) = Which is the graph of f(x)?
C.
What are the solution(s) to the quadratic equation 50 - x2 = 0?
C.
What are the zeros of the quadratic function f(x) = 8x2 - 16x - 15?
C.
Which are the solutions of the quadratic equation? x2 = 7x + 4
C.
Which function represents g(x), a reflection of f(x) =1/2 (3)x across the y-axis?
C.
Which graph represents a function with a growth factor of 5?
C.
Which graph represents a quadratic function with a vertex at (0, 0)?
C.
Which graph represents the compound inequality? n < -2 or n ≥ 4
C.
Which graph represents the function f(x) = |x| - 4?
C.
Which graph represents the function h(x) = |x| + 0.5?
C.
Which graph shows a negative correlation?
C.
Which is the graph of y = ⌊x⌋ - 2?
C.
Which number line represents the solution set for the inequality 2x - 6 ≥ 6(x - 2) + 8?
C.
Which shows the graph of the solution set of 2x + y < 4?
C.
Which shows the graph of the solution set of y < 1/3 x - 2?
C.
What is the best approximation for the solution to this system of equations?
C. (-2.2, -3)
What is the vertex of the graph of f(x) = |x + 5| - 6?
C. (-5, -6)
Which will result in a difference of squares?
C. (-7x + 4)(-7x - 4)
What is the solution to the system of linear equations?
C. (0, 2)
What is the y-intercept of the quadratic function f(x) = (x - 8)(x + 3)?
C. (0,-24)
Which product should Tomas choose?
C. (2x + 1)(4x2 - 2x + 1)
Factor -7x3 + 21x2 + 3x - 9 by grouping. What is the resulting expression?
C. (3 - 7x2)(x - 3)
What is the solution to this system of linear equations? 2x + 3y = 3 7x - 3y = 24
C. (3, -1)
The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor?
C. (y − 8)
Which two terms are missing from the diagram?
C. -3x and -6x
If Alina wrote the last term as 3y3, which must be the first term of her polynomial in standard form?
C. -8x2y
When she subtracts 4 from both sides, 1/2x = -1/2x results. What is the value of x?
C. 0
Giuliana has 22 quarters and dollar coins worth a total of $10.75. Which equation can be used to find d, the number of dollar coins Giuliana has?
C. 0.25(22 - d) + d = 10.75
What is the multiplicative rate of change of the function?
C. 0.5
Which r-value represents the most moderate correlation?
C. 0.56
What is f(−2.2)?
C. 1
Which steps should be used to graph the equation y - 4 =1/3 (x + 2)?
C. 1. Plot the point (-2,4). 2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.
Mr. Brown is creating examples of systems of equations. He wants to have a system of equations with infinite solutions that includes the equation 5x + 2y = 8. Which equation could Mr. Brown use to complete the system so that it has infinite solutions?
C. 1.25x +0.5y = 2
What is the initial value of the exponential function represented by the table?
C. 1/2
Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used. What is the value of x?
C. 10
Four cups of a salad blend containing 40% spinach is mixed with an unknown amount of a salad blend containing 55% spinach. The resulting salad contains 50% spinach. How many cups of salad are in the resulting mixture?
C. 12
Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown. q + d = 19 0.25q + 0.1d = 4 How many quarters does she have?
C. 14
What number should be added to both sides of the equation to complete the square? x2 + 8x = 4
C. 16
Sienna is solving the quadratic equation by completing the square. What is the value of A?
C. 3
Which equation is represented by the model?
C. 3x2 - 4x + 1 = (3x - 1)(x - 1)
For what values of x is x2 + 2x = 24 true?
C. 4 and -6
Which unit tiles are needed to complete the factorization?
C. 4 negative unit tiles
Eduardo's average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?
C. 40(1.25 - t)
Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum distances that the dog may be from the house can be found using the equation |x - 500| = 8. What are the minimum and maximum distances that Morgan's dog may be from the house?
C. 492 meters and 508 meters
What is the growth factor of the exponential function represented by the table?
C. 5
What is the rate of change for the interval between 0 and 2 for the quadratic equation as f(x) = 2x2 + x - 3 represented in the table?
C. 5
How could Brent use a rectangle to model the factors of x2 - 7x + 6?
C. He could draw a diagram of a rectangle with dimensions x - 1 and x - 6 and then show the area is equivalent to the sum of x2, -x, -6x, and 6.
The number of grams of calorie-free sodium in a restaurant meal is compared to the total number of calories in the meal. The correlation coefficient relating the two variables is 0.74. Which best describes the strength of the correlation, and what is true about the causation between the variables?
C. It is a strong positive correlation,and it is not likely causal.
Misha found that the equation -|2x - 10| - 1 = 2 had two possible solutions: x = 3.5 and x = -6.5. Which explains whether or not her solutions are correct?
C. She is not correct, because there are no solutions.
Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below. x - y = 7 3x - 2y = 8 Step 1: x = y + 7 Step 2: 3(y + 7) - 2y = 8 Step 3: 3y + 7 - 2y = 8 Step 4: y + 7 = 8 Step 5: y = 1 In which step did Ernesto make the first error?
C. Step 3
Tran is solving the quadratic equation 2x2 - 4x - 3 = 0 by completing the square. His first four steps are shown in the table. In which step did Tran first make an error?
C. Step 3
To eliminate the x-terms and solve for y in the fewest steps, by which constants should the equations be multiplied? First equation: 6x − 5y = 17 Second equation: 7x + 3y = 11
C. The first equation should be multiplied by 7 and the second equation by −6.
Which statement describes the graph of the system of equations below? 1.5x + 0.2y = 2.68 1.6x + 0.3y = 2.98
C. The lines intersect at (1.6,1.4).
Which best explains why the expression ______ cannot be rewritten as _____ during the next step?
C. The square root of terms separated by addition and subtraction cannot be calculated individually.
Which statement is true about the equations -3x + 4y = 12 and 1/4x -1/3 y = 1?
C. The system of the equations has no solution; the two lines are parallel.
For all functions of the form f(x) = ax2 + bx + c, which is true when b = 0?
C. The y-intercept will always be the vertex.
What is the solution to the linear equation? d - 10 - 2d + 7 = 8 + d - 10 - 3d
C. d = 1
Which exponential function is represented by the graph?
C. f(x) = 3(2x)
Which linear inequality is represented by the graph?
C. y > 2x + 1
Atraeus is solving the quadratic equation by completing the square. 7x2 - 14x + 6 = 0 7x2 - 14x = -6 A(x2 - 2x) = -6 What is the value of A?
C. 7
Which is most likely true of the data set represented by the regression model on the graph?
C. Each point in the data set is near the regression line.
Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 = 3x2 - 7x + 4 has. Which best describes the discriminant and the number of zeros?
NOT D. The equation has no zeros because the discriminant is not a perfect square.
What is the first step in solving the quadratic equation x2 - 40 = 0?
NOT D. subtracting 40 from both sides of the equation
Which is a solution to the equation? (x −2)(x + 5) = 18
NOT D. x = −2
Use the chart to multiply the binomial by the trinomial. What is the product?
NOT D. y3 + 6y2 + 27
Which statement is true about the graphs of the two lines y=-8x - 5/4 and y= 1/8x + 4/5?
The lines are perpendicular to each other because -8 and 1/8 are opposite reciprocals of each other.
The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone. Which are equivalent equations? Check all that apply.
1. 3.
Which value of m will create a system of parallel lines with no solution? y = mx - 6 8x - 4y = 12
M=2
What are the values of a, b, and c in the quadratic equation -2x2 + 4x - 3 = 0?
NOT A, C
What is the discriminant of the quadratic equation 0 = 2x2 + 3x - 5?
