#standard form of quadratic equation meaning

[seekergkfan]

The standard form of the quadratic equation is:

The standard form of the quadratic equation is: A. y = a(x – h)2 + k B. y = a(x + h)2 + k C. y = x2 + bx + c D. y = x2 + k (more…) “”

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[eduusa]

How to Write a Quadratic Function in Standard Form

Quadratic Functions are defined as second-degree polynomial equation, which means it has at least one term with a power of two. Quadratic Functions are so named because Quad stands for ‘four’ (squared), and a quadratic function’s greatest degree should be 2.

Quadratic Functions can be represented in 3 forms: 

Standard Form : ax² + bx + c = 0

Vertex Form :  a(x – h)² + k = 0

Intercept Form : a(x – p)(x – q) = 0

#Quadratic Functions

[mademains]

Quadratic inequalities

#QUADRATIC INEQUALITIES HOW TO#

To be neat, the smaller number should be on the left, and the larger on the right. The distance we want is from 10 m to 15 m: (Note: if you are curious about the formula, it is simplified from d = d 0 + v 0t + ½a 0t 2, where d 0=20 , We can use this formula for distance and time: We also know the endpoints are excluded since 3 creates a denominator of zero and we have a strict inequality.A stuntman will jump off a 20 m building.Ī high-speed camera is ready to film him between 15 m and 10 m above the ground. $$(-2)^2 - 5(-2) - 6 > 0$$ $$4 + 10 - 6 > 0$$ $$ equire$$ Since the test of the number 4 produces a false statement, we know values that are greater than 4 will not satisfy the inequality. Let's choose -2, we will plug this in for x in the original inequality. We can solve quadratic inequalities to give a range of. Let's begin with interval A, we can choose any value that is less than -1. Quadratic inequalities are similar to quadratic equations and when plotted they display a parabola. Step 3) Substitute a test number from each interval into the original inequality. This interval is labeled with the letter "C". The solution to a quadratic inequality in one variable can have no values, one value or. Let us consider the quadratic inequality x2 5x Lastly, we have an interval that consists of any number that is greater than 6. The standard quadratic equation becomes an inequality if it is represented as ax2 + bx + c 0).

This interval is labeled with the letter "B". One interval contains any number less than -1 and is labeled with the letter "A". Quadratic Inequalities Given 3 x 2 > -x + 4 Rewrite the inequality with one side equal to zero. On the horizontal number line, we can set up three intervals: We have split the number line up into three intervals. It shows the data which is not equal in graph form. Introduces a conceptual basis for solving quadratic inequalities, looking at linear inequalities and using a knowledge of what quadratic graphs look like. An equation is a statement that asserts the equality of two expressions and a linear inequality is an inequality which involves a linear function. These endpoints will allow us to set up intervals on the number line. In quadratic inequalities worksheets, we learn that a quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Therefore, set the function equal to zero and solve. For a quadratic inequality in standard form, the critical numbers are the roots. $$x^2 - 5x - 6 > 0$$ Step 1) We will change this inequality into an equality and solve for x. It is important to note that this quadratic inequality is in standard form, with zero on one side of the inequality.

The endpoints are included for a non-strict inequality and excluded for a strict inequalityĮxample 1: Solve each inequality.

If a test number makes the inequality false, the region that includes that test number is not in the solution set.

If the test number makes the inequality true, the region that includes that test number is in the solution set.

If it is less than or greater than some number or any other polynomial. Consider a quadratic polynomial ax2+bx+c.

Substitute a test number from each interval into the original inequality Graphing a quadratic inequality is easier than you might think You just need to know the steps involved This tutorial takes you through those steps to. What do you mean by Quadratic inequalities.

For example, to solve a quadratic inequality -x2+x+2>0, we can find the values of x where the parabola.

Use the endpoints to set up intervals on the number line Students will solve quadratic inequalities and match each inequality with its solution set. Quadratic inequalities are best visualized in the plane.

These endpoints separate the solution regions from the non-solution regions.

If the quadratic inequality is not in one of the. is an example of a quadratic inequality, as it contains a single variable raised to the second power at maximum.

The solutions will give us the boundary points or endpoints Hence, we obtain four possible general forms of quadratic inequalities: ax 2 + bx + c > 0.

Replace the inequality symbol with an equality symbol and solve the equation.

Quadratic Inequalities A quadratic inequality is of the form: $$ax^2 + bx + c > 0$$ Where a ≠ 0, and our ">" can be replaced with any inequality symbol.

