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WorksheetsAlgebra 1 Benchmark
Total questions: 160
Worksheet time: 8hrs 4mins
What is the slope of the line represented by 5x - 12y = 24?
-2
24/5
-12
5/12
What is the domain of f(x)=9-x2?
f(x) ≥ 9
All real numbers
-3 ≤ x ≤ 3
x ≤ 9
What is the range?
{x| x= -2, 2, 4}
{x| -2 ≤ x ≤ 4}
{y| -3 ≤ x ≤ 4}
{y|y= -3, 0, 4}
A plane can carry a maximum cargo weight of 160,000 pounds. A company uses one of these planes to ship 2,000-pound containers. The total cargo weight is a function of the number of containers in the plane. What is the greatest value in the domain for this situation?
162,000
320,000,000
80
158,000
The student council sent its members on four field trips during the school year. The number of buses needed to transport the members on each trip is a function of the number of members who went on each trip. This function consists of only the ordered pairs (52,3), (72,4), (86,5), and (105,6). What is the domain for this situation?
{52, 105}
{3, 4, 5, 6}
{52, 72, 86, 105}
{3, 4, 5, 6, 52, 72, 86, 105}
All real numbers
All real numbers greater than or equal to -8
All real numbers greater than or equal to -7
All real numbers greater than or equal to 0
Which statement is true?
The range is the set of all real numbers less than 0.
The domain is the set of all real numbers greater than -4.
The domain is the set of all real numbers less than -4.
The range is the set of all real numbers greater than 0.
The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function c = 34.95u + 6.25, where u is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the domain of the function for this situation?
0 < u ≤ 12
0 < c ≤ 425.65
{8, 9, 10, 11, 12}
{285.85, 320.80, 355.75, 390.70, 425.65}
What is the range of this situation?
All real numbers greater than or equal to 0 and less than or equal to 9
All real numbers greater than or equal to 0 and less than or equal to 28
All real numbers less than or equal to 28
All real numbers less than or equal to 9
Which graph represents a function with a domain of all real numbers greater than or equal to -7 and less than 2?
A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 20x + 4. What is the range of the function for this situation?
{0, 1, 2, 3, 4, 5, 6}
{4, 24, 44, 64, 86, 104, 124}
{0, 2, 4, 6}
{4, 44, 84, 124}
x ≥ 0
y ≥ 250,000
0 ≤ x ≤ 110
250,000 ≤ y ≤ 1,000,000
-9 < x ≤ 2
-9 ≤ x < 2
-6 < f(x) ≤ 3
-6 ≤ f(x) < 3
Which graph best represents a function with a range of all real numbers greater than or equal to -6?
Which table shows the same rate of change of y with respect to x as y = 4 - ⅝x?
The graph of the function is shown. What is the slope of the function?
-1/3
-3
1/3
3
What is the slope of a line passing through (9,2) and (-9, -6)?
9/4
-4/9
4/9
-9/4
Which of the following linear functions will have a rate of change of 2/3?
A function whose graph is a line that contains (6,10) and (10, 12)
A function whose equation is 3x - 2y = 12
A function whose equation is 2x - 3y = 9
A function whose graph has an x-intercept of (3,0) and a y-intercept of (0,2)
Look at the lines graphed. Which line appears to have a slope of 1.5?
Line a
Line b
Line c
Line d
What is the rate of change of the line graphed?
12
-0.4
-2.5
5.5
Which of the following data sets belong to a linear function with a rate of change of 3?
I and II only
I only
III only
I, II, and III
The slope of a line that passes through the points (-6, w) and (-10, 4) is 1/8. What is the value of w?
36
34
9/2
1/2
A linear function contains the point (4, 9) and has a slope of 4. Which of the following points will also belong to the function?
(0, -7)
(-1, -10)
(3, 6)
(1, 2)
Which describes the range of the function with the graph shown?
All real numbers greater than or equal to 0
All real numbers greater than or equal to -6
All real numbers
All real numbers greater than or equal to -5
0 ≤ x ≤ 3
0 ≤ x ≤ 60
0 ≤ f(x) ≤ 3
60 ≤ f(x) ≤ 90
Negative correlation
Positive correlation
No correlation
Absolute correlation
The speed of the rocket was greatest at about 6 seconds after it was fired.
The rocket traveled 180 meters.
The rocket reached its maximum height in about 6 seconds.
The rocket returned to the ground in about 6 seconds.