NOT B. -31
What is the correlation coefficient for the data in the table?
NOT C. 0.27
Which expression is equivalent to 10x2y + 25x2?
NOT C. 10xy(x + 15y)
What are the x-intercepts of the graph of the function f(x) = x2 + 4x - 12?
NOT D. (0, -12), (-6, 0), (2, 0)
Over which interval is the graph of f(x) = -x2 + 3x + 8 increasing?
NOT D. (10.25, ∞)
Keshawn is asked to compare and contrast the domain and range for the two functions. f(x) = 5x g(x) = 5x Which statements could he include in his explanation? Check all that apply.
The domain of both functions is all real numbers. The range of g(x) is y > 0
Which polynomials, given in square inches, could represent the area of a square with whole number side lengths if x is a whole number greater than 2? Remember, the formula for the area of a square is A = s2. Check all that apply.
x2 − 4x + 4 x2 + 10x + 25
Spinning a 4-section spinner twice can be described as which type of event?
A. It is an independent event. The outcome of the second spin is unaffected by the outcome of the first spin.
What are the values of a, b, and c in the quadratic equation 0 = 1/2x2 - 3x - 2?
B.
Which graph represents the compound inequality? h ≥ -5 and h < 2
B.
Which graph shows data whose r-value is most likely closest to 1?
B.
What is the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x)?
C. 2
When compared with the independent variable, how many of the remaining three columns represent a linear relationship?
C. 2
Line AB contains points A(4, 5) and B(9, 7). What is the slope of AB?
C. 2/5
Using the distributive property, Marta multiplied the binomial (2x + 3) by the trinomial (x2 + x - 2) and got the expression below. (2x)(x2) + (2x)(x) + (2x)(-2) + (3)(x2) + (3)(x) + (3)(-2) Which is the simplified product?
C. 2x3 + 5x2 - x - 6
The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4 → 10x − 5y = −20 3x + 5y = 59 → 3x + 5y = 59 13x = 39 Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
D. 13x = 39
What is the product? 2x(x - 4)
D. 2x2 - 8x
Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?
D. It is nonlinear because linear functions increase or decrease at the same rate.
The graph represents the parking fees at a mall parking lot. What does the point (1, 2) represent?
D. Parking costs $2 per hour for the first hour only.
A box contains different-colored marbles. If P(blue) = 1/4 , P(green) =1/4 , and P(blue and green) =1/12 , which statement is true?
D. The events are dependent because P(blue) P(green) P(blue and green).
Triangle ABC has vertices at A(-2, 3), B(-3, -6), and C(2, -1). Is triangle ABC a right triangle? If so, which angle is the right angle?
D. Yes, the right angle is angle C.
Which function has a vertex at the origin?
D. f(x) = -x2
Solve for k. 8k + 2m = 3m + k
D. k = m/7
What is the slope of a line that is perpendicular to the line y = 1?
D. undefined
Which input value produces the same output value for the two functions?
D. x = 1
The area, a, of an ellipse can be determined using the formula a = πxy, where x and y are half the lengths of the largest and smallest diameters of the ellipse. Which is an equivalent equation solved for y?
D. y = a ÷ (πx)
What is the range of f(x)?
D. {y | −5 ≤ y ≤ −1}
Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply. y = -2x + 4 6x + 3y = ?
-12 -4 0 4
Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Check all that apply.
-6x + 15 < 10 - 5x 4th ONE
According to the line of best fit, about how many words would a person remember if he or she is distracted by 7 text messages?
5 words
Which number line represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x?
A.
What value of x is in the solution set of 3(x - 4) ≥ 5x + 2?
A. -10
What number should be added to both sides of the equation to complete the square? x2 + 3x = 6
B
Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping?
B. x2(x + 4) + 5(x + 4)
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3?
B. y - 2 =1/3 (x - 3)
A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
B. y = 8x - 7
Which is the range of the function f(x) =1/7(9)x?
C. all real numbers greater than 0
What are the domain, range, and asymptote of h(x) = 2x + 4?
C. domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = 0
A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf's height in feet as a function of time, in seconds, after leaving the branch?
D.
Which values of m and b will create a system of equations with no solution? Check all that apply. y = mx + b y = -2x + 3/2
m = -2 and b = -1/3 m = -2 and b = -2/3
2(4 + 2x) ≥ 5x + 5?
x ≤ 3
Which linear inequality is represented by the graph?
y ≤ 1/2 x + 3
Which linear inequality is represented by the graph?
y ≤ 1/2x +1/5
What is the input value for which the statement f(x) = g(x) is true ______?
1.5
What is the product of (3a + 2)(4a2 - 2a + 9)?
12a3 + 2a2 + 23a + 18
Sari is factoring the polynomial 2x2 + 5x + 3. What is the missing number in her factorization? 2x2 + 5x + 3
3
What number fills in the blank to complete the factorization of 3x + 24? ____(x + 8)
3
What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x + 5)2 + 3?
3
What is the missing number that will complete the factorization? a2 + 8a + 12 = (a + 2)(a +___ )
6
Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x - 1 into the quadratic formula below?
A
Over what interval is the graph of f(x) = -(x + 8)2 - 1 decreasing?
A.
Which shows the correct substitution of the values a, b, and c from the equation 0 = - 3x2 - 2x + 6 into the quadratic formula?
A.
Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer?
A. x2 + 8x - 308 = 0
The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?
A. x2 + x = 42
Which function has a range of {y|y ≤ 5}?
B. f(x) = -(x - 4)2 + 5
Which algebraic expression is a polynomial with a degree of 4?
C. 9x4 - x3 - x/5
The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?
C. The range changes from {y | y > 0} to {y | y > 2}.
y + 6 = -3y + 26
C. y = 5
What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?
D. -1
What is the value of the discriminant for the quadratic equation -3 = -x2 + 2x? Discriminant = b2 - 4ac
D. 16
Which are the solutions of x2 = -7x - 8?
NOT A.
Factor -8x3 - 2x2 - 12x - 3 by grouping. What is the resulting expression?
NOT A. (2x2 - 3)(4x + 1)
What is the positive solution to the equation 0 = -x2 + 2x + 1?
NOT B.
What is the value of x in the equation 2(x - 3) + 9 = 3(x + 1) + x?
X=0
Solve for w. 5w + 9z = 2z + 3w
w =-7/2z
How many solutions does this linear system have? y = 2x - 5 -8x - 4y = -20
B. one solution: (2.5, 0)
How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)-x related to each other?
B. g(x) is the reflection of f(x) over the y-axis.
What is the side length, in inches, of the pet shop sign?
B. 4x - 5
Which input value produces the same output value for the two functions on the graph?
C. x = 1
What are the possible steps involved in solving the equation shown? Check all that apply.
Distribute 1.2 to 6.3 and -7x . Combine 3.5 and 7.56. Subtract 11.06 from both sides.
Which is a zero of the quadratic function f(x) = 9x2 - 54x - 19?
C.
What is the solution to the system of equations? y = 1/3x - 10 2x + y = 4
C. (6, -8)
What is the product? (2x - 1)(x + 4)
C. 2x2 + 7x - 4
What are the solution(s) of the quadratic equation 98 - x2 = 0?
NOT B.
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x + 6y = 7.50 10x + 5y = 8.75 What is the cost of one apple?
0.5
The function f(x) = 1/6(2/5)X is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
A.
The graph of f(x) = x2 is translated to form g(x) = (x - 5)2 + 1.
A.
What are the solutions to the quadratic equation (5y + 6)2 = 24?
A.
What is the factored form of x2 - x - 2?
A. (x - 2)(x + 1)
Melinda and Paul shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paul shoveled for 25 minutes to complete 345 square feet of driveway. 30x + 30y = 450 20x + 25y = 345 How much more can Paul shovel in 1 minute than Melinda?
