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WorksheetsEOC math 3 All questions
Total questions: 203
Worksheet time: 3hrs 37mins
What is g(-2)?
(a)
What is g(0)?
(a)
What is g(2)?
(a)
What is g(-1)-3g(2)?
(a)
What is the difference the positive roots
(a)
The increasing interval is ______________ and the negative interval is ______________.
(-∞, -1); (2, ∞)
(-∞, -2); (0, 3)
(-1, 2); (1, ∞)
(2, ∞); (-∞, -2)
Select ALL of the transformations from the parent function of g(x)=x−12+4
Right 4
Left 1
Up 4
Right 1
Vertical Stretch by 2
Select the best option below using the piecewise function below.
h(2) > h(-1)
h(2) > h(4)
h(3) < h(5)
h(0) > h(6)
Which equation is equivalent to the graph below?
f(x) = (x + 1)(x - 2)(x + 4)
f(x)=−x3+3x2−4
f(x)=−21(x−2)(x+1)(x−4)
f(x)=x3−5x2+2x+8
Which function has the lowest y-intercept?
g(x)=x3−2x−4
(x−3)2−2
A linear function passes through point (−3, 1). Which statement must be true about the function’s inverse?
The inverse is linear and passes through the point (3, −1).
The inverse is quadratic and passes through the point (1, −3).
The inverse is linear and passes through the point (−3, 1).
The inverse is linear and passes through the point (1, −3).
The expression g(x) = 600(1.08)2x can be used to determine the growth of a savings account over time. Select all of the true statements below.
The account is compounded semi-annually.
The annual interest rate is 8%.
The account is compounded annually.
The initial amount is 600.
The annual interest rate is 16%
Which exponential function is increasing?
f(x) = (8/11)x
g(x)=(9/8)x
f(x) = 0.78x
h(x)=4(0.93)x
3) Jessica invests $1,000 in an account that is compounded continuously. If after 8 years she has $1,525, what interest rate did the account earn? Round to the nearest tenth.
(a)
Which expression has the lowest value?
log53
log34
log107
log98
In order to solve the equation 3x−1−4=−2x+3+1 , a student graphs the following f(x)=3x−1−4 & g(x)=−2x+3+1 . What is the approximate solution(s) of the equation rounded to the hundreds?
(a)
Using the graph below, identify which of the following statements are true:
I. The graph is negative on (3, ∞)
II. The graph has a vertical asymptote at y=1
III. The range is (-∞,1)
II only
I, II, & III
I & III only
II & III only
None of the above
To transform g(x) = 3(x+1) − 2 into h(x) = 3(x−3)+5 , g(x) must be translated __BLANK A__ and __BLANK B__.
Blank A: (a) Blank B: (b)
Down 7
Up 4
For g(x) = (21)(3)(x+4)−5 , identify which of the following key features are true statements (select all that apply).
g(x) is decreasing
The y-intercept is 35.5
g(x) has a growth factor of 1/2
The asymptote is y = −5
g(x) has a growth factor of 3
Consider the equation, where A, B, and C are real numbers. What are the values of A, B, and C? n+55+2n+63n=(n+5)(2n+6)An2+Bn+C
A= (a) B= (b) C= (c)
A painter can finish painting a house in 8 hours. Her assistant takes 10 hours to finish the same job. How long would it take for them to complete the job if they were working together?
4 94 hours
4 103 hours
9 hours
11 hours
Find the domain of the rational function, g(x) = (x2−8x−20)(x3+2x2−5x+8x) .
(-∞, -2] ∪ [-2, 10] ∪ [10, ∞)
[-∞, -2) ∪ (-2, 10) ∪ (10, ∞)
(-∞, -2) ∪ (10, ∞)
(-∞, -2) ∪ (-2, 10) ∪ (10, ∞)
Which expression is equivalent to (b2+7b+102b)(b2b3+8) ?
b+5b2−4
b2+5bb2−4
(b2+5b)(2b2−4b+8)
(b2+5)(2b2+8)
What is the value of x in this equation? x+33=2x−62 Fill in the blank with the value of x.
(a)
What value of p must be substituted so that x−px2−10x−24=x−12 ? Fill in the blank with the value of p.
(a)
Which expression is equivalent to ? 2x−34x+3−x+13x−5
A) (x+1)(2x−3)−2x2−12x+18
B) (x+1)(2x−3)−2x2−12
C) (x+1)(2x−3)−2x2+18
D) (x+1)(2x−3)−2x2+26x−12
At which negative x-value does the function f(x) = x2−x−12x−4 have a discontinuity?
(a)
Which expression is equivalent to 4w−13w+4w−1w ?
