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astresnotes-maths · 2 years

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Lesson 1.1 — Factorising Quadratics — 20220906

My first maths class! And the first class of pure maths. We mainly just reviewed things this class, as we’re doing in all the maths classes. Most of the lessons so far involve the teacher reading to us some explanations and showing us some examples, and then all of us working to answer some questions on our own, which we then check as a class.

Regardless of the work so far being things I already know, I spent a few hours typing out a tutorial on factorising quadratics nonetheless. Probably a huge waste of my time, but I hope at least one person will come across this post in their time of need and find it helpful.

Because of how difficult it is to represent maths equations accurately by typing, and because tumblr’s layout does not support things like subscripts and indices, I will not include every question we did in all the lessons. Don’t worry though, I will include examples for every explanation, as well as some additional questions when we did more of them in class, and any homework we’re given.

Topic 1: Quadratics

Lesson 1.1 — Solving by Factorising

The standard quadratic equation has the structure — ax^2+bx+c=0

In quadratics, and only in quadratics, this is called standard form

So always convert the question into this form before trying to solve

Factorising quadratics — means turning them into the form (rx+p)(tx+q)=0

This helps you solve it by then taking each parentheses in turn and setting it equal to zero (because seeing as they multiply together to form zero, either one of them must equal zero in order for the equation to be true)

The basic principles of factorising quadratics:

pq must equal c, because these are the only solely numerical digits (no variables) in the brackets, so they multiply to give the solely numerical digit in the standard form (this being c)

q + p equal b, because you multiply each by x, making them like terms, so you then combine them through addition/subtraction to form a singular coefficient of x — which is b in the standard from

rt must equal a, because they multiply to form the coefficient of x^2

If b and c are positive, then the signs within the parentheses will both be positive too

If c is negative, then one of the signs will be positive and one will be negative:

If b is positive when c is negative, then the number (out of p and q) which multiplies (with the respective coefficient of x) to give the larger value (i.e out of rq and tp) will be positive, while the other one will be negative

If b is negative when c is also negative, then the number (out of p and q) which multiplies (with the respective coefficient of x) to give the smaller value (i.e rq or tp) will be positive, while the other one is negative

I probably worded that very confusingly, but don’t worry I will include examples and explain the steps as I do them so you can see what I mean in action

Factorising when a = 1:

Start by laying your foundation — (x )(x )

List the factors of c

Find which two factors of c add/subtract to form b — these will be p and q

Place them in the parentheses — (x p)(x q)

Figure out which signs go where — in the case of a = 1, if c is negative, then you don’t need to worry about “multiplying with the respective coefficient of x”, because the coefficient of x is 1, so simply the value of p and q dictate the signs

Always check by expanding the brackets before you move on to solve

Then solve by setting each set of brackets in turn to zero

Example: x^2 + 3x - 10 = 0

Lay the foundation — (x )(x )

List the factors of c — 5&2, 1&10

Find which factors of c add/subtract to give b — 5 - 2 = 3, so p and q must be 5 and 2

Substitute into parentheses — (x 5)(x 2)

Figure out the signs — in this case, c is negative, so one of the signs will be positive while the other will be negative

b is positive, so the larger digit out of p and q will be the positive one — in this case it’s the 5

So x^2 + 3x - 10 = (x + 5)(x - 2)

Check — (x + 5)(x - 2) = x^2 + 5x - 2x - 10 = x^2 + 3x -10 ✓

Now solve by setting each bracket to zero:

x + 5 = 0, x = -5

x - 2 = 0, x = 2

Factorising when a ≠ 1:

Start by laying your foundation, this time with a space before the x’s — ( x )( x )

See if you can divide every term by a factor of a to simplify the equation

Now find the factors of your new value of a

List the factors of c

Find which two factors of c add/subtract to form b when multiplied with a set of factors of a — these will be p, q, r and t, which form b when rq and tp are added/subtracted

Place all numbers in the parentheses — (rx p)(tx q)

Figure out which signs go where

If c is negative, then you need to see which value, out of p and q form the larger or smaller value (depending on whether b is pos. or neg.) when multiplied with the respective coefficient of x (r and t)

Check by expanding the brackets before you move on to solve

Then solve by setting each set of brackets in turn to zero

Example: 9x^2 - 39x - 30 = 0

Lay the foundation — ( x )( x )

See if you can divide every term by a factor of a to simplify the equation — all terms can be divided by 3 to give 3x^2 - 13x - 10

Now find the factors of your remaining a — 3&1

List the factors of c — 1&10, 5&2

Find which two factors of c add/subtract to form b when multiplied with a set of factors of a — 5&2 multiply with 3&1 to give 15&2, which subtract to give 13

Place all numbers in the parentheses — (3x 2)(x 5)

Figure out which signs go where — c is negative, so it must be one positive and one negative

b is also negative, so the digit (of q or p) which multiplies with the respective coefficient of x to give the larger value (rq or tp) must be negative — the values formed are: 5 x 3 = 15, and 2 x 1 = 2; the larger value is 15, which is given by 5 x 3, so 5 must be the negative value

Therefore 3x^2 - 13x - 10 = (3x + 2)(x - 5)

Check — (3x + 2)(x - 5) = 3x^2 - 15x + 2x -10 = 3x^2 - 13x - 10 ✓

Solve by setting each bracket to zero

3x + 2 = 0, 3x = -2, x = -⅔

x - 5 = 0, x = 5

**Tip: At first glance, when trying to find the correct factors of c to use, you may find multiple solutions

For instance, in the example above, you may have thought of using 1&10 as opposed to 5&2, because they multiply with 3&1 to give 3&10, which add to give the required 13

However, you have to consider the signs; because both c and b were negative, the larger of the multiplied values (rq and tp) had to be negative, while the other one positive

10&3 would both need to be positive, or both need to be negative, to give an absolute value of 13

But in order for the correct result to be obtained when the signs were different, 5&2 had to be used (as they gave rq = -15 and tp = +2)

I’m sorry if this makes things more complicated-sounding than they actually are. I hope the examples make it clearer. Feel free to send me an ask on my main blog if you don’t understand what I meant.