A. 3 square feet per minute
What is the other factor of 6x2 - 7x + 2?
A. 3x - 2
What is the fully factored form of 32a3 + 12a2?
A. 4a2(8a + 3)
Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?
B. 18 minutes
The International Business Club starts the school year with $250.50 in their account. They spend $35 each month on activities. The Future Agricultural Leaders Club starts with $300 and spends $45.25 each month. Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
B. 250.5 - 35m = 300 - 45.25m
Which algebraic expression is a polynomial with a degree of 5?
B. 2xy4 + 4x2y3 - 6x3y2 - 7x4
Scientists studied a deer population for 10 years. They generated the function f(x) = 248(1.15)x to approximate the number of deer in the population x years after beginning the study. About how many deer are in the population 3 years after beginning the study?
B. 377
What are the slope and y-intercept of the linear function graphed to the left?
B. slope: -1/2; y-intercept: 1
What are the slope and y-intercept of the linear function graphed to the left?
B. slope:-1/2 ; y-intercept: 1
At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?
B. x + y > 12
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
B. x = -2
What are the solutions to the equation?
B. x = -6, 1
Solve the equation. −10x + 1 + 7x = 37
B. x = −12
Which is a correct first step in solving 5 - 2x < 8x - 3?
C. 5 < 10x - 3
If the profit is the difference between the revenue and the cost, what expression represents the profit?
C. 5x - 260
Marta's mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online. About how many people had viewed the video once it had been online for 20 days?
C. 6,271
Zohar is using scissors to cut a rectangle with a length of 5x - 2 and a width of 3x + 1 out of a larger piece of paper. The perimeter of the rectangle is 2(5x - 2) + 2(3x + 1). If x = 4 centimeters, what is the total distance Zohar needs to cut with the scissors?
C. 62 centimeters
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
C. y - 1 = 1/2(x -5)
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
C. y - 1 =1/2 (x -5)
Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?
C. y - 7 = 4(x - 1)
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
C. y = x + 2
Which word describes the slope of the line?
C. zero
What is the range of the function f(x) = 3x2 + 6x - 8?
C. {y|y ≥ -11}
The graph represents y = ⌈x⌉ + 1. What is f(-2.75)?
D. -1
What is a correct first step in solving the inequality -4(3 - 5x)≥ -6x + 9?
D. -12 + 20x ≥ -6x + 9
What value of x is in the solution set of 4x - 12 ≤ 16 + 8x?
D. -7
Dan bought x pounds of potatoes for $0.85 per pound and y pounds of grapes for $1.29 per pound. The total cost was less than $5. Which inequality represents his purchase?
D. 0.85x + 1.29y < 5
Which number can each term of the equation be multiplied by to eliminate the decimals before solving? 5.6j - 0.12 = 4 + 1.1j
D. 100
Consider the exponential function f(x) = 1/5 (15x). What is the value of the growth factor of the function?
D. 15
What is the factored form of x2 − 4x − 5?
D. (x − 5)(x + 1)
What is the range of f(x) = (3/4)X - 4?
A. {y | y > -4}
Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4?
B. y - 1/3 = 3/4(x - 4)
What does the graph of the regression model show?
A. The height of the surface decreases from the center out to the sides of the road.
Which shows the graph of the solution set of 3y - 2x > -18?
D.
What is the slope of the line?
5/2
What is true about the sum of the two polynomials? 6s2t - 2st2 4s2t - 3st2
B. The sum is a binomial with a degree of 3.
Which polynomial is the correct product?
B. 6y3 + 17y2 + 22y + 15
Which is the graph of the linear inequality 1/2 x - 2y > -6?
D.
Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.
(-3, -2) (-1, -2) (1, -2) (1, 2)
What is the positive solution of x2 - 36 = 5x?
9
2/5 + p =4/5+3/5 p
A. p = 1
Which graph represents a function with an initial value of 1/2?
B.
Which is the graph of f(x) = -(x + 3)(x + 1)?
B.
Which trinomial did she factor?
NOT B, A
Which equation has only one solution?
D. |-6x + 3| = 0
The volume, V, of a rectangular prism is determined using the formula , where l is the length, w is the width, and h is the height of the prism. Carltren solves for w and writes the equivalent equation w = V/Ih. Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches?
4.5 inches
Nina graphs the function y = ⌊x⌋ to learn the properties of the parent floor function. What is the value of y when x =5.7?
5
In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. The inequality 64 < x < 68, where x represents height, can be used to represent the height range. Which is another way of writing the inequality?
A. x > 64 and x < 68
Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
A. y - 4 =2/5 (x + 2)
Which equation represents the graphed function?
A. y = -2x + 3
What is the multiplicative rate of change of the function?
B. 3/4
Which represents a quadratic function?
B. f(x) = -7x2 - x + 2
Which is a zero of the quadratic function f(x) = 16x2 + 32x − 9?
B. x = -2.25
What value of b will cause the system to have an infinite number of solutions? y = 6x - b -3x +1/2 y = -3
B=6
Georgianna wants to use the linear model associated with the data in the table to make a prediction. Which range of time values describes the entire interval over which she would be interpolating?
C.0 to 30 minutes
What is the factored form of the polynomial? x2 − 12x + 27?
NOT A. (x + 4)(x + 3)
Which statement describes the slope of the line of best fit for the data?
NOT A. The temperature decreases by about 0.9° for each 1 degree increase north in latitude.
Which best describes the strength of the model?
NOT A. a weak positive correlation
Which could be the dimensions of the rectangular piece of cloth when it is unfolded? Remember, the area of a rectangle can be determined using the formula A = lw.
NOT A. length = (x + 9) inches and width = (x + 3) inches
What is the square root of m6?
NOT A. m2
Which polynomial is prime?
NOT A. x3 + 3x2 - 2x - 6
Consider the graph of the exponential function in the form of f(x) = a(bx). The value of a in the function is
3
The area of a square can be represented by the expression x10. The side of the square can be written in the form xn. What is the value of n?
5
The function f(x) = 2 • 5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function?
5
Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Check all that apply.
A B C D E
Which shows the correct substitution of the values a, b, and c from the equation 1 = -2x + 3x2 + 1 into the quadratic formula?
A.
Which polynomial is represented by the algebra tiles?
A. 2x2 - 4x - 6
The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product after it has been fully simplified?
A. x3 + 5x2 + 5x - 2
Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
A. y - 4 = 2/5(x + 2)
Which set of numbers is included in the solution set of the compound inequality?
A. {-7, 5, 18, 24, 32}
Which equation best represents the data?
A. y = -1.026x2 + 1016.402x - 162075
What are the solution(s) to the quadratic equation 9x2 = 4?
B.
Using the exponential regression model, which is the best prediction of the wavelength of the key that is 8 above the A above middle C?
B. 49.44
At lunch, Kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. Her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. Which inequality represents x, the number of microwave burritos, and y, the number of peanut butter sandwiches, she can eat each week?
B. 490x + 700y ≤ 4000
Which number line represents the solutions to |-2x| = 4?
C.
What is the slope of a line that is perpendicular to the line y = -1/2x + 5?
D. 2
What is the product? (4y − 3)(2y2 + 3y − 5)
NOT C. 8y3 − 6y2 − 17y + 15
What is the first step in solving the quadratic equation x2 =9/16?
NOT C. Square both sides of the equation.
What are the solutions to x2 + 8x + 7 = 0?
NOT C. x = 1 and x = 7
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?
The slope of the line will be (ZERO).
Fiona wrote the linear equation y = x - 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona's. Which equation could be Henry's?
x - 5/4y = 25/2
Tomas wrote the equation y = 3x + 3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas's equation. Which equation could be Sandra's?