What are the solutions to the equation 0 = x2 + 3x - 10?
x = -2, x = -5
x = -2, x = 5
x = 2, x = 5
x = 2, x = -5
A function is described by the equation f(x) = 2x + 3. The domain is {2, 4, 6, 8}. What is the range?
{4, 8, 12, 16}
{2, 4, 6, 8}
{1, 5, 9, 13}
{7, 11, 15, 19}
What are the roots of the quadratic equation 2x2 + 6x - 20 = 0?
2 and 5
-2 and 5
2 and -5
-2 and -5
What is the slope of this line?
0
-3
Undefined
1
What is the equation of the linear function graphed?
x = -3
x = -4
y = -4
y = -3
Jamie and Cynthis sold a total of 84 raffle tickets. Jamie sold 3 fewer than twice the number Cynthis sold. Which system of equations could be used to determine the number of raffle tickets sold by Jamie, j, and Cynthia, c?
j + c = 84
j = 3 - 2c
j + c = 84
c = 2j +3
j + c = 84
j = 3c + 2
j + c = 84
j = 2c -3
What is the rate of change of y with respect to x of the line graphed?
5/3
-5/3
3/5
-3/5
Which graph is not a function?
Graph 1
Graph 2
Graph 3
Graph 4
What is the domain?
x = 2
All real numbers
y = 2
None of these
6(5x - 3) + 2 = 14
2(a + 4) = 2a - 8 + 4a
Rita works at a music store. On Tuesday, she sold 6 more than 3 times the number of guitars that she sold on Monday. Rita sold a total of 110 guitars over the two days. Write a system of equations that can be used to find the number of guitars she sold on Monday and Tuesday. Let m = number of guitars sold on Monday and
t = number of guitars sold on Tuesday.
m + t =9
t = 6 + 3m
m + t = 110
t = 6 + 3m
m + t = 110
m = 6 + 3t
m + t = 110
t = 3m - 6
y = 64x
y = 64 + x
y = x - 64
y = -64x
19s+16b=28
16s+19b=478
16s+19b=28
19s+16b=478
5x + y = 5
3x + 8y = 24
The graph of f(x)= x2 was transformed to create the graph of g(x) = (x - 7.5)2. Which of these describes the transformation?
A horizontal shift to the right 7.5 units
A horizontal shift to the left 7.5 units
A vertical shift down 56.25 units
A vertical shift up 56.25 units
A particular type of cell doubles in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 4 of these cells?
n= 4(1/2)h
n= 4(2)h
n= 4+ (2)h
n= 4 + (1/2)h
The population of Center City is modeled by exponential function f, where x is the number of years after the year 2015. The graph of f is shown on the grid.
x ≥ 0
y ≥ 250,000
0 ≤ x ≤ 110
250,000 ≤ y ≤ 1,000,000
The value of y is directly proportional to the value of x. If y=35 when x= 140, what is the value of y when x = 70?
18
29
17.5
15
A projectile is launched into the air from the ground. The table shows the height of the projectile, h(t), at different times. Based on the table, which function can best be used to model this situation?
h(t)= 99t2 + 858
h(t)= -4.9t2 + 295t + 0.6
h(t)= -4.9t2 +295t + 2
h(t)= 99t2 + 1,470.3
The graph of part of linear function is g shown on the grid. Which inequality best represents the domain of the part shown?
-9 < x ≤ 2
-9 ≤ x < 2
-6 < g(x) ≤ 3
-6 ≤ g(x) < 3
The graph of a quadratic function is shown on the grid. Which equations best represents the axis of symmetry?
y = 6
x = 2
y = 4
x = 0
If p(x) = 5(x2 + 1) + 16, what is the value of p(11)?
690
736
622
626
Which expression is equivalent to (7x3)2 (x8)1/2?
14x10
49x10
14x7
49x7
Range greater than or equal to 6?
Which expression is equivalent to √147?
3√7
7√3
21√7
49√3
Which graph best represents the solution set of y ≤ -4x?
Which dashed line is an asymptote for the graph?
line q
line r
line s
line t
The expression (x3) (x-17) is equivalent to xn. What is the value of n?
-20
-14
-51
-17/3
(2, 4), (5, 5), (8, 6), (11, 7)
(1, -19) and (-2, -7)
5x - 3y = -9
4x - 5y = 40
y intercept is 8
y intercept is 20
y intercept is 10
y intercept is -8
(4, -7); m = -1/4
A=1200(.85)6
What is the solution?
