The document provides an assessment review with multiple choice questions about math concepts like algebra, geometry, and coordinate planes. It includes 15 questions testing skills like simplifying expressions, solving equations, factoring polynomials, and graphing lines. The questions are formatted with explanations of steps required to arrive at the answers.
The questions have been designed to test for deep understanding of math concepts. Detailed explanations and solutions of these questions are also provided.
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2008. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
The questions have been designed to test for deep understanding of math concepts. Detailed explanations and solutions of these questions are also provided.
This is the entrance exam paper for ISI MSQE Entrance Exam for the year 2008. Much more information on the ISI MSQE Entrance Exam and ISI MSQE Entrance preparation help available on http://crackdse.com
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
1 Week 2 Homework for MTH 125 Name_______________AbbyWhyte974
1
Week 2 Homework for MTH 125
Name___________________________________ Date: ___July 20, 2021______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the equation by determining the missing values needed to plot the ordered pairs.
1) y + x = 3; ( 1, ), ( 3, ), ( 2, )
1) _______
A)
B)
C)
D)
2
Find the x- and y-intercepts. Then graph the equation.
2) 10y - 2x = -4
2) _______
A) ( -2, 0);
B) ; (0, -2)
3
C) ( 2, 0);
D) ; (0, 2)
Find the midpoint of the segment with the given endpoints.
4
3) ( 8, 4) and ( 7, 9) 3) _______
A) B) C) D)
Suppose that segment PQ has the given coordinates for one endpoint P and for its midpoint M. Find the coordinates
of the other endpoint Q.
4) P( 5, 5) and M 4) _______
A) Q( 4, 4) B) Q C) Q D) Q
Solve the problem.
5) The graphing calculator screen shows the graph of one of the equations below. Which equation is it?
5) _______
A) y + 3x = 15 B) y - 3x = 15 C) y = 3x + 3 D) y + 3x = 3
Find the slope.
6) m = 6) _______
A) -5 B) 5 C) 12 D) 8
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line
through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
7) ( -3, -5) and ( 4, -4) 7) _______
A) - ; falls B) - 7; falls C) 7; rises D) ; rises
Find the slope of the line.
5
8)
8) _______
A) B) C) - D) -
Find the slope of the line and sketch the graph.
9) 2x + 3y = 10
9) _______
A) Slope:
6
B) Slope: -
C) Slope: -
7
D) Slope:
Decide whether the pair of lines is parallel, perpendicular, or neither.
10) 3x - 4y = 12 and 8x + 6y = -9 10) ______
A) Parallel B) Perpendicular C) Neither
Choose the graph that matches the equation.
11) y = 2x + 4 11) ______
A)
B)
C)
8
D)
Find the equation in slope-intercept form of the line satisfying the conditions.
12) m = 2, passes through ( 6, -3) 12) ______
A) y = 2x - 15 B) y = 3x + 16 C) y = 2x - 13 D) y = 2x + 14
Write the equation in slope-intercept form.
13) 17x + 5y = 7 13) ______
A) y = x + B) y = 17x - 7 C) y = - x + D) y = x -
Find the slope and the y-intercept of the line.
14) 7x + 5y = 48 14) ______
A) Slope - ; y-intercept B) Slope ; y-intercept
C) Slope ; y-intercept D) Slope - ; y-intercept
Find an equation of the line that satisfies the conditions. Write the equation in standard form.
9
15) Through ( 5, 4); m = - 15) ______
A) 4x - 9y = 56 B) 4x + 9y = -56 C) 4x + 9y = 56 D) 9x + 4y = -56
...
enjoy the formulas and use it with convidence and make your PT3 AND SPM more easier..togrther we achieve the better:)
good luck guys and girls...simple and short ans also sweet formulas..
Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
B_W3: Quiz #1
Graphing Exponential Growth & Decay (15 questions)
1.
Which of the following is an example of an exponential function?
A.
f(x) = 4
B.
f(x) = 4x
C.
D.
f(x) = 6x
2.
Which of the following is an exponential decay function?
A.
B.
C.
D.
3.
The graph of has _______.