8w−24w
4w−1
w−1w
4w−12w
Lyla is covering a spherical ball with a total of 324 square centimeters of fabric. What is the maximum volume the ball can have? (Note: surface area of a sphere is 4πr²; volume of a sphere is ( 34 )πr³)
243π cm³
π243 cm³
972√π cm³
π972 cm³
In parallelogram PTQR, m∠P = (4x + 7)° and m∠T = (5x + 6.5)°. How many degrees is ∠R? round to the nearest whole number
(a)
A hockey puck has a diameter of 5.4 cm and a height of 3.2 cm. What is the volume of a cylindrical package containing four pucks? Express your answer to the nearest cubic centimeter.
(a)
Which figure(s) below can have a triangle as a two-dimensional cross section? Select the best choice.
I. Cone
II. Cylinder
III. Cube
IV. Square Pyramid
I only
II & IV
I, II, and IV
I, III, and IV
In the rhombus, m∠A = (15y)°, m∠B = (2x + y)°, & m∠C = (45z)°. What is the sum of x, y, and z?
(a)
Tim has a rectangular prism with a length of 10 cm, a width of 2 cm, and an unknown height. He needs to build another rectangular prism with a length of 5 cm and the same height as the original prism. If the volume of the two prisms will be the same, what will be the width of the new prism?
(a)
The diagonals of square DGFH intersect at E. If DE = 2x + 6 and GH = 6x – 10, find DF.
11
28
56
90
What is the value of x in rectangle ABCD
(a)
Which method is most likely to produce a random sample of 10 students from a football team?
Selecting 10 players who have brown eyes
Selecting 10 players who ran the most yards this season
Selecting the first 10 players that came to practice yesterday
Selecting 10 players from a hat that has the names of all football players
Kiana puts the tip of her pencil on the outer edge of a graph of the unit circle at point (0, 1). She moved her pencil tip through an angle of π/3 radians in the counterclockwise direction along the edge of the circle. At what angle of the unit circle did Kiana’s pencil tip stop in radians?
(a)
A high school randomly selected 80 of the 250 juniors at the school to take a sample college readiness test. The mean grade of the college readiness test of the juniors selected was 72.4 and the standard deviation was 4.8. Select ALL of the statements that are true. Note: Margin of error ≈ 2 · (s/√n) where s is the standard deviation and n is the sample size.
The margin of error would decrease if the sample size decreased to 60 juniors.
The margin of error would increase if the sample size decreased to 60 juniors.
The margin of error for the mean grade of the readiness test is about 1.073.
The margin of error for the mean grade of the readiness test is about 1.128.
For the graph below, the amplitude is __BLANK A__ and the period is __BLANK B__.
Blank A (a) Blank B (b)
A reporter wants to know the percentage of voters on the East Coast who support expansion of the I-95 highway. What is the reporter’s population?
The number of people who live on the East Coast
All voters over 20 years old on the East Coast
All eligible voters on the East Coast
The people on the East Coast who have a registered vehicle
Which function has a period of 4π and an amplitude of 5?
y = 5 cos 2θ
y = -5 cos (θ/2)
y = -5 sin (1/4)θ
y = 4 sin 5θ
Match the following descriptions to the type of study being conducted.
Survey
Experimental Study
A
Observational Study
B
Survey
C
Disney often Surveys its guests as they exit a restaurant during their vvisit. the surveyor stands at the restaurant exit, counts the number of people leaving, and surveys every 30th guest. This is a form of:
Systematic sampling
Random sampling
Convenience sampling
Cluster sampling
One decreasing interval is ______________ and one negative interval is ______________.
(−∞, −3); (0, ∞)
(−∞, −2); (1, ∞)
(−1, 4); (−4, −2)
(4, ∞); (−4, −2)
For what value of p is (x + 5) a factor of the polynomial f(x) = 2x4+px3−x2−4x+5 ?
(a)
Find the center and radius of the circle: x2+y2−10x−12y=−52 .
(−5, 6); r=3
(−5, 6); r=9
(5, 6); r=9
(5, 6); r=3
What value of p must be substituted so that x−px2−10x−24 = x−12 ?
(a)
Which exponential equation can be used to solve log₄x 216 = 2?
4x2=216
x2=54
(4x)2=216
41x2=216
Which exponential equation can be used to solve log4x216=2
4x2=216
x2=54
(4x)2=216
41x2=216
For the circle given by x2+y2+4x−10y=−20 , the center is Blank A and the radius is Blank B. Select one option for each blank from the choices below
Nadia is creating a flower bed that wraps around the corner of her house. She will put edging around
the flower bed 10 feet from the corner of the house in all directions as shown below. Which is the best
estimate of the number of feet of edging that Nadia will need?
24
48
63
16
In the figure below, the larger circle has a radius of 7 cm and the smaller circle has a radius of 3 cm.
What is the approximate area of the shaded region? Round to the nearest hundredth.
(a)
x2−10x+y2−12y+52=0 What the diameter of the circle defined by x
(a)
The coverage area for a news station can be modeled by a circle with its center at the station and a
diameter of 45 miles. The population density for the coverage area is 9.7 citizens per square mile. To
the nearest person, how many people live within the coverage area?