C. -6x + 2y = 3/2
Which is most likely the correlation coefficient for the set of data shown?
C. 0.19
What is the value of h(3)?
C. 1
Which table represents a linear function?
C. 1 / -3 2 / -5 3 / -7 4 / -9
For the polynomial -2m2n3 + 2m?n3 + 7n2 - 6m4 to be a binomial with a degree of 4 after it has been fully simplified, which must be the missing exponent on the m-term?
C. 2
What is the initial value of the exponential function shown on the graph?
C. 2
According to the line of best fit, about how many words will Jean have typed when she completes 60 minutes of typing?
C. 3,000
Which equation represents the graphed function?
C. 3/2x - 3 = y
What is the greatest common factor of 12a and 9a2?
C. 3a
A square has a perimeter of 12x + 52 units. Which expression represents the side length of the square in units?
C. 3x + 13
What is the y-intercept of the function f(x)=4 - 5x?
C. 4
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
D. 12
Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x - 2)2 + 3?
NOT B. left 2, down 3
What are the solutions to the quadratic equation 3(x − 4)2 = 75?
NOT C,B
Which equation results from taking the square root of both sides of (x - 9)2 = 81?
A. x - 9 = ±9
What is the product? (6r − 1)(−8r − 3)
A. −48r2 − 10r + 3
Which step has an incorrect instruction?
A. Step 1
What is the change in the y-values and x-values on the graph?
A. The change in the y-values is 40 and the change in the x-values is 1.
A function g(x) has x-intercepts at (1/2, 0) and (6, 0). Which could be g(x)?
B. g(x) = (x - 6)(2x - 1)
What is the justification for the step taken from line 2 to line 3?
A. the subtraction property of equality
Which shows the graph of the solution set of y > -1/2 x - 3?
B.
Sharon's turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. If Sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?
B. |x - 112| = 4
Which exponential function is represented by the table?
D. f(x) = 0.8(2x)
Which function increases at the fastest rate between x = 0 and x = 8?
NOT A, C
The equation of a linear function in point-slope form is y - y1 = m(x - x1). Harold correctly wrote the equation y = 3(x - 7) using a point and the slope. Which point did Harold use?
C. When Harold wrote his equation, the point he used was (7, 0).
In order for the data in the table to represent a linear function with a rate of change of +5, what must be the value of m?
C. m = 18
What is the solution to this system of linear equations? x + y = 4 x − y = 6
C. (5, −1)
Factor x3 + x2 + x + 1 by grouping. What is the resulting expression?
C. (x2 + 1)(x + 1)
Which is f(5) for the function -2x2 + 2x - 3?
C. -43
Which graph shows the axis of symmetry for the function f(x) = (x - 2)2 + 1?
B.
Which is the graph of f(x)= 4 (1/2)?
B.
The function g(x) = x2 - 10x + 24 is graphed on a coordinate plane. Where will the function cross the x-axis?
C. (4, 0) and (6, 0)
Which model best represents the data?
C. y = 26.9x - 1.3
A number, n, is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of n?
A. 3n - 15 + n = 101
The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool?
A. The height of the water increases 2 inches per minute.
Which statement is true about the graphs of the two lines y=-8x - 5/4 and y=1/8 + 4/5?
A. The lines are perpendicular to each other because -8 and 1/8 are opposite reciprocals of each other.
A data set contains an independent and dependent variable. Which must be true of the data set if a linear function can be used to represent the data?
A. The set must have a constant additive rate of change.
Line CD passes through points C(3, -5) and D(6, 0). What is the equation of line CD in standard form?
B. 5x - 3y = 30
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
B. Aaron's rate for mowing lawns is 0.5 acres per hour.
What is the slope of the line represented by the equation y =4/5 x - 3?
C. 4/5
Which statement is true about the graphs of the two lines y = -4/5 x + 2 and y = -4/5 x -1/2 ?
C. The lines are neither parallel nor perpendicular to each other because -4/5 and -5/4 are not opposite reciprocals of each other.
Working together, Alex and Millie can file all the papers in the file cabinets in 4 hours. It would have taken Alex 6 hours to do the job alone. What is the missing value in the table that represents the part of the papers that Alex would file if Alex and Millie worked together?
B. 4/6
clothing store uses the step function f(x) to recommend jeans sizes as a function of x, a child's height in inches. According to the function, which is the height of a child who should wear size 2 jeans?
B. 42 inches
Which equation has no solution?
B. 5 + 2(3 + 2x) = x + 3(x + 1)
Which is the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day?
B. 72 minutes
What should Lie do next?
B. Factor 3 out of the variable terms.
Johan found that the equation -2|8 - x| - 6 = -12 had two possible solutions: x = 5 and x = -11. Which explains whether his solutions are correct?
B. He is not correct because he made a sign error.
Which is true about the polynomial -8m3 + 11m?
B. It is a binomial with a degree of 3.
Which set of steps will translate f(x) = 6x to g(x) = 6x - 5 - 7?
B. Shift f(x) = 6x five units to the right and seven units down.
In which step did Fiona make an error?
B. Step 2
When she adds 2 to both sides, the equation 4x = 3x results. Which is the best interpretation of this equation?
B. The equation has one solution: x = 0.
Which conclusion about f(x) and g(x) can be drawn from the table?
B. The functions f(x) and g(x) are reflections over the y-axis.
Which statement describes the graph of f(x) = 4x2 + 20x + 25?
B. The graph touches the x-axis at (-2.5, 0).
A square with an area A2 of is enlarged to a square with an area of 25A2. How was the side of the smaller square changed?
B. The side length was multiplied by 5.
Which situation could be represented by the graph?
C. A program at a community college can be completed in no fewer than 8 months, but must be completed in less than 11 months.
Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee. Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?
C. Both gyms charge the same monthly rate and the same membership fee.
Consider the three functions below. Which statement is true?
C. The ranges of f(x) and h(x) are different from the range of g(x).
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years?
C. f(x) = 1,200(0.97)x
Which function could be a stretch of the exponential decay function shown on the graph?
C. f(x) = 2 (1/6)X
Which exponential function is represented by the values in the table?
C. f(x) = 4(1/2)X
Which equation represents an exponential function with an initial value of 500?
C. f(x) = 500(2)x
Which equation represents the function graphed on the coordinate plane?
C. g(x) = |x - 1| + 3
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
C. h < 7 or h > 9
Which is a pair of dependent events?
C. removing a marble from a bag, not putting it back, and then removing a second marble
Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?
C. x + y ≤ 8
Which compound inequality is represented by the graph?
C. x < -2 or x ≥ 4
What is the solution to -4|-2x + 6| = -24?
C. x = 0 or x = 6
Blake knows that one of the solutions to x2 - 6x + 8 = 0 is x = 2. What is the other solution?
C. x = 4
What are the solutions of the quadratic equation (x + 3)2 = 49?
C. x = 4 and x = -10
Two positive integers have a product of 176. One integer is 5 less than the other integer. Which equation can be used to find the value of x, the greater integer?
C. x(x - 5) = 176
Which equation represents a line that passes through (2, -1/2) and has a slope of 3?
C. y +1/2 = 3(x - 2)
Darius is studying the relationship between mathematics and art. He asks friends to each draw a "typical" rectangle. He measures the length and width in centimeters of each rectangle and plots the points on a graph, where x represents the width and y represents the length. The points representing the rectangles are (6.1, 12.0), (5.0, 8.1), (9.1, 15.2), (6.5, 10.2), (7.4, 11.3), and (10.9, 17.5). Which equation could Darius use to determine the length, in centimeters, of a "typical" rectangle for a given width in centimeters?