A.
an asymptote at x = 0.
B.
no asymptotes.
C.
an asymptote at y = 0.
D.
an asymptote at y = x.
4.
The graph of shifts the graph of _______ .
A.
left 1 unit
B.
right 1 unit
C.
up 1 unit
D.
down 1 unit
5.
Which exponential function matches the graph?
A.
B.
C.
D.
6.
Which is the graph of ?
A.
B.
C.
D.
7.
Which is the graph of ?
A.
B.
C.
D.
8.
Which exponential function matches the graph?
A.
B.
C.
D.
9.
What is the equation of the following graph?
A.
f(x) = 2x + 2
B.
f(x) = 2x - 2
C.
f(x) = 2x - 2
D.
f(x) = 2x + 2
10.
What is the equation of the following graph?
A.
f(x) = 2x + 7
B.
f(x) = 2x - 7
C.
f(x) = 2x - 7
D.
f(x) = 2x + 7
11.
What is the transformation that occurs to the equation y = 2x if it changes to y = 2x + 5?
A.
The graph moves 5 units to the left.
B.
The graph moves 5 units to the right.
C.
The graph moves 5 units down.
D.
The graph moves 5 units up.
12.
What is the transformation that occurs to the equation y = 2x if it changes to y = 2x-3?
A.
There is a transformation of 3 units to the right.
B.
There is a transformation of 3 units to the left.
C.
There is a transformation of 3 units up.
D.
There is a transformation of 3 units down.
13.
What is the transformation that occurs to the parent function if the equation changes to ?
A.
The graph moves 1 unit up.
B.
The graph reflects across the y-axis.
C.
The graph reflects across the x-axis.
D.
The graph moves 1 unit down.
14.
What is the transformation that occurs to the equation y = 2x if the equation changes to y = 2x-3 + 4?
A.
The transformation moves the graph 3 units to the right and 4 units down.
B.
The transformation moves the graph 3 units to the left and 4 units up.
C.
The transformation moves the graph 3 units to the left and 4 units down.
D.
The transformation moves the graph 3 units to the right and 4 units up.
15.
What is the transformation that occurs to the equation y = 2x if it changes to y = -2x – 2?
A.
The graph is reflected across the y-axis and moves 2 units up.
B.
The graph is reflected across the x-axis and moves 2 units up.
C.
The graph is reflected across the x-axis and moves 2 units down.
D.
The graph is reflected across the y-axis and moves 2 units down.
B_W3 Quiz #2
Solving Exponential Equations (10 questions)
1. Determine the value for the "?" 4?=64
A.
16
B.
3
C.
4
D.
12
2. Solve 3x+1 = 37
A.
x = 3
B.
x = 7
C.
x = 6
D.
x = 1
3. Solve:
A.
x = -4
B.
x = -2
C.
x = -5
D.
x = -10
4. What is the next step in t ...
Mid-Term Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Fill in the blank with one of the words or phrases listed below.
distributive real reciprocals absolute value opposite associative
inequality commutative whole algebraic expression exponent variable
1) The of a number is the distance between the number and 0 on the number line.
A) opposite B) whole
C) absolute value D) exponent
1)
Find an equation of the line. Write the equation using function notation.
2) Through (1, -3); perpendicular to f(x) = -4x - 3
A) f(x) =
1
4
x -
13
4
B) f(x) = -
1
4
x -
13
4
C) f(x) = -4x -
13
4
D) f(x) = 4x -
13
4
2)
Multiply or divide as indicated.
3)
60
-5
A) -22 B) 12 C) - 1
12
D) -12
3)
Write the sentence using mathematical symbols.
4) Two subtracted from x is 55.
A) 2 + x = 55 B) 2 - x = 55 C) x - 2 = 55 D) 55 - 2 = x
4)
Name the property illustrated by the statement.
5) (-10) + 10 = 0
A) associative property of addition B) additive identity property
C) commutative property of addition D) additive inverse property
5)
Tell whether the statement is true or false.
6) Every rational number is an integer.
A) True B) False
6)
Add or subtract as indicated.