3x + 2y = 16
7x + y = 19
A manager purchased a total of 21 coffee mugs and key chains. Each coffee mug cost $8.50, and each key chain cost $2.75. If the manager spent a total of $132.50, how many coffee mugs did the manager purchase?
21
8
14
13
x + 5 ≤ 13
6 > x
y < -4
y> 4
y < 4
y <- 4
k2+7x+10
k2 -2k - 24
3v2 - 4v - 7
2x2 - 13x - 70
9x2+9x-10
81m2 - 1
h = -16t2 + 64t + 960.
How many seconds did it take for the ball to reach its maximum height?
h = -16t2 + 64t + 960.
When did the ball hit the ground?
h = -16t2 + 64t + 960.
What is the maximum height?
5, 8, 11, ...
10, 20, 30, 40, ...
3, 6, 9, 12...
11, 22, 44, 88...
316 = (38)(3_)
(2a2b4z)(6a3b2z5)
4x4y3 ⋅ 2x3y-5
Express the area of the rectangle as a monomial.
What is the factored form of the expression,
6x2y4z2 + 9x3y ?
3x2(3xy + 2y4z2)
3x2y(3x + 2y3z2)
( 3x2y + 1)(3x + 2y3z2)
20x3y3z2
Which expression is equivalent to (2x2 + 4y3)(2x2 – 4y3)?
4x4 - 16y9
4x4 +16x2y3- 16y6
4x4 -16x2y3- 16y6
4x4 - 16y6
Which expression is equivalent to 30c – 18cd – 10 + 6d?
(6c + 2)(5 + 3d )
(6c + 2)(5 – 3d )
(6c – 2)(5 + 3d )
(6c – 2)(5 – 3d )
Which expression is equivalent to 22x3y2 + 55x2y4 ?
11x2y2 (5x + 2y2)
(11x2y2 + 1)(5y2 + 2x)
11x2y2 (5y2 + 2x)
11y2 ( 2x2 + 5xy2)
The dimensions of a figure are shown in the diagram.
What is the perimeter of this figure?
x2 + 6x + 10
2x2 + 2x - 2
2x4 + 2x3 - 2
2x2 + 2x + 2
A square has side length (x - 3) units. What is its area?
x2 + 9 square units
x2 - 9 square units
x2 -6x + 9 square units
x2 -6x - 9 square units
Use the dimensions in the diagram to answer the question.
What is the perimeter of this figure?
13x4 + 2
13x4 - 2
13x - 2
13x + 2
Which expression is equivalent to (x - 2)(x² + 3x - 5)?
x3 + 3x2 - 5x + 10
x3 + x2 - 11x + 10
2x² + 6x - 10
x3 + 3x2 - 5x
Which expression is equivalent to
(−4k4 + 14 + 3k2 ) + (−3k4 − 14k2 − 8)?
−7k8 − 11k4 + 6
−7k4 − 11k2 + 6
7k4 − 11k2 + 22
-7k4 − 17k2 + 22
Which expression is equivalent to xy2z + xz(x + y)?
xz(x + y2) + y
x2(x + y2)z
2xy(z + x2)z
xy2z + xyz + x2z
The owner of the local car wash wants to figure out the average time it takes his employees to wash a single car. In 1 week, 62 cars are cleaned by 5 different workers. Each employee works a 4.5-hour shift.
Which unit is most appropriate for the owner to use in calculating this information?
number of hours per car washed
number of employees per car washed
number of cars washed per week
number of shifts worked by employees
Alan rides his bicycle at a speed of 30 feet per second.
How many yards will Alan travel in 60 seconds if he maintains that speed?
180 yards
600 yards
1800 yards
90 yards
Sandy wants to determine how productive she is at writing midterm essays. She graphs the number of words typed compared to the number of hours worked while writing her last midterm.
Which statement best describes Sandy's productivity in writing midterm essays as supported by the graph?
Sandy types 50 words per hour of work on her essay.
Sandy types 150 words per hour of work on her essay.
Sandy rate of productivity doubled after 6 hours of work on her essay.
Sandy rate of productivity tripled after 6 hours of work on her essay.
In which situation would it be appropriate to use square feet as a measurement?
Joseph must determine the distance between two power lines.
Karla must determine the area of her yard.
Lyle must determine the amount of space available in a box.
Maya must determine the volume of a bathtub.
What is most reasonably in miles?
Height of a building
Height of a man
Length of a street
Length of a swimming pool
