021 lesson 11
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The document discusses various properties of multiplication, including: 1) The identity property where multiplying any number by 1 leaves the number unchanged. 2) The zero property where multiplying any number by 0 equals 0. 3) The commutative property where changing the order of factors does not change the product. It provides examples to illustrate each property and a worksheet for students to practice applying the properties.
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There are 30 problems.
Problems #1-12 are multiple choice. Record your choice for each problem.
Problems #13-21 are short answer. Record your answer for each problem.
Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.
(
Please sign (or type) your name below the following honor statement:
I have completed this
final examination
myself,
working independently and not consulting anyone except the instructor.
I have neither given nor received help on this final examination.
Name ____________
______
___
Date___________________
)
MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13.
14.
15.
16.
17.
18.
19. (a)
(b)
(c)
20. (a)
(b)
(c)
(d)
21. (a)
(b)
(c)
(d)
SHORT ANSWER with Work Shown. Record your answers and work.
Problem Number
Solution
22
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):
23
Answers:
(a)
(b)
(c)
Work for part (a):
24
Answer:
Work:
25
Answer:
Work:
26
Answers:
(a)
(b)
Work for part (a) and for part (b):
27
Answer:
Work:
28
Answer:
Work:
29
Answers:
(a)
(b)
Work for (b):
30
Answer:
Work:
College Algebra MATH 107 Summer, 2015, V1.4
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required t ...
E2
This document provides an overview of exponent rules, including:
- When multiplying or dividing terms with the same base, you add or subtract their exponents respectively
- When raising a power to another power, you multiply the exponents
- A product or quotient raised to a power means each term is raised to that power
- A number raised to the zero power is equal to 1, except for 0 raised to zero which is undefined
- A negative exponent flips the term with that exponent to the denominator
Several examples are given to demonstrate each rule and mixed practice problems are provided for application.
Write solution for these problems -Is targeting only mommy blo.docx
Write solution for these problems
-Is targeting only mommy bloggers is a good idea and why?
-how would J&J guarantee that these bloggers won't give a bad feedback?
-if J&J announced about their product only through social media, then how would it reach the other people who don't use social media?
-do you see any value in offering this type of incentive for the users? or, is all the benefit for the company only?
MATH 115 Precalculus Fall, 2018, V1.4
Page 1 of 7
MATH 115 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 28 problems.
Problems #1–6 are Multiple Choice.
Problems #7–17 are Short Answer. (Work not required to be shown)
Problems #18–28 are Short Answer with work required to be shown.
MULTIPLE CHOICE
1. Solve | 7 – 5x | 8 and write interval notation for the solution set. 1. _______
A. (−∞, −
1
5
] ∪ [3, ∞)
B. (−∞, 3] ∪ [−
1
5
, ∞)
C. [−
1
5
, ∞)
D. [−
1
5
, 3]
2. Which of the following polynomials has a graph which exhibits the end behavior of
upward to the left and upward to the right? 2. ______
A. f (x) = x3 – 3x2 – x
B. f (x) = 3x6 + x2 – x
C. f (x) = –7x4 – x3 – 5
D. f (x) = –6x5 + x3 + 8
3. Write as an equivalent expression: 9 log x – log (y + 3) + log 1 3. _______
A.
9
log
log ( 3)
x
y +
B. ( )log 9 2x y− −
C.
9 1
log
3
x
y
+
+
D.
9
log
3
x
y
+
vvvv
MATH 115 Precalculus Fall, 2018, V1.4
Page 2 of 7
4. Determine the interval(s) on which the function is decreasing. 4. ______
A. (–, –3.5) (0, 3.5)
B. (– 5.3, 5.3)
C. (– 3.5, 3.5)
D. (– 2, 2)
5. Which of the functions corresponds to the graph? 5. ______
A. ( ) 1xf x e−= +
B. ( ) 2xf x e−= +
C. ( ) 2xf x e−=
D. ( ) 2 xf x e−=
MATH 115 Precalculus Fall, 2018, V1.4
Page 3 of 7
6. Which of the functions corresponds to the graph? 6. ______
A. f (x) = 3 – sin x
B. f (x) = sin x + 3
C. f (x) = 2 cos x + 1
D. f (x) = cos(2x) + 2
SHORT ANSWER:
7. Points (–9, 2) and (–5, 8) are endpoints of the diameter of a circle.
(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________
(b) What is the center of the circle? Answer: ____________
(c) What is the equation of the circle? Answer: ___________________________
8. Find the value of the logarithm: log8 (
1
64
). Answer: ____________
9. A salesperso.
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041 about the authors
Adriel G. Roman and Myrichel Alvarez are students at Laguna State Polytechnic University studying Bachelor of Secondary Education with a specialization in Mathematics. Adriel finished elementary school in Caloocan and high school in Balian. Myrichel completed elementary and high school in Siniloan, Laguna, where she is now studying at the university.
039 references
The document lists 12 image sources from websites like Google, Yahoo, and search engines for pictures and clip art related to mathematics, cartoons, and Looney Tunes characters. Book references are also provided on basic mathematics and algebra textbooks. The sources range from 2009 to 2010.
038 math and technology
The document presents a series of math puzzles that involve using a calculator to reveal letters, words, or answers to questions. The puzzles direct the reader to perform various math operations like division and addition on calculators, then turn the calculators upside down to view letters or numbers that spell out a word or provide an answer. It includes 7 puzzles for the reader to solve that follow this format of using a calculator to reveal a hidden message or response through mathematical calculations.