C. y = 1.518x + 0.995
Which equation has no solution?
C. |5 - 3x| = -8
Using the equation for the line of best fit, what is a good approximation for the value of the function, f(x), when x = 18?
NOT C. 3
Which r-value represents the strongest correlation?
NOT D. 0.79
Assuming that the throw represents projectile motion, what are the missing values in the table?
NOT D. A = 5, B = 0
What number will complete the point-slope equation that models this scenario?
-3,000
A line contains points M(1, 3) and N(5, 0). What is the slope of MN?
-3/4
Manuela solved the equation 3 - 2|0.5x + 1.5| = 2 for one solution. Her work is shown below. The other solution to the equation is
-4
The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring. What is the constant of the quadratic expression in this equation? x2 + x + ____ = 0
-420
What is f(-3) for the function f(a) = -2a2 - 5a + 4?
1
Which best describes the range of the function f(x) = 2/3(6)x after it has been reflected over the x-axis?
B. all real numbers less than 0
4b + 6 = 2 - b + 4
B. b = 0
The ice skating rink charges an hourly fee for skating and $3 to rent skates for the day. Gillian rented skates and skated for 3 hours and was charged $21. Which equation represents the cost, c(x), of ice skating as a function of x, the number of hours of skating?
B. c(x) = 6x + 3
Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph?
C
Which products result in a difference of squares? Check all that apply.
C D F
An office supply store offers banner printing services. The store charges $4 to print each one-foot-long section of a banner that is three feet tall. Which graph represents the cost to print a three-foot-tall banner that is x feet long?
C.
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola's purchase?
C.
On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x + 2| as a solid line?
C.
What is the missing step of her solution?
A. Simplify by combining like terms.
What is the domain of g(x)?
A. all real numbers
Which is the domain of the function f(x) = -5/6(3/5)X?
A. all real numbers
A store offers packing and mailing services to customers. This table is given to customers to help them estimate the cost of shipping a box based on its weight in pounds, and a flat rate of $5 for packing. Which equation represents the shipping cost as a function of x, the weight in pounds?
A. f(x) = 2.25x + 5
Which equation represents an exponential function that passes through the point (2, 36)?
A. f(x) = 4(3)x
A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment?
A. f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0
The graphs of f(x) = 10x and its translation, g(x), are shown. What is the equation of g(x)?
A. g(x) = 10x - 3
The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?
A. g(x) = 3x - 6
What is the solution to the linear equation?
A. p = 1
Which best explains or justifies Step 1?
A. subtraction property of equality
6(x - 1) = 9(x + 2)
A. x = -8
What are the solution(s) to the quadratic equation x2 - 25 = 0?
A. x = 5 and x = -5
How many solutions exist for the given equation? 3x + 13 = 3(x + 6) + 1
A. zero
All points of the step function f(x) are graphed. What is the domain of f(x)?
A. {x| -4 < x ≤ 4}
The graph of the step function g(x) = -⌊x⌋ + 3 is shown. What is the domain of g(x)?
A. {x| x is a real number}
Which equation has no solution?
A. |4x - 2| = -6
A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can't quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has $42.80 in his wallet, which equation represents the amounts of money he may have after he sees Rita?
A. |x - 42.80| = 12
Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle?
B. 12(5x2 + 4x + 2)
What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y?
B. 15x3y
If f(x) = − 5, what is f(8.6)?
B. 4
The graph represents the balance on Harrison's car loan in the months since purchasing the car. Which statement describes the slope of the line?
B. Harrison makes a monthly payment of $250.
Sean began jogging to live a healthier lifestyle. On his first run, he ran one-half mile. He increased his workouts by adding two miles a month to his run. He wrote the equation f(x)= 0.5 + 2x to model his progress. The variable x represents the number of
B. months he runs.
What is the decay factor of the exponential function represented by the table?
A. 1/3
What is the difference of the polynomials? (8r6s3 - 9r5s4 + 3r4s5) - (2r4s5 - 5r3s6 - 4r5s4)
A. 6r6s3 - 4r5s4 + 7r4s5
What is the value of k?
-3
Two events, A and B, are independent of each other. P(A) = 1/6 and P(A and B) =1/8 . What is P(B) written as a decimal? Round to the nearest hundredth, if necessary.
0.75
What is the rate of change of the function shown on the graph? Express your answer in decimal form. Round to the nearest tenth.
2.5
Which of these values could be the slope of the line? Check all that apply.
3 7/4
Dr. Bhatia mixes 2 liters of a 5% saline solution with x liters of a 9% saline solution. The table shows the amount of each solution used. What is the value of x?
6
Four ounces of oregano and 2 ounces of garlic powder are mixed to create a poultry seasoning. Oregano costs $4 per ounce, and garlic powder costs $3 per ounce. The table shows the costs of the ingredients. What is the value of y in the table?
6
An equation has solutions of m = -5 and m = 9. Which could be the equation?
A. (m + 5)(m - 9) = 0
What are the factors of the trinomial?
A. (x + 1) and (x - 4)
What is P(heads, then 2)?
A. 1/12
Hamburgers cost $2.50 and cheeseburgers cost $3.50 at a snack bar. Ben has sold no more than $30 worth of hamburgers and cheeseburgers in the first hour of business. Let x represent the number of hamburgers and y represent the number of cheeseburgers. The inequality 2.50x + 3.50y ≤ 30 represents the food sales in the first hour. If Ben has sold 4 cheeseburgers, what is the maximum value of hamburgers Ben could have sold? Ben could have sold no more than __ hamburgers.
6
A 4% peroxide solution is mixed with a 10% peroxide solution, resulting in 100 L of an 8% solution. The table shows the amount of each solution used in the mixture. What is the value of z in the table?
8
A chef knows that ground beef used for hamburger is safe to eat once it reaches 160 degrees Fahrenheit. For optimized taste and safety, he will not allow a hamburger cooked to a temperature under 160 degrees or over 170 degrees to be served. Which graph represents the conditions under which the chef will not allow the hamburger to be served?
A.
Which are the solutions of x2 = 19x + 1?
B
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
B.
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 1/4(4x - 8y = 12) → x - 2y = 3 2x = 18 What is the solution of the system of equations?
D. (9,3)
The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph?
D. (−2, −9)
In order to be invited to tutoring or extension activities, a student's performance must be at least 20 points higher or lower than an average score. If the average score is 105, which inequality represents p, the scores for students who are eligible for tutoring or extension activities?
D. p ≤ 85 or p ≥ 125
Miriam reduced a square photo by cutting 3 inches from each side so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x - 3)2 = 64, x represents the side measure of the original photo. What were the dimensions of the original photo?
NOT C,B
Which polynomial can be simplified to a difference of squares?
NOT C. 25a2 + 6a - 6a + 36
Which is the graph of f(x) = 5(2)x?
A.
What is the greatest common factor of 24s3, 12s4, and 18s?
D. 6s
Solve x2 = 12x - 15 by completing the square. Which is the solution set of the equation?
NOT C, B
Which function could be represented by the graph on the coordinate plane?
NOT C,B
A six-sided number cube is rolled twice. Which expression can be used to find P(5, then3)?
NOT C.
Gio is solving the quadratic equation by completing the square. 5x2 + 15x - 4 = 0 What should Gio do first?
NOT C.
The theoretical probability of a couple having a baby girl is 1/2 . What is P(girl, girl, girl)?
NOT C.
Which is the approximate slope of the line of best fit for the data?
NOT C.
What factors does Jenna need to model for the sides?
NOT C. (3x - 2) and (x + 2)
Which shows the factored form of x2 - 12x - 45?