7) -5 - 12
A) 7 B) -17 C) 17 D) -7
7)
1
Name the property illustrated by the statement.
8) (1 + 8) + 6 = 1 + (8 + 6)
A) distributive property
B) associative property of addition
C) commutative property of multiplication
D) associative property of multiplication
8)
Simplify the expression.
9) -(10v - 6) + 10(2v + 10)
A) 30v + 16 B) -10v + 94 C) 10v + 106 D) 30v + 4
9)
Solve the equation.
10) 5(x + 3) = 3[14 - 2(3 - x) + 10]
A) -39 B) 3 C) -13 D) 39
10)
List the elements of the set.
11) If A = {x|x is an odd integer} and B = {35, 37, 38, 40}, list the elements of A ∩ B.
A) {35, 37}
B) {x|x is an odd integer}
C) {x|x is an odd integer or x = 38 or x = 40}
D) { }
11)
Solve the inequality. Graph the solution set.
12) |x| ≥ 4
A) (-∞, -4] ∪ [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
B) [-4, 4]
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
C) [4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
D) (-∞, -4) ∪ (4, ∞)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
12)
Solve.
13) The sum of three consecutive even integers is 336. Find the integers.
A) 108, 110, 112 B) 110, 112, 114 C) 112, 114, 116 D) 111, 112, 113
13)
2
Solve the inequality. Write your solution in interval notation.
14) x ≥ 4 or x ≥ -2
A) (-∞, ∞) B) [4, ∞)
C) [-2, ∞) D) (-∞, -2] ∪ [4, ∞)
14)
Use the formula A = P 1 + r
n
nt
to find the amount requested.
15) A principal of $12,000 is invested in an account paying an annual interest rate of 4%. Find the
amount in the account after 3 years if the account is compounded quarterly.
A) $1521.9 B) $13,388.02 C) $13,498.37 D) $13,521.90
15)
Graph the solution set ...
MATH 107 FINAL EXAMINATIONMULTIPLE CHOICE1. Deter.docxTatianaMajor22
MATH 107 FINAL EXAMINATION
MULTIPLE CHOICE
1. Determine the domain and range of the piecewise function.
A. Domain [–2, 2];
B. Domain [–1, 1];
C. Domain [–1, 3];
D. Domain [–3/2, –1/2];
2. Solve:
A. 3
B. 3,7
C. 9
D. No solution
3. Determine the interval(s) on which the function is increasing.
A. (−1.3, 1.3)
B. (1, 3)
C. (−∞,−1)and (3,∞)
D. (−2.5, 1)and (4.5,∞)
4. Determine whether the graph of y = 2|x| + 1 is symmetric with respect to the origin,
the x-axis, or the y-axis.
A. symmetric with respect to the origin only
B. symmetric with respect to the x-axis only
C. symmetric with respect to the y-axis only
D. not symmetric with respect to the origin, not symmetric with respect to the x-axis, and
not symmetric with respect to the y-axis
5. Solve, and express the answer in interval notation: | 9 – 7x | ≤ 12.
A. (–∞, –3/7]
B. (–∞, −3/7] ∪ [3, ∞) C. [–3, 3/7]
D. [–3/7, 3]
6. Which of the following represents the graph of 7x + 2y = 14 ?
A. B.
C. D.
7. Write a slope-intercept equation for a line parallel to the line x – 2y = 6 which passes through the point (10, – 4).
A.
B.
C.
D.
8. Which of the following best describes the graph?
A. It is the graph of a function and it is one-to-one.
B. It is the graph of a function and it is not one-to-one.
C. It is not the graph of a function and it is one-to-one.
D. It is not the graph of a function and it is not one-to-one.
9. Express as a single logarithm: log x + log 1 – 6 log (y + 4)
A.
B.
C.
D.
10. Which of the functions corresponds to the graph?
A.
B.
C.
D.
11. Suppose that a function f has exactly one x-intercept.
Which of the following statements MUST be true?