No homework this class, seeing as it’s the first one this year (and we have another one on Friday).

Anyways please remember to take care of yourselves and drink water!

#⭐️1.1 #⭐️Quadratics #⭐️20220906 #maths #A-Level-Mathematics #A-Levels #astresnotes #astresnotes-maths #⭐️Factorising-Quadratics #factorising quadratics

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ncertsolutionsmath · 3 years

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NCERT Solutions for Class 10 Maths PDF Download

NCERT Solutions for Class 10 Maths for all the activities from Chapters 1 to 15 are given here. These solutions are curated by our master personnel to help understudies in their board test arrangements. Understudies searching for the NCERT Solutions for Class 10 Maths can download all part shrewd pdf to locate a superior way to deal with take care of the issues.

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NCERT Solutions for Class 10 Maths Chapters and Exercises NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers In Chapter 1 of Class 10, students will explore real numbers and irrational numbers. The chapter starts with the Euclid’s Division Lemma which states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0=r<b”. The Euclid’s Division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the Fundamental Theorem of Arithmetic is defined which is used to find the LCM and HCF of two positive integers. After that, the concept of an irrational number, a rational number and decimal expansion of rational numbers are explained with the help of theorem.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials In Polynomials, the chapter begins with the definition of degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises including an optional exercise. Exercise 2.1 includes the questions on finding the number of zeroes through a graph. It requires the understanding of Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial where students have to find the zeros of a quadratic polynomial and in some of the questions they have to find the quadratic polynomial. In Exercise 2.3, the concept of division algorithm is defined and students will find the questions related to it. The optional exercise, 2.4 consists of the questions from all the concepts of Chapter 2.

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables This chapter explains the concept of Pair of Linear Equations in Two Variables. This chapter has a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and graphically. Exercise 3.2 explains the methods of solving the pair of the linear equation through Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. Students must practise these exercises to master the method of solving the linear equations.

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations In this chapter, students will get to know the standard form of writing a quadratic equation. The chapter goes on to explain the method of solving the quadratic equation through the factorization method and completing the square method. The chapter ends with the topic on finding the nature of roots which states that, a quadratic equation ax² + bx + c = 0 has

Two distinct real roots, if b² – 4ac > 0 Two equal roots, if b² – 4ac = 0 No real roots, if b² – 4ac < 0

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions This chapter introduces students to a new topic that is Arithmetic Progression, i.e. AP. The chapter constitutes a total of 4 exercises. In Exercise 5.1, students will find the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula; an = a + (n-1) d

The next exercise i.e., 5.3, contains the questions on finding the sum of first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students’ analytical and problem-solving skills.

Source: https://ncertsolutionsmath.news.blog/2021/02/07/ncert-solutions-for-class-10-maths-pdf-download/

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rncareergroup · 3 years

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studyinginstyle · 7 years

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Take a diagnostic test

There are many SAT books out there with countless SAT practice tests, but in my opinion the College Board practice tests most closely mimic the types of problems on the actual SAT. Try taking a test and correcting it to see where you need the most work, and to get a feel for the layout of the SAT. Then, you can go on to use books from companies like Princeton Review or Applerouth for more practice.

Set a goal

If you have some idea of the colleges you want to go to, do some research to figure out what the average SAT scores are for students who were admitted. Aim for a score in the upper 25th percentile of those students.

Learn what you don’t know

Many books will walk you through the steps necessary to complete various types of problems. Go through those carefully, and practice the types of problems you recently learned in order to get accustomed to them.

Practice, practice, practice

The best thing to do once you are familiar with all of the types of problems is practice. Try setting a schedule for yourself, whether it’s doing ten problems a day or one reading and one math section per day. Be sure to check every problem and understand what you got wrong. At frequent intervals, take full-length tests and time yourself within the constraints of the actual test. Check your answers and track your progress. Kahn Academy is also a great resource for online practice problems.

Basic math formulas to know

· You are provided with a list of geometry formulas—familiarize yourself with them and be sure you know what they mean

· Review your times tables up to 12x12 (flashcards)

· Right triangles—multiples of:

o 3, 4, 5

o 5, 12, 13

o 8, 15, 17

o 7, 24, 25

· Powers: squares up to 20, cubes up to 10, fourths up to 5, powers of 2 up to 2^10

· Quadratic forms—standard: y = ax^2 + bx + c, vertex: y = a(x – h)^2 + k

· Quadratic formula: x=2a−b±√b2−4ac

· Exponential standard form: y = ab^x

· Equation of a circle: (x – h)^2 + ( y – k )^2 = r^2

· Other formulas to know

Reading and Writing Strategies

· Although there is no longer a vocab section on the SAT, it is still a good idea to do some vocab practice, especially if you feel you don’t have as strong of a vocabulary as you would like to. Consider buying flashcards or using these online ones https://sat.magoosh.com/flashcards/vocabulary

· Khan Academy describes a five-step active reading method called SQ3R: “Survey, Question, Read, Recite, Review.” Read more about it here

· Familiarize yourself with basic grammar rules and standard conventions:

o tenses (a sentence that changes tenses partway through will likely be incorrect)

o run-on sentences

o modifiers

o subject-verb agreement

o transitions

o punctuation

o find more here

Essay strategies

· The essay is no longer required in the new SAT, but it is a good choice for someone if you are applying to colleges that require an essay, or if you want to show extra dedication or academic prowess. It is generally highly recommended to opt in for the essay.