NOT C. (x + 3)(x + 15)
If Jasper installs a floor himself, it will take him 7 hours. Working with Yolanda, it will take them 3 hours. If they work together, what is the missing value in the table that represents the part of the floor Jasper will install?
1/7(3)
Consider the graph of the quadratic function. Which interval on the x-axis has a negative rate of change?
NOT C. 0 to 1
Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay - 4y2 - ay - 64. What is the value of a in the polynomial?
16`
Which is most likely the correlation coefficient for the set of data shown?
NOT C. 0.35
What value should Simon write on the line?
2
The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars from two different companies are represented by the system of equations shown, where x is the number of bars purchased and y is the total cost in dollars. Company A: y = 0.75x Company B: y = 10 + 0.50x How many bars would the team need to purchase from each company in order for the total cost to be equal?
40 BARS
Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2 -1/5 x? Check all that apply.
8/5x +2/3 = 1/2 - 1/5x 18x + 20 + 30x = 15 - 6x 24x + 30x = -5
The product of a + 3 and -2a2 + 15a + 6 is -2a3 + xa2 + 51a + 18. What is the value of x?
9
On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x| - 4 as a solid line?
A.
Solve x2 - 8x = 3 by completing the square. Which is the solution set of the equation?
A.
The graph of f(x) = x2 is translated to form g(x) = (x - 2)2 - 3.
A.
Which is the graph of f(x) = 100(0.7)x?
A.
Leona has a bag containing lettered tiles. Which describes dependent events?
A. removing a vowel, not replacing it, and then removing another vowel
Which relationships would most likely be causal? Check all that apply.
A.a negative correlation between the temperature and the amount of snow still on the ground B.a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left
The graph of f(x) = 2x is shown on the grid. The graph of g(x) = ()x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
B.
A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets. Which equation is true?
D. 4r + 3(10 - r) = 37
What is the product? (5r + 2)(3r − 4
NOT C. 15r2 + 14r − 8
On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"?
D. 4x + 8y ≥ 50
The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh a total of 249 ounces. Which value could replace x in the table?
D. 5(45 - h)
Ellen makes and sells bookmarks. She graphs the number of bookmarks sold compared to the total money earned. What is the rate of change for the function graphed to the left?
D. 5/2
Which graph is the result of reflecting f(x) = 1/4(8)x across the y-axis and then across the x-axis?
D.
Which graph represents the compound inequality? -3 < n < 1
D.
Which graph represents the function p(x) = |x - 1|?
D.
Which graph shows data whose r-value is most likely closest to 0?
D.
Which is the graph of f(x) =1/4 (4)x?
D.
Which is the graph of g(x) = ⌈x + 3⌉?
D.
Which shows the correct substitution of the values a, b, and c from the equation -2 = -x + x2 - 4 into the quadratic formula?
D.
Yuto and Lian are at train stations 1,880 kilometers apart. Yuto boards a train heading east at an average speed of 220 kilometers per hour. At the same time, Lian boards a train heading west on a parallel track at an average speed of 250 kilometers per hour. How far has Lian traveled when the two trains pass each other?
D. 1,000 kilometers
What is the ratio of the change in y-values to the change in x-values?
D. 1,200:1
Which number can each term of the equation be multiplied by to eliminate the decimals before solving? -m + 0.02 + 2.1m = -1.45 - 4.81m
D. 100
A collection of 108 coins containing only quarters and nickels is worth $21. Which value could replace q on the chart?
D. 108 - n
Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. At the end of one week, she collected $97.50, selling a total of 24 boxes. The system of equations that models her sales is below. x+ y= 24 3.50x + 5.00y = 97.50 Solve the system of equations. How many 10 oz. boxes were sold?
D. 15
What value of c makes x2 − 12x + c a perfect square trinomial?
D. 36
The variables A, B, and C represent polynomials where A = x2, B = 3x + 2, and C = x - 3. What is AB - C2 in simplest form?
D. 3x3 + x2 + 6x - 9
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation (x - 8)2 = 144, x represents the side measure of the original lawn. What were the dimensions of the original lawn?
NOT A, B
Which best explains or justifies Step 4b?
NOT A,,B
Which statements are true about the linear inequality y > 3/4x - 2? Check all that apply.
The graph of y > 3/4x - 2 is a dashed line. One solution to the inequality is (0, 0). The graph intercepts the y-axis at (0, -2).
A balloon artist creates balloon hats for children at a store's grand opening. The graph shows the number of balloons the artist has remaining, y, after creating x hats. What phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? Check all that apply.
negative slope constant slope decreasing function
Which graph represents a reflection of f(x) = 6(0.5)x across the x-axis?
A.
Which graph represents the function r(x) = |x - 2| - 1
A.
Which is the graph of g(x) = 2x - 1 + 3?
A.
Which is the graph of the function f(x) = x2 + 2x - 6?
A.
Which is the graph of the linear inequality y ≥ −x − 3?
A.
Which number line represents the solutions to |x + 4| = 2?
A.
Which represents the polynomial written in standard form?
A.
Which table shows exponential decay?
A.
What is the solution to this system of linear equations? 2x + y = 1 3x - y = -6
A. (-1, 3)
Which is the approximate solution to the system y = 0.5x + 3.5 and y =3/2 −x + 1/3 shown on the graph?
A. (-2.7, 2.1)
Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 -3x + 5y = 10
A. (0,2)
What is the solution to the system of equations? y = -5x + 3 y = 1
A. (0.4, 1)
y=4x - 10 y=2 What is the solution to the system of equations?
A. (3, 2)
Which will result in a perfect square trinomial?
A. (3x - 5)(3x - 5)
A lotion is made from an oil blend costing $1.50 per ounce and glycerin costing $1.00 per ounce. Four ounces of lotion costs $5.50. Which value could replace x on the table?
A. (4 - g) 1.5
Which product is equivalent to 25x2 - 16?
A. (5x − 4)(5x + 4)
What is the solution to this system of linear equations? x − 3y = −2 x + 3y = 16
A. (7, 3)
The polynomial x3 + 8 is equal to
A. (x + 2)(x2 - 2x + 4).
Which expression is the factorization of x2 + 10x + 21?
A. (x + 3)(x + 7)
The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?
A. (−5, 41)
Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = 2x - 5 2y - 4x = ?
A. -10
The step function f(x) is graphed. What is the value of f(0)?
A. -2
What value of x is in the solution set of -5x - 15 > 10 + 20x?
A. -2
Simplify the expression -2(p + 4)2 - 3 + 5p. What is the simplified expression in standard form?
A. -2p2 - 11p - 35
Which compound inequality is represented by the graph?
A. -3 ≤ x < 1
What value of x is in the solution set of 9(2x + 1) < 9x - 18?
A. -4
Which is f(-3) for the quadratic function graphed?
A. -9
What is the multiplicative rate of change of the function?
A. 1/5
What is the product? -9x(5 - 2x)
A. 18x2 - 45x
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking. Which combination of loaves of bread and batches of muffins could Helena bake?
A. 2 loaves of bread and 4 batches of muffins
Which binomial is a factor of 9x2 - 64?
A. 3x - 8
A political polling agency predicts candidate A will win an election with 54% of the votes. Their poll has a margin of error of 4% both above and below the predicted percentage. Which inequality represents the predicted possible percent of votes, x, for candidate A?
A. 50 ≤ x ≤ 58
A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed. Which describes the meaning of f(x)?
A. A customer earns 1 free night per 10 nights stayed.
Marco has a bag of red, blue, and green tiles. Which set of events would be considered independent?
A. A tile is drawn and replaced, and then a second tile is drawn.
Which is a correct first step in solving the inequality -4(2x - 1) > 5 - 3x?
A. Distribute -4 to get -8x + 4 > 5 - 3x.
Which statement about f(x) and its translation, g(x), is true?
