WorksheetsNC Math 1 Review 102
Total questions: 79
Worksheet time: 3570secs
Which graph shows the solution for the system of inequalities below?
A
B
C
The amount of medicine in Elizabeth's blood is modeled by the function M(t) = t^2 + 10t, where t is the number of hours after she takes the medicine. How many hours after Elizabeth takes her medicine is the amount of medicine in her blood the highest?
A. 5 hours
B. 10 hours
C. 25 hours
What is the smallest positive integer for x, so that the value of f(x) = 200(2)^x is greater than the value of g(x) = 500x + 400?
A. 1
B. 2
C. 3
What is the y-intercept of the function f(x) = 3(2x - 4)?
A. (0, -4)
B. (0, -2)
C. (0, 1)
A girl drops a ball from a height of 10 feet. Each time the ball hits the ground, it bounces to 2/3 its previous height. Which equation gives y, the height of the ball after x bounces?
A. y = 10(2/3)^x
B. y = 10(3/2)^x
C. y = 3(10)^x
Which expression is equivalent to 3(x - 4)^2?
A. 3x^2 + 48
B. 3x^2 - 24x + 48
C. 9x^2 - 72x + 144
Jane owns x comic books. Derrek owns y comic books. The number of comic books Jane owns is 1 less than 2 times the number Derrek owns. Together they have a total of 11 comic books. How many comic books does Derrek own?
A. 3
B. 4
C. 5
James is at a gift sale where everything costs $6 (tax included). James has $50. James must have at least $28 remaining when he is finished buying gifts. What is the greatest number of gifts James can buy?
A. 3
B. 4
C. 5
The expression 5t^2 + 40t predicts the height, in meters, of an object t seconds after a person launches it into the air. Using this expression, how many seconds will it take the object to hit the ground?
A. 0 seconds
B. 5 seconds
C. 8 seconds
The function f(x) = 1/2 x - 6 was replaced with f(x) + k = 1/2 x - 4. What is the value of k?
A. 2
B. -2
C. 4
The function f(x) = 10,000 - 1,500x can be used to predict the number of termites in an area x days after the area has been treated. How many termites are predicted in the area after 5 days?
A. 2,500
B. 5,000
C. 7,500
Avis used a quadratic function to solve a problem. The factored form of the function is shown below. (4x + 3)(x - 3) = 0. What is the positive solution to the problem?
A. -3/4
B. 3
C. 4
The cost to rent a construction crane is $750 per day plus $250 per hour of use. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed $2500 per day?
A. 4 hours
B. 5 hours
C. 6 hours
The average daily high temperature for the month of May in Ocala, Florida is approximated by the function f(n) = 0.2n^2 + 80, where n is the day of the month. May has 31 days. The maximum daily high temperature occurred on May 31st. What was the maximum temperature?
A. 99.2°F
B. 100°F
C. 102.2°F
Jorge graphed the line shown below.
1
2
3
4
Shirley graphed the line shown on the coordinate plane below.
2.00
4.00
6.00
8.00
The table below shows the amount of money Bernard earned selling newspapers during a 6-week time period.
A weak, positive relationship
A strong, negative relationship
A strong, positive relationship
No relationship
The volume of a cone can be found using the formula V = 1/3 π B h, where B is the area of the base of the cone and h is the height. A cone has a volume of 262 cubic inches and a height of 10 inches. What is the approximate length of the radius of the cone?
2.5 inches
5 inches
25 inches
10 inches
A quadrilateral has vertices located at (3, 5), (4, 2), (4, 1), and (2, 1). Which best describes the figure?
Rhombus
Rectangle
Trapezoid
Square
A school opened with 100 students. The number of students has increased by 25% each year since the school opened. Which function can be used to determine the number of students at the school x years after it opened?
f(x) = 0.25x + 100
f(x) = 100(1.25)^x
f(x) = 100(1.25x)
f(x) = 100x + 25
Jenna cut a piece of cloth several times. The table below shows the number of pieces of cloth she had after making several cuts.
y = 2x
y = 2^x
y = x^2
y = x + 2
A teacher surveyed 160 students to see how many students leave school during lunch. The results of the survey are shown in the relative frequency table below.