(a)
(x+4)2+(y−1)2=12 What is the coordinate pair fo rthe center of the circle represented by
(4,-1)
(-1,4)
(1,-4)
(-4,1)
Given the graph, select all of the true satements
The x-value of the center is -3
There are 4 intercepts
The y-value of the center is 3
The diameter is 6
The area is approximately 19.63 square units
What is the measure of a circle’s central angle if its arc length is 14π and the radius is 18 inches?
(a)
In the diagram below, ∠ACD = 88°. What is the value of arc ABD?
(a)
Divide ( 2x3−7x+5 ) by (x − 3). Which expression is equivalent to the result?
2x2+6x+11−x−338
2x2−x+2−x−338
2x2+6x+11+x−338
2x−1+x−32
Given g(x) = x4+2x3−5x2+13x−7 , what is the remainder when g(x) is divided by x + 4?
The function f(x) = (3x3+10x2+8x−5)∕(x+2) can be rewritten as p(x) + t(x)∕r(x). Which expression represents p(x)?
3x2+4x
3x + 4
3x2+4x2−5
3x2+4x−5
Which expression is equivalent to (4x4+2x3−4x2−15x)∕(2x2+5) ?
2x2+x−7+(2x2+5)(5x+20)
2x2+x−7+2x2+55x−20
2x2+x−7−(5x−20)∕(2x2+5)
2x2+x−7−(5x+50)∕(2x2+5)
The function h(x) = (6x3−11x2+3)∕(x−2) can be rewritten as q(x) + r(x)∕b(x). Which statement is not true?
q(x) is 6x + 1
r(x) is 7
The degree of q(x) will be 2
Since the remainder is nonzero, x − 2 is not a factor of 6x3−11x2+3
If the expression x4−5x3+2x2+kx−9 , in which k is a constant, is divided by x + 1, the remainder is 5. What is the value of k?
The polynomial function g(x) = x3+kx2−11x+30 has roots at −3, 2, and 5. What is the value of k?
The function f(x) is represented in the table below. What is the value of f−1(3) ?
Which of the following functions could be the graph shown? The graph shows a cubic crossing the x-axis at x = −1 and x = 3 with a double root at x = −1? It opens upward for large x and has a local maximum above the x-axis near x = −2 and a local minimum below near x = 2.
g(x) = −1(x−3)2(x+1)
g(x)=(x+1)2(x−3)
g(x)=x3+7x2+15x+9
g(x)=x3−5x2+3x+9
What is the inverse of the function g(x) = log_4(3x + 1)?
g−1(x)=4x+1
g−1(x)=34x−1
g−1(x)=log434x−1
g−1(x)=log3(4x−1)
A cubic function f has a negative leading coefficient and exactly two distinct real zeros. One zero is x = 1 with multiplicity two, and the other is x = −4 with multiplicity one. Which function could be f(x)?
f(x)=−3x3−6x2+21x−12
f(x)=2x3+4x2−14x+8
f(x)=−x3−7x2−8x+16
f(x)=−x3+2x2+7x+4
Given f(x) = 2x2−3x+6 and g(x) = x+4 , find the product f(x)·g(x).
A= (a) B= (b) C= (c) D= (d)
The graph of y = g(x) is piecewise linear. Use the graph to evaluate g−1(4) .
(a)
The graph of f(x) shown is increasing and passes through the point (0,0) with a vertical asymptote near x = -2 and a horizontal asymptote near y = 3. What type of function best represents f−1(x) ?
Quadratic function
Exponential function
Radical function
Linear function
Create an absolute value inequality to model Leonardo’s 50-meter freestyle times if his average time is 28.4 seconds with a typical variation of 1.1 seconds.
|x- (a) |≤ (b)
A scientist places 60 bacteria in a petri dish at 2 pm. The bacterium doubles every half hour. How many bacteria are present at 5 pm?
(a)
Lizbeth can mow a lawn twice as fast as Edvina. Working together, they finish in 3 hours. How long would it take Lizbeth working alone?
(a)
Sophia bought a house for 380,000 in 2017 and its value increases each year by 6.5%. In what year will the house be worth 520,000?
(a)
Members of the track team can run 800 m in an average time of 2 minutes 31 seconds. The fastest and slowest times varied from the average by 14 sec. What was the maximum time for the track team? Express your result as a decimal if necessary.
(a)
What is the approximate solution to the equation 2⋅5(3x+1)=18 to the nearest hundredth?
(a)
Which equation is equivalent to 2(4)5x = 22?
51log411
51log444
5log4111
11log451
Which scenario matches the function P(x)=26000(0.79)x ?
A car that originally costs $26000 decreases at a constant rate of 21 each year.
A car that originally costs $26000 decreases by 79% each year.
A car that originally costs $26000 increases by 21% each year.