A. f is a linear function.
B. f (x) ≥ 0 for all x in the domain of f.
C. The equation f(x) = 0 has exactly one real-number solution.
D. f is an invertible function.
12. The graph of y = f(x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f(x)?
y = f (x) y = g(x)
A. g(x) = f (x – 3) + 1
B. g(x) = f (x – 1) + 3
C. g(x) = f (x + 3) – 1
D. g(x) = f (x + 1) .
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
4. 2) Complete the function table below with the missing values for y. Based on the function table, write a function rule that shows the relationship between x and y. Answer ___________ y = m x + b 19 23 4 1 y = 4 x + ? 0 b y = 4 x + -1 y = 4 x + -1 -1 Bring x back to 0 .
5.
6. 4) Plot the ordered pairs from the table onto the graph paper below. Then draw a line segment connecting the points. Line Segment: No Arrows Need to Label Graph Pool Being Filled 160 180 Time (min) Water (gal) 180 160 140 120 100 80 60 40 20 0 0 1 2 3 4 5 6 7 8
7. 5) Graph the line with equation y = 2x – 3. a) Slope: m = 2 b) y-intercept: b = -3
8. 6) Given the linear equation, y = -2x + 3, identify the slope and y-intercept. m = ________ b = ________ Coordinates of y-intercept: _______ What does the slope tell you? _____________________________ What does the y-intercept tell you? Down 2 to the Right 1 -2 3 (0,3) Point where line crosses y-axis
9. A) 2 - 6 h B) 2h - 6 C) 6 - 2h D) 6h - 2 7) This month, Drew worked six hours less than twice the number of hours, h , he worked last month. What expression represents the number of hours Drew worked this month? 6 - 2h LESS THAN REVERSE ORDER 6 - 2h
10. 8) Luisa works in her grandfather’s jewelry shop. She deposits her earnings in a savings account. Her savings account balances for five of the last six weeks are shown in the function table below. Part A: According to the data in the function table, write a function rule that shows how much money Luisa saves each week. Rule ______________ y = m x + b y = 110 x + ? y = 110 x + 400 b = 110 w + 400 110 1 b x y Don’t forget to change equation using b and w !!! 0 400 Week (w) Savings Balance (b) 1 $510 2 $620 3 $730 4 $840 5 ? 6 $1,060
11. 8) Part B Based on the table, how much money is in Luisa’s savings account in week 5? Show Work Answer $__________ 950 b = 110 w + 400 Plug in w =5 b = 110(5) + 400 b = 550 + 400 b = 950 950 Week (w) Savings Balance (b) 1 $510 2 $620 3 $730 4 $840 5 ? 6 $1,060 840 +110 950
12. 9) Find the greatest common factor (GCF) of 12x and (4x 2 + 8x). GCF: 4: 1, 4 12: 1, 2, 3, 4, 6, 12 8: 1,2,4,8 GCF: x: x x 2 : x x x: x GCF: 4x
13. 10) Steve drew figure ABCD. He plans to create figure A'B'C'D' by reflecting it over the x-axis. Label the new figure A'B'C'D‘. What are the coordinates of A’? ________ D’ A’ B’ C’ (-9,-7)
14. A dd M ultiply Multiply to +8 (1)(8) (2)(4) (-1)(-8) (-2)(-4) 11) Factor into two binomials Step #1 Step #2 Step #3 (x +4 )(x +2 ) or (x +2 )(x +4 ) Which pair adds up to +6?
15. 12) In the diagram below, line f and line h are parallel, and line n is a transversal. a) Name two angles that are vertical angles. b) Name two angles that are corresponding angles. c) Name two angles that are alternate interior angles. 5 and 8 6 and 7 2 and 6 4 and 8 4 and 5 3 and 6
16. 13) Graph a line with the given values. x -4 -2 0 4 y 0 1 2 4
18. 1) Which figure below shows a reflection? Rotation Translation Translation Reflection
19. 2) Gary drew a triangle on the coordinate grid shown below. If Gary reflects the triangle in the y-axis, what will be the new coordinates of the vertices of the triangle? Which figure below shows a reflection? A) (-1, -1), (4, -3), (-5, 1) B) (-1, -1), (-4, -3), (-5, -1) C) (-1, 1), (-4, 3), (5, -1) D) (1, 1), (4, 3), (5, 1)
20. 3) Triangle ABC and triangle A’ B’C’ are plotted on the coordinate plane below. What is the name of the transformation applied to triangle ABC that resulted in triangle A’B’C’? A’B’C is a reflection over the y-axis.