· You will be evaluated with sub-scores out of 4 for three categories: reading, analysis and writing.

· Read sample essays and pay attention to patterns—what did higher-scoring essays do more of? (https://collegereadiness.collegeboard.org/sample-questions/essay/1)

· Begin by reading the prompt or the passage carefully and construct a thesis

· Outline your essay. Be sure all body paragraphs address your thesis.

· Longer essays generally score higher, but try to make it as dense as possible. It will be obvious if you are using a lot of “filler” sentences and ideas.

· Leave enough time to edit. Although it’s handwritten, that shouldn’t stop you from going back to make changes.

Some other useful resources

· Find a tutor in your area or enroll in an SAT class

· This explanation of all the different areas of the test from College Board

· SAT practice strategies, problems, videos and explanations from Khan Academy

· Princeton Review book of 11 different practice tests

· Find flashcards for various topics on Quizlet

· Read a lot from reputable journals or periodicals such as the New York Times

On the day of the test

Relax! You have done all you can to prepare, so be confident that you can do well. Take deep breaths and try not to get too nervous. Good luck!

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ss1986us · 5 years

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NCERT Solutions for class 10 maths

Class 10th maths is crucial of all the subjects, as it helps in building the foundation of the future technical courses. The ncert solutions for class 10 maths provided comprises of solutions to all the exercises given in CBSE textbook. The expert team at entrencei have keenly evaluated and reviewed the complete set of material. And to help you we have uploaded Maths formula in one page for effective revision .We solely believe in providing the best of ncert solutions for class 10 maths in order to ease the process of learning. In case if you face any issue regarding the material provided, then you can directly reach to our executives.

The level of education provided by NCERT helps in creating a strong base for the one looking to higher technical studies. the continuous effort of the team at entrencei have led to provide you with an extensive list of chapters solution to ncert solutions for class 10 maths of which chapters are mentioned below:

Chapter 1 – Real Numbers

This topic of ncert solutions for class 10 maths comprises of extension provide to 9th class. One would be made aware of the intrinsic details of Euclid’s division algorithm, rational numbers. The ncert solutions for class 10 maths provide help in understanding divisibility of integers.

Chapter 2 – Polynomials

This part of ncert solutions for class 10 maths comprises of four exercises. All the exercise mentioned deal around determining zeroes of polynomials, quadratic polynomials.

Chapter 3 – Pair Of Linear Equation In Two Variables

The introduction to this chapter mentioned in ncert solutions for class 10 maths comprises of laying concepts of linear equations in two variables. In this chapter detailed study could be made of the graphical method and algebraic method of solving linear equations. Elimination method, substitution method, cross-multiplication method are explained in exercises format.

Chapter 4 – Quadratic Equation

This ncert solutions for class 10 maths comprises of methods to find roots of the quadratic equation. The exercises mentioned would comprise of questions related to our day to day life problems. One will study regarding completing the square and factorization method to determine roots of quadratic equations. Nature of roots are the main topics to be studied in this ncert solutions for class 10 maths.

Chapter 5 – Arithmetic Progressions

This topic of ncert solutions for class 10 maths has minor complex problems related summation of consecutive terms. This topic helps in finding solutions to real-life problems.

Chapter 6 – Triangles

This chapter consists of questions based upon properties of triangles which are very extensively explained in ncert solutions for class 10 maths provided by us. The main 9 theorems mentioned in it are of main importance with respect to exams.

Chapter 7 – Coordinate Geometry

This chapter has been holding a very crucial place, as it helps in finding the distance between two coordinates provided. The ncert solutions for class 10 maths to this chapter have been made very entreating to understand for students.

Chapter 8 – Introduction to Trigonometry

This chapter comprises of determining trigonometric ratios of acute angles of triangles. The ncert solutions for class 10 maths provide for ratios of complementary angles are main topics to be focused upon.

Chapter 9 – some applications of Trigonometry

This chapter will bring you some new sides of solving mathematics as provided by our team in ncert solutions for class 10 maths.

Chapter 10 – Circles

Here you will be brought some untouched theorems and formula of the circle.

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Here you will be using ruler and compass to draw some geometric figures. Carving out bisector of angle and triangles construction has been very extensively mentioned in ncert solutions for class 10 maths.

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You must be well acquainted with finding areas of different geometric plane figures. The reference of ncert solutions for class 10 maths would the chapter very easy.

Chapter 13 – Surface Areas and Volumes

Well, this chapter is the continuation of 9th standard. One will be made acquainted with volumes and areas of cubes, cuboid, and cylinders.

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Chapter 15 – Probability

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angeltriestoblog · 7 years

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Your Comprehensive Guide to Surviving Grade 11

WARNING: The longest post I’ve ever made in the history of my blogging “career” is up ahead. Nevertheless, please read it so my efforts won’t be wasted.

In a nutshell, last school year was me trying to secure the Guinness World Record for the number of breakdowns on a bedroom floor. The amount of workload was unforgiving, the pressure to perform was crippling, the competition was inadvertently fierce and the standards set were higher than fun.'s friends in the Empire State. (Please get this reference.) Surprisingly, I survived and lived not only to tell the tale but to also help incoming Grade 11 students prepare for the year that is to come so they won't have to deal with the many risks of premature stress like I did! This is where this guide (with some unnecessary blabber on the side because will it really be an Angel Martinez post without it) comes in. Though it's a given that not everything that happened to me won't apply to you, I still hope you use these to better your experiences and emerge as a stronger and more productive person! Like me, I guess. In a way.