A car that originally costs $26000 decreases by 21% each year.
What is the value of x in 6 · 4(x−2) = 41. Round your answer to the nearest tenth.
(a)
A parent invests $1500 at a 6.25% interest rate to help his daughter save for college. How long will it take her money to double? Round the nearest whole year.
(a)
Which expression is the complete factorization of x3−3x2+4x−12 ?
(x−3)(x2+4)
(x+3)(x2−4)
(x + 2)(x + 2)(x − 3)
(x + 2)(x − 2)(x − 3)
Which expression is equivalent to (x−5)3+10x(x−5) ?
x3+125
(x−5)2(x+5)
x3−5x2−25x+125
x3−5x2+25x−125
Which of the following is a factor of 8w3+64 ?
w + 2
2w + 4
w2+2w+4
4w2−8w+16
The area for a rectangle is 4x2−100 . Which binomial factor could represent the width of the rectangle?
x + 10
x + 5
2x − 5
2x + 5
Given that (2x−1) and (x+4) are factors of a polynomial, 2x^3 + 3x^2 - 18x + 8, what is the third factor?
x + 2
x − 2
4 + x
2 − x
The area of a rectangle is x^2 − 13x + 30. Which binomial could represent the length of the rectangle if the length is larger than the width?
x + 10
x − 10
x + 3
x − 3
Which of the following is equivalent to 2x−57x−2x−53x ?
2x−510x
2x−54x
4x−104x
−52
Below is an equation. What value for k will make the equation true given that x ≠ -2? x+22x3+kx+15=2x2−4x+1+x+213
(a)
Simplify the following expression x+110÷21+x+13 .
x+720x
x+710
x+110(x+7)
x+720
Which expression is equivalent to x−46x−5+2x+33x−1 ?
(2x+3)(x−4)9x2+21x−19
(2x+3)(x−4)18x2−21x+5
(2x+3)(x−4)15x2−5x−11
(2x+3)(x−4)15x2−5x−19
Which of the following is equivalent to w2+4w−21w2−3w÷w+7w−1 ?
A) ww−1
B) w−3
C) w−1
D) w2−ww−3
What coordinate pair is the center of the circle represented by (x+2)2+(y−5)2=41 ?
(-2, 5)
(-2, -5)
(2, -5)
(2, 5)
What is the radius of the circle defined by x2−8x+y2+4y−29=0 ?
(a)
For the circle given by x2+y2+10x+11y=−43 , the center is __BLANK A__ and the diameter is __BLANK B__. Select one option for each blank from the choices below.
Blank A: (a) Blank B: (b)
A circle is represented by the equation -15 = x2+y2+6x+10y . Which of the following statements are true? Select all that apply.
The center is (-3, -5).
The radius is less than 5 units.
The graph is never positive.
An equivalent equation of the circle is (x+3)2+(y+5)2=20 .
There are 3 intercepts.
What is the diameter of the circle defined by (x−9)2+(y+2)2=32 ?
Approximately 11.3 units
Approximately 5.7 units
16 units
32 units
Adriana is comparing two functions: A quadratic function, w(t)=−t2+4t+3 and the graph of s(t) shown below. What is the distance between the maximum value of w(t) and the maximum value of s(t) ?
9
7
5
3
Which scenario matches the graph of the function g(x)=350(0.982)x ?
A) A population of 350 deer decreases by 1.8% each year.
B) A population of 350 deer decreases by 18% each year.
C) A population of 350 deer decreases by 98.2% each year.
D) A population of 350 deer decreases by approximately 2 deer each year.
13) What is the largest real root of q(x)=2x4−6x3+7x−5 ? Round to the nearest hundredth.
(a)
Which of the following has the smallest average rate of change over the interval x = -1 to x = 3?
g(x) = -(x - 2)(x + 1)(x - 1)
h(t)=−2x−3
A function is shown below. Which choice most accurately describes x=−4 for this function? g(x) = x2−16x2−3x−28
A) A nonremovable discontinuity of g(x)
B) A removable discontinuity of g(x)
C) A horizontal asymptote of g(x)
D) A vertical asymptote of g(x)
A local gas station is having a promotion based on the amount of gas you buy. The piecewise function below models the cost C based on the number of gallons, x. C(x) = { 3.42x, 0 < x ≤ 5 3.37x, 5 < x ≤ 12 3.30x, 12 < x ≤ 30 } If Marco paid $31.34 for his gas, how many gallons did he get? Round to the nearest tenth.
(a)
A cubic function, f(x), is shown in the table while h(x) is represented by the quadratic function h(x)=2x2−x−10 . What is the sum between the largest x-intercept of h(x) and the smallest x-intercept of f(x)?
-3
1.5
2
3.5
The function h is defined by h(x) = −21x2−2x−4 while the graph of j is shown below. Which statement is not true?
A) Both h(x) and j(x) are increasing on (-5, -3).