036 lesson 24
The document discusses the rules for dividing integers. It states that if both integers have the same sign, divide the absolute value of the first integer by the absolute value of the second integer. If the integers have different signs, divide the absolute value of the first integer by the absolute value of the second integer and assign the result a negative sign. It provides examples to illustrate these rules and a worksheet for students to practice dividing integers.
035 lesson 23
The document discusses the rules for multiplying integers. It states that if two integers have the same sign, their product is positive, and if they have opposite signs, their product is negative. It also notes that if one or both integers being multiplied is 0, the product is 0. Examples are provided to illustrate multiplying integers with the same sign, opposite signs, and where one factor is 0. The rules are then generalized to multiplying more than two integers. An example problem demonstrates multiplying several integers together and determining the sign of the product based on the number of negative factors.
034 lesson 22
This document discusses subtracting integers and provides examples of how to perform integer subtraction. It explains that to subtract an integer, you convert the subtracted integer to its opposite and add the two numbers. It then gives several practice problems for students to solve by subtracting integers.
033 lesson 21
The document provides lesson objectives and rules for adding integers:
1) When adding integers with the same sign, add their absolute values and use the same sign for the result.
2) When adding integers with opposite signs, take the absolute values, subtract the smaller from the larger, and use the sign of the integer with the larger absolute value for the result.
3) The sum of any integer and its opposite integer is always zero.
032 lesson 20
The document defines integers as natural numbers including zero and their negatives. It explains that positive integers are whole numbers greater than zero, while negative integers are the opposites of positive integers. The number line is used to demonstrate that integers increase from left to right and how the absolute value of a number is always positive or zero.
031 chapter v
This document introduces the next chapter on integers in a math workbook. It explains that the chapter will provide an in-depth understanding of integers, including the different types of integers, how they are used in math, and their real-world applications. It notes that integers are a fundamental part of high school math and that the reader has mastered the foundational whole number operations to now move on to applying those same operations with integers.
030 unit ii
This unit overview discusses fundamental integer operations, including the four basic arithmetic operations (addition, subtraction, multiplication, division) and order of operations. The objectives are for students to discuss integers, perform the four operations on integers, appreciate integers, gain knowledge about integers to prepare for algebra, and discuss order of operations. This unit contains lessons to skillfully perform integer operations and critically think through exercises to solve.
029 lesson 19
The ski resort sold a total of 111,359 day ski tickets in January. To calculate the average number of tickets sold per day, the total number of tickets was divided by 31, the number of days in January. The average number of tickets sold per day was 3,589.
028 lesson 18
The document provides instructions on dividing whole numbers using the method of cancelling insignificant zeros. It defines cancelling insignificant zeros as removing the same number of trailing zeros from both the dividend and divisor when performing long division. The document includes examples of cancelling zeros when dividing numbers such as 300/100, 2500/100, and 38175/638175. It then provides a 20 question worksheet for students to practice dividing numbers using this method.
026 lesson 16
This document defines division and its key components. It discusses division as the inverse of multiplication, with division being described as repeated subtraction and multiplication as repeated addition. Examples are provided to illustrate division with a dividend, divisor, and quotient. Special cases of division by 1 and 0 are also explained. Division by 0 is said to be impossible.
025 chapter iv
Division is one of the fundamental mathematical operations that is explained in this chapter. It will cover the different parts of division and how it can be used to solve word problems. Mastering division is an important part of learning mathematics.
024 lesson 15
The document provides examples of word problems involving multiplication to calculate quantities over time or between groups. It gives step-by-step work for problems such as calculating the number of screws a machine can produce in an hour given its 1-minute rate, or the number of radios a store has if it bought a certain number of crates each containing a set quantity. The document includes practice problems for students to solve using multiplication, such as calculating total seats in a stadium based on the number of sections and rows.
022 lesson 13
This lesson introduces the "99 multiplier" shortcut for multiplying whole numbers mentally. It works by annexing zeros to the multiplicand equal to the number of 9s in the multiplier, then subtracting the original multiplicand. Examples show 999×364 equals 364,000 minus 364, which is 369,636. The lesson aims to help students appreciate exploring multiplication and the multiplication operation.
023 lesson 14
This lesson teaches students about multiplying numbers with factors that are powers of ten. It explains that when multiplying numbers where one factor is a power of ten, such as 10, 100, 1000, students should multiply the non-zero digits and add the appropriate number of zeros to the product based on the power of ten. Some examples are provided. It also notes that when both factors end in zeros, students should multiply the significant digits and use the total number of zeros in both factors for the product. A worksheet with practice problems is included for students.
021 lesson 12
Lesson 12 aims to teach students how to multiply whole numbers quickly and correctly. It introduces multiplication as a shortcut for repeated addition and shows students how to use a multiplication table to solve problems efficiently. Students are given examples and a worksheet to practice their multiplication skills. The objectives are for students to multiply whole numbers easily, develop speed in multiplication, and perform multiplication accurately.
020 lesson 10
The document defines multiplication as repeated addition. It provides an example of 3 x 5 being solved by adding 5 three times to get 15. The document identifies the terms in a multiplication problem, with the number on top called the multiplicand and on bottom called the multiplier, and the answer called the product. It includes a worksheet for students to identify terms in multiplication problems and calculate products.
019 chapter iii
This chapter teaches students about multiplication, including its parts, methods for solving multiplication problems, and how to apply multiplication to word problems. Lessons and exercises are provided to help students master multiplying whole numbers.
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021 lesson 11
- 2. develop the knowledge in the properties of multiplication;
- 3. apply the properties of multiplication in solving problem.