D. The asymptote of g(x) is the asymptote of f(x) shifted six units up.
Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y. 750x + 17y = 141.61 300x + 30y = 75.90 Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina's solution?
D. The cost of natural gas is $0.83 per unit.
What are the domain and range of the function on the graph?
D. The domain includes all real numbers, and the range is y > 0.
Which statement is true?
D. The equation -0.3|3 + 8x| = 0.9 has no solution.
Jillana begins to solve a linear equation that results in a variable expression set equal to the same variable expression. Which is the best interpretation of this solution?
D. The equation has infinite solutions.
To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied? First Equation: 5x − 4y = 28 Second equation: 3x - 9y = 30
D. The first equation should be multiplied by 9 and the second equation by −4.
To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size?
D. c ≤ 4.5 or c ≥ 12
What is the equation of the translated function, g(x), if f(x) = x2?
D. g(x) = (x - 5)2 + 2
Which function represents a reflection of f(x) = 3/8(4)x across the y-axis?
D. g(x) = 3/8(4)-x
The function h(x) is quadratic and h(3) = h(-10) = 0. Which could represent h(x)?
D. h(x) = 2x2 + 14x - 60
y= -6x+2 -12x - 2y = -4 How many solutions does this linear system have?
D. infinite number of solutions
Bao Yu is completing the square to solve the polynomial equation. x2 - x - 3 = 0 What should be her first step?
D. isolating the constant, -3
Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?
D. x + y ≥ 45
8 - 2x = -8x + 14
D. x = 1
What is the domain for the piece of the function represented by f(x) = x + 1?
D. x > 1
Which shows one way to determine the factors of x3 + 11x2 - 3x - 33 by grouping?
D. x2(x + 11) - 3(x + 11)
What is the domain of f(x) = 5x - 7?
D. {x | x is a real number}
What is the domain of the step function f(x) = ⌈2x⌉ - 1?
D. {x| x is a real number}
Which best describes her prediction?
D. extrapolation, because a key that is 12 keys from middle C is outside the data set
What is true about the domain and range of the function?
NOT C. The domain is all real numbers such that -6 ≤ x ≤ -2, and the range is all real numbers greater than or equal to -4.
Which function has only one x-intercept at (−6, 0)?
NOT C. f(x) = (x + 6)(x − 6)
Solve x2 + 14x = −24 by completing the square. What is the solution set of the equation?
NOT C. {−6, −4}
Which graph has a negative rate of change for the interval 0 to 2 on the x-axis?
NOT D
What are the solutions to the quadratic equation x2 - 16 = 0?
NOT D,C
A spinner has three equal sections labeled 1, 2, and 3. It is spun twice. Which expression can be used to determine P(2, then 1)?
NOT D.
Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x = ________ after substituting the values of a, b, and c into the formula. Which is Ramiya's quadratic equation?
NOT D. 0 = 2x2 - 3x + 1
What is the greatest common factor of 4k, 18k4, and 12?
NOT D. 4k
What is the product of (2p + 7)(3p2 + 4p - 3)?
NOT D. 6p3 + 29p2 + 34p - 21
Which term is the perfect square of 3x4?
NOT D. 9x16
Ryan gathered data about the age of the different dogs in his neighborhood and the length of their tails. Which best describes the strength of the correlation, and what is true about the causation between the variables?
NOT D. It is a strong negative correlation, and it is likely causal.
Deirdre is factoring the polynomial x2 + 2x - 24. Which combination can she use to replace the middle term, 2x?
NOT B. -6x and -4x
Which are the solutions of x2 = -13x - 4?
NOT B. 0, -13
For which temperature will the model most accurately predict the time spent cooling?
NOT B. 100
Which is equivalent to (4xy - 3z)2, and what type of special product is it?
NOT B. 16x2y2 + 9z2, a perfect square trinomial
What expression represents the profit, and what is the profit if 240 cell phones are sold?
NOT B. 40x - 30; $9,570
Which statement is true about the quadratic equation 8x2 − 5x + 3 = 0?
NOT B. The constant term is −5.
When the polynomial is written in standard form, what are the values of the leading coefficient and the constant? 5x + 2 - 3x2
NOT B. The leading coefficient is 2, and the constant is 5.
What is true about the completely simplified sum of the polynomials 3x2y2 − 2xy5 and −3x2y2 + 3x4y?
NOT B. The sum is a trinomial with a degree of 6.
Consider a situation in which P(X) = 4/5 and P(Y) = 1/4 . If P(X and Y) is =1/5 , which best describes the events?
NOT B. They are independent because P(X) + P(Y) = P(X and Y).
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
NOT B. a base area of 8y2 square units and height of y2 + 2y + 4 units
Which best describes the strength of a model with an r-value of 0.29?
NOT B. a strong positive correlation`
Which type of model best describes the relationship?
NOT B. exponential, because the r value for the exponential model is closest to 0
Which polynomial was factored?
NOT B. x2 + 2x - 8
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches. Which equation can be used to solve for x, the increase in side length of the square in inches?
NOT B. x2 + 4x - 65 = 0
Which shows one way to determine the factors of 4x3 + x2 - 8x - 2 by grouping?
NOT B. x2(4x - 1) + 2(4x - 1)
In simplest radical form, what are the solutions to the quadratic equation 0 = -3x2 - 4x + 5?
NOT C
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?
NOT C, A
She calculates two regression models. Which is true?
NOT C, B
Which model best represents the data set?
NOT C, B
John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width. Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?
NOT C. 2w(w - 2) = 48
What value of c makes x2 − 24x + c a perfect square trinomial?
NOT C. 48
Use the chart to multiply the binomial by the trinomial. Which polynomial is the correct product?
NOT C. 6y3 + 20y2 + 22y + 15
Which functions are symmetric with respect to the y-axis? Check all that apply.
f(x) = |x| f(x) = |x| + 3 f(x) = |x| + 6
Which functions represent a piece of the function? Check all that apply.
g(x) = −2x + 6, x ≥ 1 g(x) = X/2+ 1, -2 ≤ x < 1 g(x) = −2, x < −2
Which are correct representations of the inequality 6x ≥ 3 + 4(2x - 1)? Check all that apply.
1 ≥ 2x 6x ≥ 3 + 8x - 4 3rd ONE
In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. She writes the equation as F = ma, then realizes that each of her homework problems asks her to solve for acceleration. She rewrites the formula as F/M= a. Using this formula, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms? Express your answer to the nearest tenth.
2.2 m/s2
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is
A. C = K - 273.15
Pablo folds a straw into a triangle with side lengths of 4x2 - 3 inches, 4x2 - 2 inches, and 4x2 - 1 inches. The perimeter of the triangle is 12x2 - 6 inches. If x = 1.5, what was the length of the straw before it was folded?
21
Consider the quadratic function f(y) = 8y2 - 7y + 6. What is the constant of the function?
6
What are the zeros of the quadratic function f(x) = 6x2 + 12x - 7?
A.
Which function represents g(x), a reflection of f(x) = 2/5(10)x across the x-axis?
A.
Which model shows the correct factorization of x2 + 2x - 8?
D
In which step did Mia make an error?
D Step 4
Juan rolls a 6-sided number cube 4 times. Each time, the result is 2. Which best describes the events?
D.
Which is the graph of the linear inequality y < 3x + 1?
D.
Which number line represents the solutions to -2|x| = -6?
D.
Which quadratic function has a leading coefficient of 2 and a constant term of -3?
D.
Which shows the graph of the solution set of y < -4x + 3?
D.
hich table could be used to graph a piece of the function?
D.
The tables represent two linear functions in a system. What is the solution to this system?