13%
24%
31%
40%
A liquid is evaporating. The amount of a liquid remaining, in liters, after x weeks is modeled by the equation y = 1000(0.78)^x. Approximately what percent of the liquid evaporates per week?
47%
53%
78%
22%
The function y = 45x + 6 can be used to determine the cost for a person to purchase x tickets to a concert. A person can purchase up to 8 tickets. What is an appropriate domain for the function?
All integers x
All positive integers x
All integers x ≤ 8
All positive integers x ≤ 8
Using the line of best fit for the data in the table, what is the approximate predicted monthly expense for owning 3 pets?
A) $66
B) $75
C) $80
D) $100
What is the area of the rectangle below?
A) 5x + 4
B) 6x² + 14x - 12
C) 6x² - 22x - 12
D) 6x² + 14x + 12
How many units of merchandise does the company need to sell to make the maximum profit?
A) 100
B) 300
C) 500
D) 400
Which equation has a graph which is perpendicular to the line y = -2x and which passes through the point (-2, 3)?
A) x - 2y = 8
B) x + 2y = 8
C) x - 2y = -8
D) x + 2y = -8
Which situation could be best modeled with an exponential function?
A) The value of a car that loses 6% of its value per year
B) The cost to purchase different weights of bananas at a store
C) The total number of miles run by a person who runs 8 miles per day
D) The cost of a meal at a restaurant
Fred has $200. Each week he will save an additional $50. If Fred does not spend any of the money, how many weeks will it take for Fred to have $650?
A) 9
B) 13
C) 17
D) 11
Which expression is equivalent to (x^8)^(1/2)?
A) x^2
B) x^4
C) x^8
D) x^16
What is represented by the y-intercept of the line of best fit for this data set?
A. The predicted average change in ticket price per year
B. The predicted number of years per $1 increase in ticket price
C. The predicted price of a ticket in 1990
Which formula could be used to determine the volume of an object?
A. V = mD
B. V = D/m
C. V = m/D
Kerry wants to simplify the following: \[ \frac{20x^2 + 5x}{5x} \]. Which of the following is the correct result?
A. 4x
B. 4x + 1
C. 20x^2
D. 20x^2 + 1
John collected data on the number of new movies produced in different years. Suppose that the number of movies made in 2005 was 595, and the number made in 2010 was 895. What is the average rate of change in the number of new movies between 2005 and 2010?
A. 50 movies per year
B. 60 movies per year
C. 300 movies per year
Yanice needs to solve the problem below using the quadratic formula. \[ x^2 + 8x - 7 = 8 \]. Which use of the following shows the quadratic formula being used correctly to determine the solutions for this problem?
A. \[ x = \frac{-8 \pm \sqrt{8^2 - 4(1)(7)}}{2(1)} \]
B. \[ x = \frac{-8 \pm \sqrt{8(-7) - 4(1)(8)}}{2(1)} \]
C. \[ x = \frac{8 \pm \sqrt{8^2 - 4(1)(15)}}{2(1)} \]
D. \[ x = \frac{-8 \pm \sqrt{8^2 - 4(1)(15)}}{2(1)} \]
What is the range of the relation shown in the graph below?
A. All \( y \leq 5 \)
B. All \( x \leq 5 \)
C. All values of \( y \)
D. All values of \( x \)
The surface area, \( S \), of a cylinder is calculated using the formula \( S = 2\pi r l + 2\pi r^2 \). Which equation is equivalent to this formula solved for \( l \), the length of the cylinder?
A. \( l = \frac{S}{2\pi} \)
B. \( l = \frac{S - 2\pi r^2}{2\pi r} \)
C. \( l = \frac{S - 2\pi r}{2\pi r^2} \)
D. \( l = \frac{S - 2\pi r^2}{2r} \)
Rogelio divides a trinomial by a monomial, as shown below. \[ \frac{3x^4 + 9x^2 + 15x}{3x} \]. Which of the following is the correct result?
