This is the course or teachers in Indonesia on number sense for Primary 4 to 6. It covers place values, regrouping, large number multiplication and division and some ideas on estimation and multiples.
Pre-Calculus Quarter 4 Exam
1
Name: _________________________
Score: ______ / ______
1. Find the indicated sum. Show your work.
2. Locate the foci of the ellipse. Show your work.
𝑥2
36
+
𝑦2
11
= 1
Pre-Calculus Quarter 4 Exam
2
3. Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4. Graph the function. Then use your graph to find the indicated limit. You do not have to
provide the graph
f(x) = 5x - 3, f(x)
5. Use Gaussian elimination to find the complete solution to the system of equations, or state
that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
Pre-Calculus Quarter 4 Exam
3
6. Solve the system of equations using matrices. Use Gaussian elimination with back-
substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per
minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336
calories in her workout. Write an inequality that describes the situation. Let x represent the
number of minutes running and y the number of minutes swimming. Because x and y must be
positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that
each of these statements is true. Show your work.
Sn: 1
2
+ 4
2
+ 7
2
+ . . . + (3n - 2)
2
=
𝑛(6𝑛2−3𝑛−1)
2
Pre-Calculus Quarter 4 Exam
4
9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying
Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and
70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast
blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea
and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade
tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on
each pound of the afternoon blend, how many pounds of each blend should she make to
maximize profits? What is the maximum profit?
11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86
and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a
$35 profit on each one. You expect to sell at least 100 laser printers this month and you need to
make at least $3850 profit on them. How many of what type of p
Pre-Calculus Quarter 4 Exam
Name: _________________________
Score: ______ / ______
1.
Find the indicated sum. Show your work.
2.
Locate the foci of the ellipse. Show your work.
3.
Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4.
Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph
f(x) = 5x - 3, f(x)
5.
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
6.
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8.
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 12 + 42 + 72 + . . . + (3n - 2)2 =
9.
A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10.
Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit?
11
Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?
12
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2 + 5 + .
Support your children's understanding of this important topic by using the quality resources in our Money Pack! Includes a wide variety of teaching, activity and display resources based on a number of different currencies used around the world.
Available from https://www.teachingpacks.co.uk/the-money-pack/
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
This is the course or teachers in Indonesia on number sense for Primary 4 to 6. It covers place values, regrouping, large number multiplication and division and some ideas on estimation and multiples.
Pre-Calculus Quarter 4 Exam
1
Name: _________________________
Score: ______ / ______
1. Find the indicated sum. Show your work.
2. Locate the foci of the ellipse. Show your work.
𝑥2
36
+
𝑦2
11
= 1
Pre-Calculus Quarter 4 Exam
2
3. Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4. Graph the function. Then use your graph to find the indicated limit. You do not have to
provide the graph
f(x) = 5x - 3, f(x)
5. Use Gaussian elimination to find the complete solution to the system of equations, or state
that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
Pre-Calculus Quarter 4 Exam
3
6. Solve the system of equations using matrices. Use Gaussian elimination with back-
substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per
minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336
calories in her workout. Write an inequality that describes the situation. Let x represent the
number of minutes running and y the number of minutes swimming. Because x and y must be
positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that
each of these statements is true. Show your work.
Sn: 1
2
+ 4
2
+ 7
2
+ . . . + (3n - 2)
2
=
𝑛(6𝑛2−3𝑛−1)
2
Pre-Calculus Quarter 4 Exam
4
9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying
Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and
70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast
blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea
and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade
tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on
each pound of the afternoon blend, how many pounds of each blend should she make to
maximize profits? What is the maximum profit?
11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86
and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a
$35 profit on each one. You expect to sell at least 100 laser printers this month and you need to
make at least $3850 profit on them. How many of what type of p
Pre-Calculus Quarter 4 Exam
Name: _________________________
Score: ______ / ______
1.
Find the indicated sum. Show your work.
2.
Locate the foci of the ellipse. Show your work.
3.
Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4.
Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph
f(x) = 5x - 3, f(x)
5.
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
6.
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8.
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 12 + 42 + 72 + . . . + (3n - 2)2 =
9.
A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10.
Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on each pound of the afternoon blend, how many pounds of each blend should she make to maximize profits? What is the maximum profit?
11
Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?
12
A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2 + 5 + .
Support your children's understanding of this important topic by using the quality resources in our Money Pack! Includes a wide variety of teaching, activity and display resources based on a number of different currencies used around the world.
Available from https://www.teachingpacks.co.uk/the-money-pack/
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
3. Learning Objective-To add amounts of money.
Success Criteria –
I can identify different denominations of UK currency.
I know I pound = 100 pence.
I can add pounds and pence.
I can solve word problems on money.
Week – 3 (17th -21st Jan)
NC Goals-Adds and subtracts amounts of
money to give change, using both £ and p in
practical contexts.
5. Money
a. What do you know about
money?
b. How is money important in your
life.
c. How would the world be if there
was no money?
d. What are the different
currencies you kow?
7. Remember
£ 1 = 100 pence
£ 2 = 200 pence
50 p + 50 p = 100 pence (£ 1 )
£ 1 + 20 p = £ 1.20 or 120p
(100p + 20p= 120p)
8. Keep the UK currency- pounds & pence ( money)
from your math resource pack ready with you.
Those who don’t have can print & cut the sheet of
UK currency uploaded on Class material.
Your math teacher will ask you to show
any 2 or 3 coins and add them & write
the total amount.
14. Collaborative Task -1
According to Neha amount B
is more than amount A . Is she
correct?
= 55p
2 4 7
Amount A is £1.01 and amount B
is 98p.
Yes, Neha is correct because
amount A is more than amount B.
15. Collaborative Task -1
You will get some coins &
2 objects with price
written on them.
1. Count the money &
write the amount in
pounds & pence.
2. If you had to buy any
1 object given, what
amount will be left
with you?
According to Neha amount B is
more than amount A . Is she
correct?
17. Collaborative Task -2
You will get some coins &
2 objects with price
written on them.
1. Count the money &
write the amount in
pounds & pence.
2. If you had to buy
both the objects
given, what amount
will be left with you?
How much
money does
Sofia have?
Power Math 3B pg-70
18. Collaborative Task -3
You will get some coins & 2
objects with price written
on them.
1. Count the money &
write the amount in
pounds & pence.
2. Which object would
you buy so that you
save more money?
Sofia is trying to make £ 1 with different
coins. Complete the table.
£1
50p 50p
Power Math 3B pg-71
19. Plenary
Log on to Education city and complete the task
assigned as classwork
Title– Till We Meet Again.