B) Both h(x) and j(x) have a maximum.
C) h(x) and j(x) have the same y-intercepts.
D) h(x) has a smaller value at x = -2 than j(x).
What is the vertical distance between the y-intercept of m(x) , where m(x)=21(x−1)2(x+2)(x+4) is a quartic function with a leading coefficient of 21 , a root that bounces at x=1 , a root at x=−2 , and a root at x=−4 , and the y-intercept of p(x) , where p(x)=−2(x−1)(x+3)2 ?
(a)
Which of the following functions have only one zero in common with the graph below?
f(x) = log(x - 2)
g(x)=(x−2)2−9
h(x) = (x2+8x+12)(x−4)
j(x)=3x2−3
A square pyramid with a base area of 16 square inches and a height of 6 inches is made of metal. If the density of the metal is 4.3 g/in^3, what is the mass, in grams, of the pyramid? Round to the nearest tenth.
(a)
Jami spent 30 minutes inflating a beach ball while at the beach. If the inflated beach ball has a surface area of 100\pi in^2. What is the approximate volume of air that was needed to inflate the ball?
4188.8 cubic inches
3141.6 cubic inches
523.6 cubic inches
392.7 cubic inches
23) The circular coverage area of a local radio station has a diameter of 40 miles. The population density for the coverage area is 16.6 residents per square mile. To the nearest thousand, how many people live within the radio station’s coverage area?
(a)
A roll of duct tape has the dimensions shown below. To the nearest tenth of a cubic centimeter, what is the volume?
7.2 cubic centimeters
9.4 cubic centimeters
15.3 cubic centimeters
21.6 cubic centimeters
25) A farmer has 100 feet of fencing to enclose a rectangular garden. One side of the garden will be the barn while the other three sides will be fenced in. What is the maximum area the farmer can enclose?
(a)
26) What is the solution to the equation shown below?
x−3x2+8x−33=−4
(a)
Mr. Twindall is having a birthday party at the local roller rink for his daughter and wants to spend an average of 15perkid.Itcosts 6 per kid for the roller skate rental and $135 to rent the party room. How many children can Mr. Twindall invite to stay on budget?
(a)
It takes Lyla 7 more hours to paint a kitchen than it takes Christopher to complete the same job. Together, they can complete the same job in 12 hours. How long does it take Christopher to complete the job if he works alone?
21 hours
16.8 hours
4.4 hours
3 hours
What is the value(s) of x that satisfy the equation below? Drag and drop all values of x into the box below from the answer bank.
x/(2x-3) = 3x/(x+11)
(a) (b)
Sandra's car uses 20 gallons of gas to travel 360 miles. If Sandra currently has 3 gallons of gas in her car, how many more gallons of gas does she need to travel 198 miles for her weekend trip?
(a)
The increasing interval is ______________ and the negative interval is ______________.
(-∞, -1); (2, ∞)
(-∞, -2); (0, 3)
(-1, 2); (1, ∞)
(2, ∞); (-∞, -2)
Select ALL of the transformations from the parent function of g(x)=x−12+4
Right 4
Left 1
Up 4
Right 1
Vertical Stretch by 2
Select the best option below using the piecewise function below.
h(2) > h(-1)
h(2) > h(4)
h(3) < h(5)
h(0) > h(6)
Which equation is equivalent to the graph below?
f(x) = (x + 1)(x - 2)(x + 4)
f(x)=−x3+3x2−4
f(x)=−21(x−2)(x+1)(x−4)
f(x)=x3−5x2+2x+8
Which function has the lowest y-intercept?
g(x)=x3−2x−4
(x−3)2−2
A linear function passes through point (−3, 1). Which statement must be true about the function’s inverse?
The inverse is linear and passes through the point (3, −1).
The inverse is quadratic and passes through the point (1, −3).
The inverse is linear and passes through the point (−3, 1).
The inverse is linear and passes through the point (1, −3).
The expression g(x) = 600(1.08)2x can be used to determine the growth of a savings account over time. Select all of the true statements below.
The account is compounded semi-annually.
The annual interest rate is 8%.
The account is compounded annually.
The initial amount is 600.
The annual interest rate is 16%
Which exponential function is increasing?
f(x) = (8/11)x
g(x)=(9/8)x
f(x) = 0.78x
h(x)=4(0.93)x
3) Jessica invests $1,000 in an account that is compounded continuously. If after 8 years she has $1,525, what interest rate did the account earn? Round to the nearest tenth.
(a)
Which expression has the lowest value?
log53
log34
log107
log98
In order to solve the equation 3x−1−4=−2x+3+1 , a student graphs the following f(x)=3x−1−4 & g(x)=−2x+3+1 . What is the approximate solution(s) of the equation rounded to the hundreds?
(a)
To transform g(x) = 3(x+1) − 2 into h(x) = 3(x−3)+5 , g(x) must be translated __BLANK A__ and __BLANK B__.
