1. This document contains 12 math word problems divided across 5 worksheets. The problems cover topics like derivatives, limits, probability, complex numbers, trigonometry and sequences and series.
2. The document tests a variety of calculus, trigonometry and algebra skills through problems involving derivatives, limits, sums, probabilities, graphs and equations.
3. Many problems ask students to use concepts like derivatives, limits, sequences, series, trigonometric identities and equations to solve word problems step-by-step and demonstrate mathematical reasoning and problem solving abilities.
Chapter wise important questions in Mathematics for Karnataka 2 year PU Science students. This is taken from the PU board website and compiled together.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...Bagalkot
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
Chapter wise important questions in Mathematics for Karnataka 2 year PU Science students. This is taken from the PU board website and compiled together.
II PUC (MATHEMATICS) ANNUAL MODEL QUESTION PAPER FOR ALL SCIENCE STUDENTS WHO...Bagalkot
My dear Students,
Wishing you all happy SHIVRATRI. & ALL THE BEST IN YOUR ANNUAL EXAMS-2014
Here I have uploaded II- P.U.C MATHEMATICS MODEL QUESTION PAPER FOR the year 2014 Which i have designed according to New syllabus of CBSE. I hope this model paper will be helpful to all the students who are writing annual exams on 18-March-2014.
wish you all the best
Regards,
A. NAGARAJ
Director-Faculty
Shree Susheela Tutorials
BAGALKOT-587101
mob: 9845222682
This is a 3 hour sample paper for cbse class 12 board exam. This covers all chapters of ncert 12th math book. For more such papers visit clay6.com/papers/.
The Quadratic Function Derived From Zeros of the Equation (SNSD Theme)SNSDTaeyeon
This is my first upload in slideshare. I hope you guys like it~! and... Note: My fonts used are the ff:
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This is a 3 hour sample paper for cbse class 12 board exam. This covers all chapters of ncert 12th math book. For more such papers visit clay6.com/papers/.
The Quadratic Function Derived From Zeros of the Equation (SNSD Theme)SNSDTaeyeon
This is my first upload in slideshare. I hope you guys like it~! and... Note: My fonts used are the ff:
1. exoziti.zip;
2. exoplanet.zip;
3. vlaanderen.zip;
4.Girls Generation Fonts.zip; and,
5. kimberly-geswein_over-the-rainbow.zip...
I hope you guys like it~!
add me on fb: www.fb.com/iamsieghart
In pursuit of excellence, the CBSE board conducts a thorough research on emerging educational requirements. While designing the syllabus, the board ensures that every topic meets the learning needs of students in the best possible manner. CBSE Class 12 Maths - http://cbse.edurite.com/cbse-maths/cbse-class-12-maths.html
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.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
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?
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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.
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.
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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.
1. WORK SHEET – 1 ( FOR MANASTHALI) CLASS XI
1. Find the derivative of 𝑒 𝑥
by first principle.
2. Find sum to n terms of series 0.7 + 0.77 + 0.777 + .......
3. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on a second
day, 4 more workers dropped out on 3rd
day & so on it took 8 more days to finish the work. Find the number
of days in which the work was completed.
4. If the coefficient of ar – 1
, ar
& ar + 1
in exp of (1 + a)n
are in A.P., prove that n2
– n (4r + 1) + 4r2
– 2 = 0.
5. Using P.M.T. prove that :- (1 + x)n
1 + nx for all x > -1.
6. Find the value of cos 20o
cos 40o
cos 60o
cos 80o
.
7. Draw the graph of f(x) = [x] & find its domain & range
8. f (x) =
𝑘 cos 𝑥
𝜋−2𝑥
𝑥 <
𝜋
2
3 𝑥 >
𝜋
2
, find k if lim 𝑥 →
𝜋
2
𝑓 𝑥 exists
9. Find the rank of the word “: MOTHER”.
10. Prove that the product of lengths of the perpendiculars drawn from ( 𝑎2 − 𝑏2 , 0) & (− 𝑎2 − 𝑏2 , 0) to
line
𝑥
𝑎
cos 𝜃 +
𝑦
𝑎
sin 𝜃 = 1
WORKSHEET – 2( FOR MANASTHALI) CLASS XI
1. If 4 digit numbers greater than 5000 are formed from the digit 0, 1, 3, 5 & 7. What is the probability of family
a number divisible by 5 when digits can be repeated.
2. Solve :- x2
– (7 – i) x + (18 – i) = 0
3. Find the coefficient of x40
in (1 + 2x + x2
)27
.
4. The first, second & last terms of an A.P. are a, b, c respectively. Prove that the sum of n terms is
𝑎+𝑐 (𝑏+𝑐−2𝑎)
2 (𝑏−𝑎)
.
5. If x = a +
𝑎
𝑟
+
𝑎
𝑟2 +, , , , , , , , , ∞, y = b -
𝑏
𝑟
+
𝑏
𝑟2 + .............. ∞ , z = c -
𝑐
𝑟2 +
𝑐
𝑟4 + .............. ∞, prove
𝑥𝑦
𝑧
=
𝑎𝑏
𝑐
6. If the image of the point (2, 1) with respect to line mirror is (5, 2), find the equation of the mirror.
7. Find the centre & radius of a circle passing through (5, -8), (2, -9) & (2, 1).
8. Evaluate :- lim 𝑥→0
1−cos 𝑥 cos 2𝑥
𝑥2 .