To kick this off, let me just say that I know this notice might be coming in a little late, since enrollment for most schools (in the metro, at least) have already come to a close. Thus, by the time you've read this, you may have already chosen a strand of your own! The selection of some schools may be limited to the basics: Science, Technology, Engineering and Math (STEM), Accountancy, Business and Management (ABM) and Humanities and Social Sciences (HUMSS) which are all pretty self-explanatory in terms of the topics of focus. But from what I know, others also offer Arts and Design and Sports for those who wish to devote their full attention to the talents they wish to hone and even a general academic strand for the benefit of those who remain undecided. I, for one, chose ABM: I didn’t feel like committing to a certain career yet and wanted to opt for the safest option among the choices.

The process of choosing which way to go is pretty intimidating at first especially once you figure out that the rest of your life may very well be at stake. But, it isn't that much of a pain once you reflect on your interests enough and see if those align with what you want to do and where you want to be in the future, if that’s not too forward looking for you! I know a couple of people who’ve had to compromise their true passions for the sake of pleasing their families. Whether it’s to continue a legacy that’s been passed down for several generations or fulfill a dream that belonged to someone else, some parents believe they have every reason in the world to demand their children’s future, even if it’s obviously against their will. Yes, I believe that it’s their responsibility to guide their kids through the process of figuring out what they want to be in such a fast-paced and ever-changing world where anyone can influence and be influenced for better or for worse. They must be able to provide the insight that only they possess after all the years they’ve spent collecting wisdom. They should help us plan out what’s gonna be on the blueprint of our lives, not finish it by themselves, present it and expect us to follow without any questions.

But as per usual, I digress. TL:DR choose the track you want, you don’t owe anything to anyone.

Generally, Grade 11 will be the hardest year on you. It doesn’t care if you came terribly unprepared, if you haven’t slept a wink in eons or if the people you live with barely even know who you are anymore. It’s unforgiving and relentless in the pursuit of giving you the biggest ordeal of your life. Based on my personal experience, I reckon it’s due to the fact that our teachers stand by their decision to treat us as young adults, seeing as we’d be in first year college anyway if the K-to-12 program wasn’t a thing. When we were children, everything we needed to know about a certain topic would be put on a silver platter and handed over to us, usually in the form of photocopied sheets of old handouts. All we’d have to do is memorize whatever was on them and eventually ace the tests that usually came in multiple choice or matching type form.

But now, we’re in charge of making our own notes, deciphering cryptic explanations for a certain lesson and most of all, making our own creative output based on what we could be often inaccurate interpretations. Grade 11 gave big importance to the performance task, much to the dismay of everybody. Whether individual or by group, it was always half our grade and due way before any of us were ready to face the task at hand. It also required coming up with original ideas, or solutions to the most common problems and it’s either bland when working alone or chaotic when with classmates, because everyone wants to be heard when we’re actually fighting for metaphorical spots.

I didn’t feel it much during the first semester though, because I had the best schedule on campus. Classes ended at 2:30PM for me so I had plenty of time at my disposal. I could hang out with friends, have a chat with my mom and procrastinate (responsibly) before proceeding with my work and still be able to go to sleep before the clock struck ten. My subjects weren’t terrible as well. Yeah, not all of them were anchored in the very foundation of my track but I was able to get grades far better than I would have expected, so it’s all good. Here’s a briefer on each:

General Math

A solid 8/10, which is a big deal considering the fact that Math has never been my strong suit. First quarter covers topics I barely understood when they were discussed to me in Grades 9 and 10, namely functions (linear, quadratic, polynomial, The Problematic Trio aka rational, exponential and piecewise) and equalities and inequalities. Second quarter focuses on business math, weirdly enough when there’s an entirely different subject for that, but the lessons don’t overlap. Annuities, stocks and bonds, and loans were explained plus a little bit of logic towards the end.

The key to Math is a heck lot of practice. Practice, practice, practice. Even when you know the answers, or more preferably when there’s no key given. Answer every problem in the book on a separate sheet of paper, make up your own, explain the procedure of solving to yourself, help a friend out and refresh your memory simultaneously. Do it when you get home, or when you have a free period at school or you have no idea what else to do seeing as that’s the only way you’ll develop the skills needed to become a human calculator.

Business Math

A more practical Math subject: every single topic discussed was something that could be applied in real life and useful to us when we have careers. The first few weeks consisted of our reviewing our favorites: fractions, decimal and percentage, and ratio and proportion, so it evidently started on a good note. It later on proceeds to buying and selling, computation for salaries and wages then the presentation and analysis of business data in table and graph form.

Though the lessons here are undeniably easier than our previous Math subject, it still wouldn’t hurt to practice, especially if everything isn’t clear to you from the get go. If your teacher is anything like mine and thrives on class participation, recite as often as you can whether it’s to give a recap of yesterday’s lesson or show the solution on the board. Her personal favorites in our class were those who made it a point to raise their hands as often as possible.

Physical Science

A mix of the deadliest sciences mixed in one subject. Physics and chemistry, folks. Just as appealing as it sounds. If you like both of them, you’ll breeze past this, no sweat. But if you’re like me and you stopped paying attention in science class after the teacher was done discussing the body system, you’ll have a lot of catching up to do. Subject matter included motion, energy, chemical reactions, force and energy. Don’t be too excited that there are only five, because these took two semesters to properly shove in our craniums.

There’s no downtime in this subject, you have to hustle every single day or else you’ll fall behind while the work just keeps piling up. Read up on everything and do not leave out even a single detail: know which causes what, and why well enough to the point that you can recite it in your sleep. Memorize the formulas and most importantly, invest in a double liner calculator! It’s a bit pricey but spending the amount required is far better than having to enter multiple parentheses to work your way around an equation.

Earth and Life Science

Personally the superior science for me, considering that the topics were genuinely interesting and made me gain a better understanding of how the world works. We studied the origin and structure of the earth and beyond, earth processes, natural hazards, bioenergetics, perpetuation of life, evolution, organ systems and interaction and interdependence.