Blank A: (a) Blank B: (b)
Down 7
Up 4
Using the graph below, identify which of the following statements are true:
I. The graph is negative on (3, ∞)
II. The graph has a vertical asymptote at y=1
III. The range is (-∞,1)
II only
I, II, & III
I & III only
II & III only
None of the above
For g(x) = (21)(3)(x+4)−5 , identify which of the following key features are true statements (select all that apply).
g(x) is decreasing
The y-intercept is 35.5
g(x) has a growth factor of 1/2
The asymptote is y = −5
g(x) has a growth factor of 3
Consider the equation, where A, B, and C are real numbers. What are the values of A, B, and C? n+55+2n+63n=(n+5)(2n+6)An2+Bn+C
A= (a) B= (b) C= (c)
A painter can finish painting a house in 8 hours. Her assistant takes 10 hours to finish the same job. How long would it take for them to complete the job if they were working together?
4 94 hours
4 103 hours
9 hours
11 hours
Find the domain of the rational function, g(x) = (x2−8x−20)(x3+2x2−5x+8x) .
(-∞, -2] ∪ [-2, 10] ∪ [10, ∞)
[-∞, -2) ∪ (-2, 10) ∪ (10, ∞)
(-∞, -2) ∪ (10, ∞)
(-∞, -2) ∪ (-2, 10) ∪ (10, ∞)
Which expression is equivalent to (b2+7b+102b)(b2b3+8) ?
b+5b2−4
b2+5bb2−4
(b2+5b)(2b2−4b+8)
(b2+5)(2b2+8)
What is the value of x in this equation? x+33=2x−62 Fill in the blank with the value of x.
(a)
What value of p must be substituted so that x−px2−10x−24=x−12 ? Fill in the blank with the value of p.
(a)
Which expression is equivalent to ? 2x−34x+3−x+13x−5
A) (x+1)(2x−3)−2x2−12x+18
B) (x+1)(2x−3)−2x2−12
C) (x+1)(2x−3)−2x2+18
D) (x+1)(2x−3)−2x2+26x−12
At which negative x-value does the function f(x) = x2−x−12x−4 have a discontinuity?
(a)
Which expression is equivalent to 4w−13w+4w−1w ?
8w−24w
4w−1
w−1w
4w−12w
What is the remainder when x3−1 is divided by (x+2) ?
(a)
The function below, f(x), has (x - 7) and (x + 4i) as factors.
f(x) = 2x5−13x4+22x3−187x2−160x+336
What is the total number of real zeros of f(x)?
(a)
The graph of the function m(x)=x3+3x2−2x−4 has a zero at -1. What are the other zeros of the function?
-2 and 2
-1 and 4
-1 ± √5
1 ± 2√3
Which expression is equivalent to (x2−2x−37)÷(x2−3x−40) ?
A. 1 + x2−3x−40x+3
B. 1 - x2−3x−40x+3
C. 1 + (x2−3x−40)(2x−37)
D. 1 - x2−3x−402x−37
Place (click and drag) into the appropriate boxes the values of A, B, and C that will make the equation shown below true. 4x+33x−5 + 7x−2−2x+1 = (4x+3)(7x−2)Ax2+Bx+C Select the correct value for each variable.
A= (a) B= (b) c= (c)
Which expression is equivalent to (x−2)2(x2−5x+6)−1÷(x−2)2(x−3)−1 ?
(x−3)2(x−2)2
(x+3)2(x+2)3
x−31
x−21
A company makes and boxes spaghetti. One machine fills each box with approximately 32 ounces of spaghetti. After the boxes are filled, another machine weighs each box. A box is discarded if the weight of the box differs by more than 0.25 ounce from the target weight of 32 ounces. Which inequality can be used to find the range of acceptable weights, x, of the spaghetti?
|x - 0.25| ≤ 32
|x + 0.25| ≤ 32
|x - 32| ≤ 0.25
|x + 32| ≤ 0.25
Which equation represents the graph?
y = |x| - 2
y = |2x| - 2
y = |x - 2|
y = |2x - 2|
Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?
(a)
Two functions are shown below
f(x)=2x3+2x−3
g(x)=−0.5∣x−4∣
Select the y-value when f(x) = g(x).
(a)
Which choice is equivalent to the expression shown below? 48x3−243xy2
3(4x2−9y)(4x2−9y)
3(4x2−9y)(4x2+9y)
3x(4x - 9y)(4x - 9y)
3x(4x - 9y)(4x + 9y)
A polynomial, p(x), has a lead coefficient of 1 and exactly three distinct zeros. • x = -1 is a zero of multiplicity two • x = 2 is a zero of multiplicity one • x = 4 is a zero of multiplicity one What choice shows p(x)?
p(x)=x3−5x2+2x+8
p(x)=x3+5x2+2x−8
p(x)=x4−4x3−3x2+10x+8
p(x)=x4+4x3−3x2−10x+8
If f(x) = k(x−2)4 , where k is positive, what is the effect on the graph of f(x) as k increases?