9. Find the derivative of sin 𝑥 by first principle.
10. Prove :-
cos 8𝐴 cos 5𝐴−cos 12𝐴 cos 9𝐴
sin 8𝐴 cos 5𝐴+cos 12𝐴 sin 9𝐴
= tan 4A
11. Find domain & range of f(x) =
𝑥−2
3−𝑥
2. WORK SHEET – 3 ( FOR MANASTHALI) CLASS XI
1. Let R1 be a relation on R : (a, b) R1 1 + ab > 0 a, b R Show that
a. (a, 0) R1 for all a R
b. (a, b) R1 ⇒ (b, a) R1 for all a, b R
2. Find domain & range of f(x) =
𝑥2
𝑥−4
3. If 10 sin4
+ 15 cos 4
= 6, find the value of 27 cosec 6
+ 8 sec6
.
4. Evaluate :- lim 𝑥 →2 𝑓(𝑥)if f(x) =
𝑥 − [𝑥] 𝑥 < 2
4 𝑥 = 2
𝑥 − 5 𝑥 > 2
5. Prove that
𝑑
𝑑𝑥
𝑖𝑛 𝑥−𝑥 cos 𝑥
𝑥 sin 𝑥+cos 𝑥
=
𝑥2
(𝑥 sin 𝑥+cos 𝑥)2
6. The letters of word SOCIETY are placed at random in a row. What is the probability that three vowels come
together?
7. Find the probability of getting an even numbers on first die or a total of in a single throw of two dice.
8. An arc is in form of semi ellipse. It is sin wide & 2m high at centre. Find the height of arch at a point 1.5 m
from one end.
9. If a is the A.M. of b & c and two G.M. are G1 & G2, prove G1
3
+ G3
2 = 2abc
10. Find sum of 24 terms of AP if it is known that a1 + a5 + a10 + a15 + a20 + a24 = 225.
WORK SHEET – 4( FOR MANASTHALI) CLASS XI
1. If the first term of an A.P. is z & sum of first 5 terms is equal to ¼ of sum of rent 5 terms. Find S30 .
2. Prove that :-
tan 3𝑥
tan 𝑥
never lies between
1
3
& 3.
3. Prove that :- sin2
72 – sin2
60 =
5− 1
8
.
4. Find real value of x & y:- (x4
+ 2xi) – ( 3x2
+ iy) = (3 – 5i) + (1 + 2iy) .
5. Solve :-
5𝑥
4
+
3𝑥
8
>
39
8
,
2𝑥−1
12
−
𝑥−1
3
<
3𝑥+1
4
6. The letter of word “RANDOM” are written in all possible orders in dictionary. Find the rank of word “
RANDOM”.
7. Prove by PMI that :-
𝑥5
5
+
𝑥3
3
+
7𝑛
15
is a natural number for all n N .
8. Using concept of slope, prove that the line joining the mid points of the two sides of a triangle is 11 to third
side.
9. Evaluate :- lim 𝑥 →2
𝑥2− 4
3𝑥−2− + 2
10. Prove that :- lim 𝑥 →
𝜋
4
𝑡𝑎𝑛 3 𝑥−tan 𝑥
cos (𝑥+
𝜋
4
)
= -4
11. Find the derivative of cos3
x by first principle.
12. Three dice are thrown together. Find the probability of getting a total of at least 6.
3. WORKSHEET – 5( FOR MANASTHALI) CLASS XI
1. f(x) =
5𝑥
𝑥 − 2𝑥2 𝑥 ≠ 0
0 = 0
does lim 𝑥 →0 𝑓(𝑥) exist ?
2. if a1, a2, a3 ....... an are in A.P. where ai > 0. Show that
1
𝑎1+ 𝑎2
+
1
𝑎2+ 𝑎3
+ … . +
1
𝑎 𝑛−1+ 𝑎 𝑛
=
𝑥− 1
𝑎1+ 𝑎 𝑛
.
3. the natural number are grouped as follows : (1), (2, 3), (4, 5, 6), (7, 8, 9, 10) ....... find the first term of nth
group.
4. If z1 , z2 are complex numbers :-
𝑧1− 3𝑧2
3− 𝑧1 𝑧2
= 1 & 𝑧2 ≠ 1, then find 𝑧1 .
5. Find all non zero complex numbers z satisfying 𝑧 = iz2
.
6. If 𝑛 𝑐𝑟 : 𝑛 𝑐𝑟+2 = 1 : 2 : 3 find n & r.
7. Find the derivative of tan 𝑥 by first principle.
8. Solve :- sin 3x + cos 2 x = 0
9. In a triangle ABC. If a cos A = b cos B, then prove that either triangle is isosceles or right angled.
10. Prove :- 3 cosec 20o
– sec 20o
= 4.
11. Find the least value of n for which 1 + 3 + 32
+ ............. to n terms is greater than 7000.
12. Find the derivative of
a. sin
𝑥2
3
− 1 b. log (sec x + tan x) c.
1
𝑎2− 𝑥2
.