The only downside for some is that many terms will be introduced throughout the course of this subject, and you’ll obviously be required to memorize them all and at the very least, identify their definitions. Making flash cards for each lesson would definitely come in handy, even if takes a while and could very well cramp your hand but there’s this app called Quizlet which basically serves the same purpose and is easily accessible in any device you download it on.

Oral Communication

I think I was the only one in class who actually enjoyed what was going on for the most part of Oral Com, since I enjoy talking to a crowd and writing. If the mere mention of that phrase alone gives you shivers down to your spine, I guess you’ll have a lot of mental and emotional preparation to do. Normally, this subject would heavily rely on application of learnings through exercises and presentations but there was still a bit of (unnecessary) discussion here and there on topics like public communication skills and communicative strategies.

Expect a lot of speaking in front of the classroom! Tasks will range from impromptu (no time to think beforehand), extemporaneous (short preparation time upon receiving the question) and prepared speaking. Groupwork is also high in number: the teacher will give you a situation (e.g. you’ll be selling a product, your house is on fire and you need to call the fire department, ya know… the usual [?]) and you’ll need to propose your solution in the most eloquent and spontaneous way possible. Which means no reading aloud of lines scribbled on your hand with a G-Tec.

Organization and Management

Basically an introduction to the world of business and thus an essential subject for my strand. Points discussed were the nature of management, the firm and its environment, environmental scanning (PEST and SWOT analysis) and the functions of a manager in detail (planning, organizing, staffing, leading and controlling).

This subject was very detail-heavy so as much as I was willing to learn, I couldn’t avoid being overwhelmed by the number of things we were trying to run through in around sixteen weeks. It also didn’t help that we didn’t have a book to refer to and had literal stacks of photocopied handouts to lug around instead. But I guess by now, your school has a textbook to provide you with and if not, there are some published by Rex Bookstore available in big branches of National Bookstore like in Quezon Avenue. The best thing to do to survive this subject is to read so you can understand all the concepts. Everything discussed is important and the quizzes and quarterly tests you’ll take will require not only what you think it means, but also how you’ll use it IRL

Understanding Culture, Society and Politics

Potentially one of your favorite subjects, if you’re given the right teacher, since it focuses on the intricacies of our lives as human beings. From the study of humans past and present and the complexity of our cultures (anthropology), we head on to the analysis of government systems and activity (political science) and the nitty-gritty of our development and functions in human society (sociology).

I didn’t have a problem with this step the lessons were comprehensible enough to grasp my attention but just make sure that you exert effort to understand everything! Because even though a chunk of the activities also include matching type, true or false or fill in the blanks, essays are a mainstay. Usually, they’re not based on facts too but on your own personal opinion and the teacher will be able to tell if you don’t have a particular stand or you do yet you fail to back it up with actual evidence, so be sure to find a basis for everything you say.

Unfortunately, all fun and games were over when the second semester rolled in. Our privileges were taken back and our schedule was reverted back to the usual 4:20PM. Thanks to the fact that my busmates never went straight to the bus upon dismissal and liked roaming around the campus, leaving our conductor to search for them like she was in some sort of treasure hunt, I went home at 6:00PM every day. To make matters worse, this just so happened to be the season when the research papers started rolling in, one by one, all poised and ready to kill us ever so slowly. Let me give you another quick recap:

Pagbasa at Pagsuri

Definitely not the kind of “Pagbasa” I was expecting, if I’m being frank. I thought we were going to be reading and analyzing contemporary Filipino literature, which excited me since my knowledge in that genre was close to non-existent. Turns out, we would be looking at different kinds of texts (informative, persuasive, analytical, etc) then finding out how to write them afterwards. There’s a chance you might not experience this unless we go to the same school, but our teacher invented the ADIDS method in order to help us learn this more effectively through application. I forgot what it stands for, but basically all you do is discuss each facet of a very broad topic thoroughly in the form of a well thought out class presentation.

Meanwhile, the research paper takes up one whole semester. Not to sound boastful, but I had thought that I would be able to do this with ease because all I ever do with my life is write I mean I practically came out of my mother’s womb with a pen and paper in hand and I speak more Filipino than English these days seeing as I spend a bigger portion of my day in school. But, the finished product is often bland and makes use of the same words over and over in a failed attempt to accurately describe what I want to put on paper. And as if that wasn’t bad enough, the topic also had to be narrowed down repeatedly to suit a particular audience, from a specific place within a specific time frame so we ended up doing a research on the effects of Jason Derulo’s songs on the opinions of Grade 11 students from our school in the academic year 2016-2017. Please don’t laugh at us.

You also don’t just write the entire paper, but also be briefed on its parts, their functions and determine what sets them apart from each other, and the specifications in making each of them. Which includes stuff as minuscule as the measurement of the margins, font sizes and types to use et cetera. It’s not that hard though because as you’re working on the paper, you familiarize yourself even more.

Komunikasyon at Pananaliksik

The easiest one I took the entire semester, and for obvious reasons, my favorite. Our teacher was brilliant in the sense that he was well-versed in the subject matter and got work done yet let us watch Train to Busan or Seklusyon on the TV if the schedule permitted. The topics weren’t mind-boggling either: we just covered the history of the Filipino language and communicative skills (which further cemented my belief that this was basically the counterpart of Oral Com). They may be confusing at first but the key is to notice sentence patterns! The number of activities given to us was reasonable and not particularly stress-inducing: just quizzes that were few and far-between, a groupwork and reaction paper for a performance task.