21. 4) Which property does the equation below demonstrate? 7(x - 4) = 7x - 28 A) Associative B) Commutative C) Distributive D) Identity 7(x) 7(-4) +
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23. A) 4k + 5 B) 5k - 4 C) 5k + 4 D) 5k(k + 4) 6) Cindy has four more than five times as many cousins as Kathy, k. Which expression represents how many cousins Cindy has compared with Kathy? 4 + 5x 4 + 5k or 5k + 4
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25. 8) Melissa drew the shape on the grid shown below. Draw the reflection of this shape in the x-axis. Label the coordinates of each point on the new figure. Explain how you determined the reflection of the shape. (4,-2) (6,-6) (4,-8) (2,-6) I counted how many boxes each point was away from the x-axis. I then counted that many boxes on the other side of the x-axis. I plotted the new point. OR I kept the same x-coordinate and negated the y-coordinate for each point. 2 boxes to x-axis 2 boxes away from x-axis 6 boxes to x-axis 6 boxes away from x-axis
26. 9) A translation has the rule (x- 2, y+1). If the point R at ( 7 , -4 ) is put through the translation, what are the coordinates of its image location at R’? (x – 2, y + 1) R’( 7 – 2 , -4 + 1) R’( 5 , -3
27. 10) Shawn drew figure ABCD. He plans to create figure A'B'C'D' by translating figure ABCD 6 units down and 4 units to the right. On the coordinate plane below, draw and label Shawn's figure A'B'C'D'. (MARCH 2009) D’ A’ B’ C’ Next Shawn plans to create a figure A”B”C”D” by translating figure A’B’C’D’ 2 units up and 8 units to the right. What will be the coordinates of point A’’? A’’(3,3) A’’(3,3)
28. 11) Simplify. (3x 2 y 3 )(-4xy -4 ) (3)(-4)= -12 x 2 x= x 3 y 3 y -4 =y -1 -12x 3 y -1 Explain using the laws of exponents how you arrived at your answer. I multiplied 3 & -4 and got -12. I multiplied powers by keeping base and adding the exponents.
29. A dd M ultiply Multiply to -12 (1)(-12) (2)(-6) (3)(-4) (-1)(12) (-2)(6) (-3)(4) 12) Factor into two binomials Step #1 Step #2 Step #3 (x +3 )(x -4 ) or (x -4 )(x +3 ) Which pair adds up to -1?
30. 13) Find the product of the two binomials (x – 6) and (3x + 7) 3x 2 -18x +7x - 42 3x x +7 -6 3x 2 3x 2 - 11x - 42 +7x -18x -42 Multiply (x - 6)(3x + 7)
31. A) 2 + d – 3 B) 3 + d – 2 C) 2d – 3 D) 3 – 2d 14) Janine’s dog weighs three pounds less than twice the weight of Wanda’s dog, d. Which expression represents the weight of Janine’s dog? 3 - 2d LESS THAN REVERSE ORDER 3 - 2d
32. 15) Erika is assigned to graph the line of the equation y = 2x+1. Use Erika’s equation to complete the table below for the given values of x. Using the information from the table, graph the line of the equation y =2x+1 on the coordinate plane below. Be sure to plot all points from the table and draw a line connecting the points. y=2x+1 x y -2 -3 -1 -1 0 1 2 5 4 9
36. 3) Solve for x in the equation below. 2(x + 6) = 8x - 42 Show your work. Answer __________ USE CALCULATOR!! 6 6 x = 9 2x +12 = 8x - 42 2(x + 6) = 8x - 42 +12 = 6x - 42 54 = 6x Multiply Cancel 2x x = 9 -2x -2x +42 +42 Cancel -42 x + 6 2 2x +12 Distribute