A. \( x^3 + 9x^2 + 15x \)
B. \( x^4 + 3x^2 + 5x \)
C. \( x^3 + 3x + 5 \)
D. \( 3x^4 + 9x^2 + 5 \)
Patrick compared the slope of the function \( g(x) = -2x - 8 \) to the slope of the linear function shown in the table below. Let \( m \) be the slope of \( g(x) \) and \( n \) be the slope of \( h(x) \). Which statement is true?
A. \( m < n \)
B. \( m > n \)
C. \( m = n \)
Shelly has been asked to factor the following expression completely. \[ 36y - 81t^2y \]. Which answer choice shows her completely factored expression?
The function below can be used to describe the path of a bird flying through the air. \[ f(x) = x^2 - 4x - 32 \] Which of the following shows the correct factorization of this function \( f(x) = 0 \)?
(x + 4)(x + 8) = 0
(x + 4)(x - 8) = 0
(x - 4)(x + 8) = 0
(x - 4)(x - 8) = 0
Yanet needs to simplify the expression below before she substitutes values for \( x \) and \( y \). \[ \frac{x^3y^2 + x^2y^3}{x^2y} \] If \( x \neq 0 \) and \( y \neq 0 \), which of the following is a simplified version of the expression above?
xy^5
x^3y^5
x^3y + x^2y^2
x + y + x^2y^4
Which of the following is the graph of the function \( y = x^2 + 2x - 3 \)?
Which best represents the graph of \( y = 2x - 2 \)?
Which graph best represents \( 2x - y < 10 \)?
The formula below illustrates how to calculate body mass index (BMI), using weight (w) and height (h). \[ BMI = \frac{703w}{h^2} \] Which of the following shows this equation correctly solved for \( w \)?
What are the solutions for the quadratic equation \( x^2 + 6x = 16 \)?
(a)
Solve \( 6 - 3(4x - 5) = 7 \).
\( \frac{4}{3} \)
\( \frac{7}{6} \)
\( \frac{11}{6} \)
\( \frac{7}{3} \)
Which expression represents ( y^4 - 36 ) in simplest factored form?
( (y^2 + 4)(y^2 - 9) )
( (y^2 + 4)(y - 3)(y + 3) )
( (y^2 + 6)(y^2 - 6) )
( (y^4 - 36)(y + 1) )
Solve ( x^2 - 7x + 10 = 28 ).
{ -4, -7 }
{ -2, 9 }
{ 5, 2 }
{ 30, 33 }
Which inequality is shown on the graph below?
( y <= 1/2x - 1 )
( y <= 1/2x + 1 )
( y >= 1/2x - 1 )
( y >= 1/2x + 1 )
What is the value of ( x ) in the equation: ( 6(4x + 5) = 3(8x + 8) + 3 )?
-3
( -1/7 )
( 1/3 )
7
Which is an equation of a line that is parallel to line ( MN )?
2x - y = 3
x - 2y = 3
8x + 4y = 4
9x + 18y = -9
What is the slope of the line between the balloon and the point where it was tied?
( 6/11 )
( 11/6 )
30
55
A computer is purchased for $1,200 and depreciates at $140 per year. Which linear equation represents the value, ( V ), of the computer at the end of ( t ) years?
Which equation is equivalent to ( 5x - 2(7x + 1) = 14x )?
9 - 2x = 14x
-9x + 1 = 14x
-9x - 2 = 14x
12x - 1 = 14x
At a local grocery store, watermelons are sold for $4 each plus an additional $0.25 per pound. Write a function that describes the relationship between x, the number of pounds of a watermelon, and f(x), the total cost of the watermelon.
f(x) = 4.25x
f(x) = 4 + 0.25x
f(x) = 4(0.25x + 1)
f(x) = 4(x) + 0.25x + 4
A group of 3 children and 2 adults pay a total of $120 to take a karate class. A group of 5 children and 1 adult take the same karate class for $95. What is the total cost for 1 child and 1 adult to take the karate class?