Fundamentals of Accounting

A lot of people are intimidated by the idea of studying Accounting, and I’m not surprised. It’s always described as something that relies on analysis and numbers, two things that we normally don’t excel in at school. But it’s actually nothing to fuss about as long as you do your reading, understand the basic guidelines, practice at home and have a qualified teacher who has the proper training and skill set. The first few chapters don’t even involve computation of any kind yet. You’ll just be acquainted with the very foundation of the subject: the branches of accounting, the users of accounting information, the forms of business organizations and types of businesses. Maybe the most important lessons that you could pick up are the accounting equation (assets = liabilities + equity), types of major accounts and the generally accepted principles because they serve as the rules to follow for making your accounting-related decisions.

Eventually, you’ll make it to business transactions and their analysis, where you’ll be taking a trip around the whole accounting cycle. You’ll have to fill out a journal, ledger and unadjusted trial balance then adjust that trial balance using the adjusting entries normally provided to create your income statement, balance sheet, closing entries and the end goal, the post-closing trial balance. Sounds like a lot of work, but it’s seriously not that difficult if you do your homework! It’s also best to invest in an actual journal and worksheet, instead of solving on sheets of yellow pad that can easily be misplaced.

Statistics and Probability

Stat was weird for me in the sense that our lessons were generally ambiguous unlike what their names insinuated and I seemed to understand everything while it was being discussed but the minute I got home to work on assignments, I found myself staring at a wall until a friend who actually knows what to do goes online on Messenger. Later on, I found out it was because I needed to practice on my own to be familiar with the procedure instead of trying to memorize all the steps when it depends on the type of problem. We covered random variables, probability distributions, normal distributions, sampling, estimation of parameters and hypothesis testing (which was actually quite fun).

If you’re not keeping up to speed with everyone else, please do work on it as early as possible. The lessons here are somewhat connected to each other so if you failed to catch the drift on one of them, it’ll create a chain reaction and by the last topic, you’ll have zero knowledge of how to solve anything. Ask help, preferably from your teacher because not only do they explain it most accurately but it helps them see your initiative to do better, which they take into consideration when computing for your final grade. Do not settle for the exercises found on the book. Make your own, if you’re in the mood to cramp your hand, or turn to websites like The Oxford Math Center for useful worksheets with answer keys.

Contemporary Art

The very bane of my existence. The perfect way to sum up this subject in six words. Art was never my strength, anyone who knows me is aware that I can’t draw to save my life, but it didn’t really have much of a dent on my report card since it happened to be a minor subject. But thanks to the implementation of the new curriculum, it is given a new sense of purpose as a core subject with a weight of O N E. We had dealt with the different periods of Philippine art extensively, the National Artists of the country and different contemporary art forms such as film and the oddly interesting performance art. (Trigger warning for some graphic content though, so do be careful when searching these up!)

Activities ranged from making presentations similar in format to those in Pagbasa at Pagsuri, creating manifestos for the Philippine youth in relation to their role in the art world, holding a class exhibit to display the work you’ve made and my favorite: going on a fieldwork to hunt for contemporary art in the city. All this will lead to the culminating activity: the creation of your very own output, where anything is possible and depends solely on the one calling the shots.

This art class is no longer focusing solely on the physical aspects of a certain work, but also on what it actually means and what its relevance to society actually is. So, a good tip would be to always look at the bigger picture when given something to analyze! It’s hard at first, I admit I didn’t have much to say during the first few meetings but as the floor is opened to more interpretation and intellectual discussion, you’ll get the hang of it and instinctively feel the need to join in.

** We are about to dive in a zone that is fittingly named The Deadly Trio. ** Actually, if these were stand-alone subjects, I’d be fine but the fact that there are three of them in one semester when they’re basically discussing the same things and giving the same ridiculous amount of take home work was enough to drive me up the wall.

Practical Research

As implied by the very name of this subject, the main focus would be the creation of a qualitative practical research paper throughout the entirety of the semester. Discussions here were very minimal, as the teacher thankfully wanted us to focus on getting as much work done in the classroom as possible. I slacked off moderately during her period instead of lessening what I’d have to do at home, and in the end I ultimately suffered. But anyway, topics discussed include the importance of qualitative research, finding a good topic and sources to build it up, reviewing different types of literature, understanding and collecting data and further analyzing it to later on be able to report our findings.

One another thing to look forward to (not in a good way) is the dreaded thesis defense, where your paper will be dissected and closely examined for any possible shortcomings and held against you in front of a panel. It doesn’t always have to be the bane of your existence: as long as you contributed to the making of the project, you’ll know enough that you won’t be humiliated the minute you open your mouth.

A tip to take into consideration is to choose the right groupmates. Unless teachers pre-determine who you end up working with for two straight quarters (in that case, you’ll just have to learn how to accept your fate, whether it is for better or for worse), as much as possible, go for those who are responsible and actually care about their grades. It’s never fun to work with people who send you a montage of copy-pasted statements from Wikipedia pages and pass it off as their “contribution”, go offline Messenger the minute you even think about asking for help and think that printing the paper is a valuable addition to the team.

Reading and Writing

Contrary to what I initially thought, this was not the counterpart of Pagbasa at Pagsuri in the English language and I was thankful in a way because God knows the pain that inflicted upon me. The first quarter starts off quite easy, with critical thinking, fundamental reading skills, selecting and organizing information and critical reading skills. It may sound like a mouthful, but most of these are stuff you’ve picked up long before, without the assistance of a teacher! Some people may find patterns of development a hard topic, but if you read books, I guess identifying them just comes natural to you.

The latter part of this subject is where the ugly stuff goes in. I personally felt deceived into thinking that it would be as simple as our first lessons: identifying and writing the thesis statement and topic statement then it suddenly escalates and turns into SO MUCH ACADEMIC WRITING. When I saw that we were going to be making book reports and article critiques, I shelled out some of my favorite fictional reads and Man Repeller stories of the month only to find out that we’d be reviewing serious, educational material with very specific and strict guidelines to follow to make it as formal and cohesive (and basically not fun) as possible. Research reports, project proposals and position papers will also be in the works at some point: they are very structured and usually have to revolve around topics that are related to your strand, so there is a chance you may find it boring.