D. (-14, -54)
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)?
D. (-6,0)
Which expression is equivalent to 6x2 - 19x - 55?
D. (6x + 11)(x - 5)
Factor 6x4 - 5x2 + 12x2 - 10 by grouping. What is the resulting expression?
D. (6x2 - 5)(x2 + 2)
he tables represent two linear functions in a system. What is the solution to this system?
D. (8, -22)
Which is a factor of x2 + 8x - 48?
D. (x + 12)
Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the number of nickels in the collection?
D. 0.1(175 - n) + 0.05n = 13.30
Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs. x + y = 3,500 x - y = 2,342 Solve the system of equations. How many contemporary titles does Jarred have?
D. 2,921
It took Amir 2 hours to hike 5 miles. On the first part of the hike, Amir averaged 3 miles per hour. For the second part of the hike, the terrain was more difficult so his average speed decreased to 1.5 mile per hour. Which equation can be used to find t, the amount of time Amir spent hiking during the second, more difficult part of the hike?
D. 3(2 - t) + 1.5t = 5
What value of x is in the solution set of 8x - 6 > 12 + 2x?
D. 5
For one photography session, Dexter earns no less than $50, but no more than $100. Which inequality can be used to represent his earnings, e?
D. 50 ≤ e ≤ 100
It takes Dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. He has been making bracelets for longer than 120 minutes. If x represents the number of simple bracelets that he has made and y represents the number of deluxe bracelets he has made, the inequality 9x + 20y > 120 represents the scenario. Which is a possible combination of bracelets that Dimitri may have made?
D. 7 simple bracelets and 3 deluxe bracelets
What is the square root of 64y16?
D. 8y8
What is the missing step in solving the inequality 5 - 8x < 2x + 3?
D. Add 8x to both sides of the inequality.
Casey is deciding which of two landscapers to hire. Each landscaper charges an hourly rate plus a fee for each job. Casey correctly wrote and solved a system of linear equations by substitution. In his work, he substituted an expression for one variable and solved for the other. This resulted in the equation 5 = 20. What can Casey conclude?
D. Both landscapers charge the same hourly rate, but not the same fee per job.
Sharina simplified the expression 3(2x - 6 - x + 1)2 - 2 + 4x. In Step 1 she simplified within the parentheses. In Step 2 she expanded the exponent. Which is a possible next step?
D. Distribute the 3 to each term in the parentheses by multiplying.
Which steps will translate f(x) = 3x to g(x) = 3x + 1 + 4?
D. Shift f(x) = 3x one unit to the left and four units up.
What are the factors of x2 + 3x - 4?
NOT A. (x + 4) and (x - 4)
The expression 40x2 - 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles?
NOT A. 2x2(20 - 32x + 25x2)
What is the product? (x − 3)(2x2 − 5x + 1)
NOT A. 2x3 − x2 + 16x + 3
What value of c makes x2 + 6x + c a perfect square trinomial?
NOT A. 3
What is the completely factored form of the expression 16x2 + 8x + 32?
NOT A. 4(4x2 + 2x + 8)
Which statement is true about the polynomial 5s6t2 + 6st9 - 8s6t2 - 6t7 after it has been fully simplified?
NOT A. It has 3 terms and a degree of 9.
Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5?
NOT A. The difference is a binomial with a degree of 5.
Which statement is true about the factorization of 30x2 + 40xy + 51y2?
NOT A. The factorization of the polynomial is 10(3x2 + 4xy + 5y2).
Dependent events can best be described as
NOT B, A
What are the solutions to the quadratic equation 4x2 = 64?
NOT B, A
What are the values of a, b, and c in the quadratic equation 0 = 5x - 4x2 - 2?
NOT B, A
Which are the solutions of the quadratic equation? x2 = 9x + 6
NOT B, A
What are the solution(s) to the quadratic equation 40 − x2 = 0?
NOT B, C
Which is the graph of a quadratic equation that has a positive discriminant?
NOT B, C
Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0 by completing the square. Her first four steps are shown in the table. In which step did Yvonne first make an error?
NOT B, C
Events A and B are independent. The probability of A occurring is 2/5. The probability of B occurring is 1/4. What is P(A and B)?
NOT B.
Rhett is solving the quadratic equation 0= x2 - 2x - 3 using the quadratic formula. Which shows the correct substitution of the values a, b, and c into the quadratic formula?
NOT B.
What values of b satisfy 3(2b + 3)2 = 36?
NOT B.
Which algebraic expression is a polynomial?
NOT B.
Which best describes how many real number solutions the equation has?
NOT B.
Which is the graph of f(x) = (x - 1)(x + 4)?
NOT B.
Which model represents the factors of x2 + 9x + 8?
NOT B.
What is the x-intercept of the graph of the function f(x) = x2 − 16x + 64?
NOT B. (0, 8)
Which expression is equivalent to 36x2 − 25?
NOT B. (18x)2 − (5)2
Which shows the factored form of x2 - 12x - 45?
NOT B. (x - 3)(x - 15)
Which is the factorization of 8x2 + 13x - 6?
NOT B. (x - 6)(8x + 1)
Factor x3 - 4x2 + 7x - 28 by grouping. What is the resulting expression?
NOT B. (x2 + 4)(x - 7)
Which r-value represents the strongest negative correlation?
NOT B. -0.22
Over which interval on the x-axis is there a negative rate of change in the function?
NOT B. -1.5 to 0.5
What is the value of the discriminant for the quadratic equation 0 = 2x2 + x - 3? Discriminant = b2 - 4ac
NOT B. -23
The cost of a single ticket depends on the number of tickets, t, purchased in a group, as represented by the function C(t). What is the total cost for 20 tickets?
c. $290.00
Which linear inequality is represented by the graph?
y > 2/3x + 3
The table shows the number of grapes eaten over several minutes. What is the rate of change for the function on the table?
A. 15 grapes eaten per minute
What is the rate of change for the function on the table?
A. 15 grapes eaten per minute
Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit?
A. 5n - 300 = 1,500
The final cost of a sale item is determined by multiplying the price on the tag by 75%. Which best describes the function that represents the situation?
A. It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.
Which equation represents the shipping cost as a function of x, the weight in pounds?
A. f(x) = 2.25x + 5
The point-slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y - 1 = (x - 12). What is the standard form of the equation for this line?
A. x - 4y = 8
What is the slope of a line that is perpendicular to the line y = 8x + 5?
B. -1/8
What is the slope of a line that is parallel to the line y = -1/5?
B. 0
The Apache Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?
B. 1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
B. y = -1/3x + 5
Which statement is true about the graphs of the two lines y = -6 and x = 1/6?`
D. The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = 1/6 is a vertical line with a slope that is undefined.
The equation 9(u - 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u - 2) equals the number of hours sledding down the hill. Which is the value of u?
D. u = 2.5
Which input value produces the same output value for the two functions on the graph?
D. x = 3
Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable.
A. k - 2 = 1/9(t - 18)
The table represents the profit earned by a concession stand for each hot dog sold. Which equation represents y, the profit earned by the concession stand for x hot dogs sold?
C. y = 2x - 48
Which equation represents a line that passes through (-9, -3) and has a slope of -6?
D. y + 3 = -6(x + 9)
The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -2/3x + 6. What is the point-slope form of the equation for this line?
D. y - 8 = -2/3(x + 3)
What is the slope-intercept form of the equation of the line that passes through the point (-6, 1) and is perpendicular to the graph of 2x + 3y = -5?
D. y = 3/2x + 10
Four lines are drawn on a coordinate plane to form trapezoid WXYZ. Which statements are true about the lines? Select all that apply.
Line WZ has the same slope as line XY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line WZ. Line XY has a greater y-intercept than line XW.