The graph of f(x) is shifted up.
The graph of f(x) is shifted down.
The graph of f(x) is stretched vertically.
The graph of f(x) is stretched horizontally.
Two piecewise functions are shown.
What is the value of 3h(2)+4g(1) ?
39
28
10
-6
A function is shown
What is the value of h(-4) + 3h(-2)?
(a)
The graph of a function is shown
Place each interval that decribes the function on that interval
Decreasing (a) Increasing (b)
Positive (c) Negative (d)
A function is shown below
H(x)=4x3−5x2−23x+6
What is the distance, to the nearest hundredth of a unit, between the two zeros that are closest to each other?
(a)
Which function does not have the set of all real numbers as its domain?
f(x)=5x−3
f(x)=x+3x+1
f(x) = |2x - 1|
f(x) = cos(x) + 1
An equation is shown below. 9−3x+2 = 48 What is the value of x to the nearest ten-thousandth?
0.0794
0.0995
0.4243
0.4774
The diagram shows an angle, θ, graphed in the xy-coordinate plane. Segment RT is the initial side of the angle, and segment RM is the terminal side. Segments RT and RM are radii of the unit circle centered at the origin R(0, 0).
The x-coordinate of point M is -1/2. What is the measure of θ to the nearest thousandth of a radian?
4.712
4.189
3.927
3.665
A function, f(x) = Asin(Bx) + H, has the following properties: - a period of 6, - a minimum value of 2, - f(2.5) = 5, and - A, B, and H are all positive constants.
Choose the value in the appropriate cells below that will create this function.
A= (a) B= (b) H= (c)
The vertices of a triangle are at (0, 0), (6, 6), and (9, 3). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x?
54√2
324√2
36π√2
108π√2
In parallelogram MNPT, m∠M = (6x + 10)° and m∠N = (5x + 10.5)°. How many degrees is ∠T?
(a)
In rectangle FGHI, diagonals FH and GI intersect at E.
• IE = 3x + 4
• EG = 5x – 6
What is the length of FH?
5 units
10 units
19 units
38 units
Triangle PMT is shown below.
* mGH=x+3
*mPG=4x+1
*mGJ=2x+1
What is the measure of segment PG?
4 units
7 units
14 units
17 units
What is the length of a radius of the circle represented by the equation x2+y2−4x−4y+4=0 ?
2 units
4 units
8 units
16 units
David plans to cover the floor of his room with new material.
The floor is an isosceles trapezoid whose bases are 16 feet and 26 feet and sides are 13 feet in length.
Each piece of new material has an area of 2.5 square feet.
Assuming the pieces of new material can be cut as needed, how many pieces does David need?
101
126
202
252
Which method is most likely to produce a random sample of 5 students from a school club?
selecting 5 club members who have brown hair
selecting the 5 club members who have raised the most funds for the club
selecting 5 club members from a hat containing the names of all members
selecting the 5 club members who arrive last to a club meeting
A high school randomly selected 75 of the 200 seniors at the school to take a sample college entrance exam. The mean grade point average (GPA) of the seniors selected was 2.85, and the standard deviation was 0.4. Select (click) all of the statements that are true. Which of the following statements are true?
(Note: Margin of error ≈ 2 * (s/√n), where s is the standard deviation and n is the sample size.)
The margin of error for the mean grade point average is about 0.057.
The margin of error for the mean grade point average is about 0.092.
The margin of error would decrease if the sample size were changed to 125 seniors.
The margin of error would increase if the sample size were changed to 125 seniors.
The police chief of a town is trying to determine the average speed of drivers on a specific road.
The police chief took a random sample of the speeds of 100 drivers on the road.
The mean was 48.5 miles per hour, with a standard deviation of 2.5 miles per hour.
The police chief wanted to decrease the margin of error of his next sample.Which choice would decrease the margin of error?
decreasing the sample size
increasing the sample size
changing the time that the data is collected
changing the road on which the data is collected
Lyla is covering a spherical ball with a total of 324 square centimeters of fabric. What is the maximum volume the ball can have? (Note: surface area of a sphere is 4πr²; volume of a sphere is ( 34 )πr³)
243π cm³
π243 cm³
972√π cm³
π972 cm³
In parallelogram PTQR, m∠P = (4x + 7)° and m∠T = (5x + 6.5)°. How many degrees is ∠R? round to the nearest whole number
(a)
A hockey puck has a diameter of 5.4 cm and a height of 3.2 cm. What is the volume of a cylindrical package containing four pucks? Express your answer to the nearest cubic centimeter.
(a)
Which figure(s) below can have a triangle as a two-dimensional cross section? Select the best choice.