English for Academic and Professional Purposes

When I saw I had this for a subject, I was actually glad at first since English has always been my forte. So I was anticipating a repeat tutorial on all parts of speech and the basics of the subject-verb agreement when in reality, all I got was a dupe of Reading and Writing. Which is why, I had no idea why we had to take up both of them during the same semester.

Besides all subjects that required the submission of a research paper as some sort of culmination, this was the most demanding in terms of written output. During the first quarter, it’s still permissible to chill as you’re only going through reading and writing different types of academic texts (does this sound familiar to any of you?) but as the next one rolls along, BOOM. Reaction paper. Reflection paper. (Yes, there is a difference.) Concept paper. ANOTHER position paper. Report.

Now, if you’re already thinking about how you’re going to make it through when your writing is as lifeless and flat as can be (e.g. It is a sunny day, I ate an apple, I need to pee), don’t sweat it. That is exactly what your EAPP teacher will be looking for anyway. Academic texts do not require flowery writing that went through EDSA traffic before getting to the point (which was obviously an inconvenience for me): nobody cares about your opinion unless they say so and even if they do, they’ll probably require a sentence limit.

Well, that’s a wrap! I spent approximately twelve hours working on this post: one of which was spent on the Kitkat bench in Landmark trying to find a catchy way to start it off, and my eyes hurt and I may be suffering from carpal tunnel but all of that means nothing as long as I’ve been able to guide one hopeless soul out of the dark. I’ll be back with much lighter content very soon if I can factory reset my head and get it to work properly again.

Stay in school, kids!

Angel

#advice #grade 11 #senior high school #k to 12 curriculum #philippines #angeltriestoblog #pagod na ako #recs #life dump

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bestinlucknow-blog · 5 years

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Best National Defence Academy Coaching in Lucknow

Are you tired of searching here for getting NDA Coaching in Lucknow? Did you find a right institute which can provide you classes for NDA coaching in Lucknow so that you can crack the NDA exam and get admission in prestigious Army, Navy and Air force for serving India? If not, then no need to worry anymore because Path Finder Defence Academy is here for your help by providing the top level and advanced level of coaching classes with experienced faculties. Path Finder Defence Academy is considered as the most effective institution for NDA aspirants as we provide one of the Best Coaching and Training in Lucknow. We have one of the best faculties for providing professional training of the highest quality. We have set the standards of excellence in NDA Coaching through our detailed and quality training conducted by the best teachers. Our course covers the entire NDA Syllabus as set by the UPSC.

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Trigonometry: Angles and their measures in degrees and in radians. Trigonometrical ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications – Height and distance, properties of triangles.

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Differential Calculus: Concept of a real-valued function – domain, range, and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits – examples. Continuity of functions – examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative – applications. Derivatives of the sum, product, and quotient of functions, derivative of a function with respect of another function, a derivative of a composite function. Second order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

Integral Calculus and Differential equations: Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equations of various types – examples. Application in problems of growth and decay.

Vector Algebra: Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, the addition of vectors, scalar must

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pathfinderdefenceacademyposts · 4 years

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Best NDA Coaching Classes in Lucknow | Best NDA Coaching Center in Lucknow

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Citizen of Bhutan.

Citizen of Nepal.

Tibetan refugee who came over to India before January 1, 1962, with the intention of permanently settling in India.

AGE LIMITS

Nationality: Apart from Indian origin, candidates from other countries can also appear for NDA. Candidates must either be.

Minimum Age: 15-1/2 years. (For Form Filling)

Maximum Age: 18-1/2 years. (For Form Filling)

Marital Sex: Candidates must be unmarried.

Gender: Only male candidates are eligible to apply for NDA.

EDUCATIONAL QUALIFICATION

Army Wing of Pathfinder Defence Academy: Candidates applying for the Indian Army must have passed class 12/HSC in 10+2 pattern of School Education or equivalent examination conducted by a State Education Board or a University.

Air Force, Navy and Naval Academy of PathFinder Defence Academy: Candidates applying for Air Force, Navy and Naval Academy must have passed class 12/HSC in 10+2 pattern of School Education with Physics and Mathematics conducted by a State Education Board or a University.

Physical standard required for NDA: Candidates appearing in NDA must be physically and mentally fit according to the prescribed physical standards. A candidate recommended by the Services Selection Board (SSB) will undergo a medical examination by a Board of Service Medical Officers. Only those candidates will be declared qualified NDA and admitted to the academy who is declared fit by the medical board. The candidate must be in good physical and mental health and free from any disease/disability which is likely to interfere with the efficient performance of military duties. The minimum acceptable height is 157 cm for Army, Navy and Naval Academy while 162.5 cm for Air Force. For Gurkhas and individuals belonging to hills of North-Eastern, the minimum acceptable heights will be 5 cm less. For more detail required physical standards candidates are advised to read the NDA notification.

SYLLABUS

Paper-I Mathematics (Maximum Marks – 300) :

Algebra: Concept of set, operations on sets, Venn diagrams. De Morgan laws. Cartesian product, relation, equivalence relation. Representation of real numbers on a line. Complex numbers – basic properties, modulus, argument, and cube roots of unity. Binary system of numbers. Conversion of a number in decimal system to binary system and vice-versa. Arithmetic, Geometric and Harmonic progressions. Quadratic equations with real coefficients. The solution of linear inequations of two variables by graphs. Permutation and Combination. Binomial theorem and its application. Logarithms and their applications.