$60
$55
$51
$48
Find an equation for the line with y-intercept 3 that is perpendicular to the line 3y = 2x - 4.
2y = 6 - 3x
2y = 3x + 6
3y = 9 - 2x
3y = 2x + 9
Which is the line parallel to the line y = 8x - 2?
y = 2x - 8
y = 1/8x + 3
y = 4 + 8x
y = 8x + 3
The sum of two binomials is 8x² - 6x. If one of the binomials is 3x² - 2x, what is the other binomial?
2x² - 4x
2x² - 8x
8x² - 4x
5x² - 4x
If f(x) = (3 - x²) / (3 - x), what is f(2)?
-2
-1
1
2
The equation of line j is 6x + 5y = 3, and the equation of line q is 5x - 6y = 0. Which statement about the two lines is true?
Lines j and q have the same y-intercept.
Lines j and q are parallel.
Lines j and q have the same x-intercept.
Lines j and q are perpendicular.
(4x² - 2x + 8) - (x² + 3x - 2) =
3x² + x + 6
3x² + x + 10
3x² - 5x + 6
3x² - 5x + 10
Which best represents the graph of y = 2x - 2?
Graph A
Graph B
Graph C
Graph D
The data in the table show the cost of renting a bicycle by the hour, including a deposit. If hours, h, were graphed on the horizontal axis, and cost, c, were graphed on the vertical axis, what would be the equation of a line that fits the data?
c = 5h
c = 1/5h + 5
c = 5h + 5
c = 5h - 5
Harry determined that every time he tapped his wand the sound increased 4 decibels. He noticed that after tapping his wand three times, the sound measured 34 decibels. Which equation best represents the sound when w represents a move of the wand and s represents the loudness of the sound?
s = 4w - 22
s = w + 22
s = 4w - 43
s = 4w + 22
The total cost f(d) in dollars of renting a sailboat for d days is given by the function f(d) = 120 + 60d. If the total cost was $360, for how many days, d, was the sailboat rented?
2
4
6
8
According to the graph, which statement best describes the slope?
As the distance traveled increases by 20, the amount of gas in the tank decreases by 3.
As the distance traveled increases by 3, the amount of gas in the tank increases by 20.
As the distance traveled increases by 30, the amount of gas in the tank increases by 2.
As the distance traveled decreases by 20, the amount of gas in the tank decreases by 3.
At what rate does Ryan write his composition?
0.5 sentence per minute
1 sentence per minute
1.5 sentences per minute
2 sentences per minute
Which of the following equations describes the same function in the table below?
y = 5x - 2
y = \frac{1}{5}x - 2
y = 5x + 2
y = 5x + 2
What is the slope of the equation 2x - 5y = 10?
-2
\frac{2}{5}
5
\frac{5}{2}
Brock is six feet tall. He climbs a ladder to paint some trim on his house. For each rung that he climbs, Brock is 1.2 feet higher above the ground. Which equation could you use to calculate the distance, d, from the top of Brock's head to the ground if r represents the number of ladder rungs he has climbed?
d = 1.2r + 6
d = 1.2r
d = r + 6
d = 6r + 1.2
If this trend continues, in which week will she give a 12-minute speech?
2
12
15
24
How many rosebushes will Dr. Chait have to buy from the Garden Club before he would begin to save money?
5
7
25
50
The side length of a square is 4x\frac{1}{2}y^{2} units. What is the area of the square?
Each month Jessie's phone bill includes a $25 basic fee plus a charge of $0.07 per minute for the number of minutes of long-distance calls she makes. Which equation best describes the total amount of Jessie's monthly phone bill, t, in terms of m, the number of minutes of long-distance calls she makes?
(a)
Shaniqua is constructing an isosceles triangle to use as a model in her Algebra class. The perimeter of her triangle is 24 inches. Shaniqua uses the equation s + s + b = 24 to find b, the length of the triangle's third side, in terms of s, the length of each of its two congruent sides. What is her equation for b in terms of s?