I. Cone
II. Cylinder
III. Cube
IV. Square Pyramid
I only
II & IV
I, II, and IV
I, III, and IV
In the rhombus, m∠A = (15y)°, m∠B = (2x + y)°, & m∠C = (45z)°. What is the sum of x, y, and z?
(a)
Tim has a rectangular prism with a length of 10 cm, a width of 2 cm, and an unknown height. He needs to build another rectangular prism with a length of 5 cm and the same height as the original prism. If the volume of the two prisms will be the same, what will be the width of the new prism?
(a)
The diagonals of square DGFH intersect at E. If DE = 2x + 6 and GH = 6x – 10, find DF.
11
28
56
90
What is the value of x in rectangle ABCD
(a)
Which method is most likely to produce a random sample of 10 students from a football team?
Selecting 10 players who have brown eyes
Selecting 10 players who ran the most yards this season
Selecting the first 10 players that came to practice yesterday
Selecting 10 players from a hat that has the names of all football players
Kiana puts the tip of her pencil on the outer edge of a graph of the unit circle at point (0, 1). She moved her pencil tip through an angle of π/3 radians in the counterclockwise direction along the edge of the circle. At what angle of the unit circle did Kiana’s pencil tip stop in radians?
(a)
A high school randomly selected 80 of the 250 juniors at the school to take a sample college readiness test. The mean grade of the college readiness test of the juniors selected was 72.4 and the standard deviation was 4.8. Select ALL of the statements that are true. Note: Margin of error ≈ 2 · (s/√n) where s is the standard deviation and n is the sample size.
The margin of error would decrease if the sample size decreased to 60 juniors.
The margin of error would increase if the sample size decreased to 60 juniors.
The margin of error for the mean grade of the readiness test is about 1.073.
The margin of error for the mean grade of the readiness test is about 1.128.
For the graph below, the amplitude is __BLANK A__ and the period is __BLANK B__.
Blank A (a) Blank B (b)
A reporter wants to know the percentage of voters on the East Coast who support expansion of the I-95 highway. What is the reporter’s population?
The number of people who live on the East Coast
All voters over 20 years old on the East Coast
All eligible voters on the East Coast
The people on the East Coast who have a registered vehicle
Which function has a period of 4π and an amplitude of 5?
y = 5 cos 2θ
y = -5 cos (θ/2)
y = -5 sin (1/4)θ
y = 4 sin 5θ
Match the following descriptions to the type of study being conducted.
Survey
Experimental Study
A
Observational Study
B
Survey
C
Disney often Surveys its guests as they exit a restaurant during their vvisit. the surveyor stands at the restaurant exit, counts the number of people leaving, and surveys every 30th guest. This is a form of:
Systematic sampling
Random sampling
Convenience sampling
Cluster sampling
One decreasing interval is ______________ and one negative interval is ______________.
(−∞, −3); (0, ∞)
(−∞, −2); (1, ∞)
(−1, 4); (−4, −2)
(4, ∞); (−4, −2)
For what value of p is (x + 5) a factor of the polynomial f(x) = 2x4+px3−x2−4x+5 ?
(a)
Find the center and radius of the circle: x2+y2−10x−12y=−52 .
(−5, 6); r=3
(−5, 6); r=9
(5, 6); r=9
(5, 6); r=3
What value of p must be substituted so that x−px2−10x−24 = x−12 ?
(a)
Which exponential equation can be used to solve log4x216=2 ?
4x2=216
x2=54
(4x)2=216
41x2=216
Which exponential equation can be used to solve log4x216=2
4x2=216
x2=54
(4x)2=216
41x2=216
For the circle given by x2+y2+4x−10y=−20 , the center is Blank A and the radius is Blank B. Select one option for each blank from the choices below
Nadia is creating a flower bed that wraps around the corner of her house. She will put edging around
the flower bed 10 feet from the corner of the house in all directions as shown below. Which is the best
estimate of the number of feet of edging that Nadia will need?
24
48
63
16
In the figure below, the larger circle has a radius of 7 cm and the smaller circle has a radius of 3 cm.
What is the approximate area of the shaded region? Round to the nearest hundredth.
(a)
x2−10x+y2−12y+52=0 What the diameter of the circle defined by x
(a)
The coverage area for a news station can be modeled by a circle with its center at the station and a
diameter of 45 miles. The population density for the coverage area is 9.7 citizens per square mile. To
the nearest person, how many people live within the coverage area?
(a)
(x+4)2+(y−1)2=12 What is the coordinate pair fo rthe center of the circle represented by
(4,-1)
(-1,4)
(1,-4)
(-4,1)
Given the graph, select all of the true satements
The x-value of the center is -3
There are 4 intercepts
The y-value of the center is 3
The diameter is 6
The area is approximately 19.63 square units
What is the measure of a circle’s central angle if its arc length is 14π and the radius is 18 inches?
(a)
In the diagram below, ∠ACD = 88°. What is the value of arc ABD?
(a)