Matrices and Determinants: Types of matrices, operations on matrices Determinant of a matrix, basic properties of determinant. Adjoint and inverse of a square matrix, Applications – Solution of a system of linear equations in two or three unknowns by Cramer’s rule and by Matrix Method.

Trigonometry: Angles and their measures in degrees and in radians. Trigonometrically ratios. Trigonometric identities Sum and difference formulae. Multiple and Sub-multiple angles. Inverse trigonometric functions. Applications – Height and distance, properties of triangles.

Analytical Geometry of two and three dimensions: Rectangular Cartesian Coordinate system. Distance formula. Equation of a line in various forms. The angle between the two lines. The distance of a point from a line. Equation of a circle in standard and in general form. Standard forms of parabola, ellipse, and hyperbola. Eccentricity and axis of a conic. The point in a three-dimensional space, distance between two points. Direction Cosines and direction ratios. Equation of a plane and a line in various forms. The angle between the two lines and the angle between the two planes. Equation of a sphere.

Differential Calculus: Concept of a real-valued function – domain, range, and graph of a function. Composite functions, one to one, onto and inverse functions. Notion of limit, Standard limits – examples. Continuity of functions – examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative – applications. Derivatives of sum, product, and quotient of functions, a derivative of a function with respect of another function, derivative of a composite function. Second-order derivatives. Increasing and decreasing functions. Application of derivatives in problems of maxima and minima.

Integral Calculus and Differential equations: Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expressions, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals – determination of areas of plane regions bounded by curves – applications. Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of the first order and first-degree differential equations of various types – examples. Application in problems of growth and decay.

Vector Algebra: Vectors in two and three dimensions, magnitude and direction of a vector. Unit and null vectors, the addition of vectors, scalar multiplication of vector, scalar product or dot product of two vectors. Vector product and cross product of two vectors. Applications-work did by a force and moment of a force, and in geometrical problems.

Statistics and Probability:

Statistics: Classification of data, Frequency distribution, cumulative frequency distribution – examples Graphical representation – Histogram, Pie Chart, Frequency Polygon – examples. Measures of Central tendency – mean, median and mode. Variance and standard deviation – determination and comparison. Correlation and regression.

Probability: Random experiment, outcomes, and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability – classical and statistical – examples. Elementary theorems on probability – simple problems. Conditional probability, Bayes’ theorem – simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binominal distribution.

PAPER-II

General Ability Test (Maximum Marks-600)

PART – A

ENGLISH (Maximum Marks 200).

The question paper in English will be designed to test the candidate’s understanding of English and workmanlike use of words. The syllabus covers various aspects like Grammar and usage, vocabulary, comprehension, and cohesion in extended text to test the candidate’s proficiency in English.

PART – B

SYLLABUS OF PHYSICS

Physical properties and states of matter. Mass Weight, Volume, Density, and Specific Gravity, Principle of Archimedes, Pressure Barometer.

The motion of objects: Velocity and acceleration. Newton’s Laws of motion. Force and Momentum. Parallelogram of Forces. Stability and equilibrium of bodies. Gravitation, elementary ideas of work, Power and Energy.

Effects of heat: Measurement of temperature and heat. Change of state and latent heat. Modes of transference of heat. Sound Waves and their properties. Simple musical instruments. Rectilinear propagation of light. Reflection and Refraction. Spherical mirrors and lenses. Human eye.

Natural and artificial magnets: properties of a magnet. Earth as a magnet.

Static and current electricity: Conductors and non-conductors. Ohm’s law. Simple electrical circuits. Heating, lighting and magnetic effects of current. Measurement of electrical power. Primary and Secondary Cells. Use of X-rays.

General principles in the working of the following: Simple pendulum, Simple Pulleys, Siphon, Levers, Balloon. Pumps, Hydrometer, Pressure Cooker, Thermos Flask, Gramophone, Telegraphs. Telephone, Periscope, Telescope, Microscope, Mariner's Compass, Lightning Conductors and Safety Flues.

Syllabus of General Science :

Basis of Life – Cells, Protoplasms and Tissues, Elementary knowledge of human body and its important organs, Food – Source of Energy for man, Constituents of food, Balanced Diet, Achievements of Eminent Scientists, Difference between the living and non-living, Growth and Reproduction in Plants and Animals, Common Epidemics, their causes and prevention, The Solar System – Meteors and Comets, Eclipse.

History: Freedom Movement in India, elementary knowledge of five-year plans of India, Bhutan, Sarvodaya, National Integration and Welfare State, Basic Teachings of Mahatma Gandhi, A broad survey of Indian History, with emphasis on Culture and Civilisation, Elementary study of Indian Constitution and Administration, Panchayati Raj, Co-operatives and Community Development, Forces shaping the modern world; Renaissance, Exploration, and Discovery; War of American Independence. French Revolution, Industrial Revolution, and the Russian Revolution. Impact of Science and Technology on Society. Concept of one World, United Nations, Panchsheel, Democracy. Socialism and Communism. Role of India in the present world.

Geography: Origin of Earth, Rocks, and their classification; Weathering – Mechanical and Chemical, Earthquakes and volcanoes, Atmosphere and its composition; Temperature and Atmospheric Pressure, Planetary Winds, cyclones, and Anti-cyclones; Humidity; Condensation and Precipitation; Types of Climate. Major Natural regions of the World, Important Sea ports and main sea, land, and air routes of India. Main items of Imports and Exports of India, The Earth, its shape and size. Lattitudes and Longitudes, Concept of time, International Date Line, Movements of Earth and their effects, Ocean Currents and Tides, Regional Geography of India – Climate, Natural vegetation. Mineral and Power resources; location and distribution of agricultural and industrial activities.

Current Events: Current important world events, Knowledge of Important events that have happened in India in recent years, prominent personalities – both Indian and International including those connected with cultural activities and sports.

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