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40. Always smallest exponent GCF: 6 (Biggest) Second: List factors of x 3 and x 4 x 3 : x x x x 4 : x x x x GCF: 6x 3 7) What is the greatest common factor of 18x 3 and 24x 4 ? GCF: x 3 First: List factors of 18 and 24 18: 1, 2, 3, 6, 9, 18 24: 1, 2, 3, 4, 6, 8,12, 24
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44. 11) Factor the expression below using the greatest common factor (GCF). 18n 6 – 12n 4 + 6n A) 6n(3n 5 -2n 3 + 1) B) 6n(3n 5 -2n 3 + n) C) 6n(12n 6 -6n 3 + 1) D) 6n(12n 6 -6n 3 + n) GCF: 18:1, 2, 3, 6, 9, 18 12: 1, 2, 3, 4 ,6, 12 6: 1, 2, 2, 3, 6 GCF: n 6 : n ,n , n , n ,n ,n n 4 : n ,n ,n ,n n: n You can check by multplying answer out GCF: 6n 3n( ? ) =18n 6 -12n 4 +3n
47. 14) Complete the table of values given the line below. (-2,-1) -1 0 2 (0,0) (2,1) (6,3) 6 4 (8,4) x y -2 0 1 3 8
48. 15) In the diagram below, line f and line h are parallel, and line n is a transversal. a) Name two angles that are vertical angles. b) Name two angles that are corresponding angles. c) Name two angles that are alternate interior angles. 5 and 8 6 and 7 2 and 6 4 and 8 4 and 5 3 and 6
50. 1) What is 18a 11 b 7 divided by 3a 3 b? Dividing Powers Keep Base & Subtract Exponents “ I divided 18 by 3 to get 6. When dividing powers with same base you keep the base and subtract the exponents.”
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52. 3) Which expression is equivalent (14a - 4a) + (5a -3a)? Combine Like Terms 10a + 2a (14a- 4a) + (5a – 3a) 12a
53. 4) Simplify the expression 3x 2 +4x - 3 + -2x + 1 -2 3 x 2 +2 x Rewrite without Parenthesis 3x 2 4x -2x -3 +1 Need to show how signs change!
54. 5) Simplify the expression. (x 3 y 2 )(xy 4 ) x 4 y 6 MULTIPLY Powers Keep Base & Add Exponents
55. 6) Simplify the expression. 5 7 5 2 5 9 MULTIPLY Powers Keep Base & Add Exponents
56. 7) Simplify the expression. Dividing Powers Divide Coefficients. Keep Base & Subtract Exponents “ I divided 3 by 6 to get ½ . When dividing powers with same base you keep the base and subtract the exponents.”
57. 8) Simplify the expression below . A) 9a 2 b B) 9a 4 b 2 C) 18a 2 b D) 18a 4 b 2 Combine Like Terms 3a 2 b + 6a 2 b 9a 2 b
58. 9) Simplify the expression 3a 2 + a – 7 + 9a 2 + 3a – 4 -3 -6 a 2 - 2 a Rewrite without Parenthesis + – – 3a 2 +a – 7 - 9a 2 -3a +4 3a 2 -9a 2 +a -3a - 7 +4
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60. 11) On the coordinate plane below, draw the image of polygon ABCDE translated 8 units to the right and 4 units up. Label the image A'B'C'D'E'. (MARCH 2008) SLIDE!!! A’ B’ E’ D’ C’
61. 12) Write an equation that represents the table below. Answer ___________ y = m x + b +3 +2 x y -2 -5 0 -2 2 1 4 4 Wh y is “ y ” on top?
62. 13) Using the slope formula, , find slope of the line given two points A(3,4) and B(-3,-2). Show Work Slope: ____ Describe the slope: 1 Up 1 to the right 1 Wh y is “ y ” on top?
63. 14) Given the linear equation, y + 2x = 7, identify the slope and y-intercept. m = ________ b = ________ Coordinates of y-intercept: _______ What does the slope tell you? _____________________________ What does the y-intercept tell you? Down 2 to the Right 1 -2 7 (0,7) Point where line crosses y-axis -2x -2x y = -2x + 7