#QUADRATIC INEQUALITIES HOW TO#

In this lesson, we will learn how to solve quadratic and rational inequalities.

#Quadratic inequalities

[astresnotes-maths]

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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[class-xyznotes]

Economics Chapter 3 (Some Mathematical and Statistical Concepts)- Class 11

Exercise Economics Chapter 3 (Some Mathematical and Statistical Concepts)- Class 11 for KPK textbook board. Q.1) Write notes: i) Continuous variables ii) Discontinuous variables  iii) Independent and dependent variables  iv) Function v) Degree of an equation vi) Exponent  vii) Coefficients viii) Linear equation ix) Quadratic equation x) Increasing function xi) Decreasing function xii) Parameter Answer: i) Continuous variables: A Continuous variable is the one that assumes all values within its range is called a continuous variable. In a Continuous variable, the value of the variable is never an exact point. It is always in the form of an interval, the interval may be very small. For example, the age and height of a person. ii) Discontinuous variables: A discontinuous variable is the one that does not assume all values in its range is called a discontinuous variable. It takes up some values and leaves the other. Thus there is a gap in its values. For example, the price of Rice per kg changes from Rs.20 to 30 and Rs.30 to Rs. 40 and then to 50. iii) Independent and dependent variables : A variable which can assume any value independently is called an independent variable. If the change in the value of an independent variable brings a change in the value of another variable, that will be the dependent variable. For example, the case of price and quantity supplied. According to the law of supply, quantity supplied increases with an increase in price and vice versa. Here, the price changes independently and quantity supplied changes due to change in price. Therefore, the price is an independent variable whereas the quantity supplied is the dependent variable. iv) Function: A function is defined as a relationship between two variables such that for on value of the first variable, there is only one value of the second variable. In other words, if there exists one to one (1 -1) correspondence between two variables, then the relationship between the variables would be - 'Functional relationship". e.g. y= f(x) In this equation, for one value of x, there exists a unique value of y. Therefore we read it as "y is a function of x". v) Degree of an equation: The maximum or larger power in the equation is known as the degree of the equation. For example, ax2+bx+c=0 is equation of degree 2. vi) Exponent  It is also known as index or power. It is a quantity that is written over the head of the variable e.g x4. It means that x is multiplied four times x.x.x.x= x4. vii) Coefficients: Co-efficient is the quantity that appears on the left side of the unknown. For example, 2x2+3x+5=0. 2 and 3 are co-efficient. viii) Linear equation If the maximum power of the variable is one then the equation is said to be linear. We have a standard linear equation as: ax+b=0 where 'a' and 'b' are constants. Examples are 4x+3=11. ix) Quadratic equation: If the maximum power of the variable is two then the equation is said to be quadratic. We have a standard quadratic equation is: ax2+bx+c=0, where 'a', 'b' and 'c' are constants and a≠0. Examples are x2+2x-9=0. x) Increasing function Whenever two variables have a functional relationship i.e y=f(x), when the value of one variable increases, the value of other variables also increases or when one variable has decreasing tendency, the other variable also has a decreasing tendency or both variables have same tendency to change shows an increasing function. For example y=2x+3. xi) Decreasing function: Whenever two variables are related in the sense that one variable has an increasing tendency, while the other variable has a decreasing tendency or there exists a negative correlation between the two, it will be a decreasing function. For example y=20-3x. xii) Parameter There are some variables whose values keep on changing in real life but they are assumed to remain constant for illustration of economic laws. They are called parameters. Read more: Class 11 KPK Economics Notes Chapter 2 (Consumer behavior) Q.2) Distinguish between function and relation. Answer: A relation is a set of inputs and outputs that are related in some way. When each input in relation has exactly one output, the relation is said to be a function. To determine if a relation is a function, we make sure that no input has more than one output. Q.3) Discuss methods of collecting data. Answer: Methods of collecting data are as follows: i) Questionnaire Method ii) Direct personal observations iii) Indirect personal observations iv) Official Statistics v) Collection through enumerators Q.4) Write notes on: i) Tabulation  ii) Classification of data. Answer: i) Tabulation: The orderly arrangement of data into various rows and columns is called tabulation. Tabulation is a stage where data are ready for reading, for quick understanding, for publication, and for further statistical work. When the qualitative or quantitative raw data are classified according to one characteristic or one variable, the tabulation is called single or one-way. The tabulation is two-way when there are two variables. Similarly the tabulation is manifold when the data are divided into different categories on the basis of more than two criteria. ii) Classification of data: "Classification is the process of arranging things in groups or classes according to their resemblances and affinities". or The process of arranging data in groups or classes according to resemblances and similarities is called classification. The classification of the data mainly depends upon the nature, scope, and purpose of the statistical inquiry. Some characteristics of a good classification are: (1) The classification should be unambiguous (2) The classification should be stable (3) The classification should not be rigid. Q.5) Make a hypothetical table using two-way classification of data about Intermediate students of Lahore (Make the classes as science / Arts and Male / Female). Answer:

Q.6) Make the time series for years 2010-2015 for number of cars in Pakistan (Values in millions). Answer:

Q.7) Explain the concept of function. What are kinds of functions? Answer: Function: A function is defined as a relationship between two variables such that for on value of first variable there exists one and only one value of the second variable. In other words, if there exists one to one (1 -1) correspondence between two variables, then the relationship between the variables would be - 'Functional relationship". e.g. y= f(x).  Kinds of function are: i) Increasing function Whenever two variables have a functional relationship i.e y=f(x), when the value of one variable increases, the value of other variables also increases or when one variable has decreasing tendency, the other variable also has to decrease tendency or both variables have same tendency to change shows an increasing function. For example y=2x+3. ii) Decreasing function: Whenever two variables are related in the sense that one variable has an increasing tendency, while the other variable has a decreasing tendency or there exists a negative correlation between the two, it will be a decreasing function. For example y=20-3x. Single Valued Function: In the classical terminology, the function corresponds to a Valued Function " where for one value of independent variable i.e. x In y = f(x) there will be one single value for the dependent variable i.e. Y. Therefore, this one to one correspondence shows the single-valued function. Multi-Valued Function :  In the older (classical) terminolog} relation corresponds to .0.valued function in which one value of independent variable results in more than one value (multi-values) of the dependent variable. This is the multi-valued function. For example Y2 = X2. Implicit Function: Whenever two variables are dependent upon each other and by putting a value of one (X or Y) variable we get the value of the other variable i.e. (X or Y), this function is said to be implicit function. This term should be written in the form, F(x,y)=0 y-f(x)=0 For example xy=12 Explicit Function :  If a function is defined in a sense in which one is the dependent variable and the other is the independent variable, it is called an explicit function. The funtion Y= f(x) and x=g(y) are called explicit functions. For example, Y = 3x + .2 is an explicit function as Y is depending upon X. Inverse Function: Whenever we interchange the dependent and independent variables of a function Y = f(x), we get inverse function. i e X = f-1(y). This will be read as X is an inverse function of Y. For example, xy=5 gives y =5x-1. Constant Function: A function whose range consists of only one element is called a constant function. We can write the function Y = f(x) = 9. Hence the value of Y remains the same as 9, regardless of the value of X. In economics, we use T F C and autonomous investment as examples of this function. Linear Function : A function Y = f(x) of a single variable is linear if it takes the form. Y = f(x) = ax + b. where a, b are constants e.g. Y = 4x + 9 Quadratic Function : A function Y=f(x) is called quadratic function if it takes the form. Y = f(x) = ax2+ bx + c e.g. = x2+ 6x + 5. Log Function: When a variable is expressed as a function of the logarithm of another variable, the function is referred to as logarithmic function. For example Y = log10x and Y= loge x(In x). Exponential Function: If a variable appears in the exponent or power of the fixed base. i.e. 2x,  the function is called the exponential function. e.g. Y= 2x or Y = Cx. Q.8) Express the following statements in functional notation and give specific forms if possible. i) Profit is a function of the quantity of output (Q). Each unit gives Rs. 10/- as profit ii) Utility (U) is a function of quantity consumed (Q) iii) Saving (S) is a function of income (Y). People save 20 % of their incomes. Answer: i) P=f(Q) = 10Q ii) U=f(Q) iii) S=f(Y), S=20% of Y S=(20/100) × Y S=(1/5)× Y Q.9) Make the graphs of the equations 2x - 3y = 20, Q - 2 P = 20, Y = 10 + x2. Answer:

Q.13) Explain the method for constructing : i) Simple price index number. ii) Weighted price index numbers Answer: i) Simple price index number: A simple index number measures a relative change in single variable with respect to the base. A simple index number is the ratio of two values representing the same variable, measured in two different situations or in two different periods. For example, a simple index number of the price will give the relative variation of the price between the current period and a reference period. Weighted price index numbers: An index number that measures a relative change in a group of variables keeping in view the relative importance of variables. There are two methods of calculating weighted index numbers. i) Weighted aggregative price index numbers Price index= (Current year expenditure/ Base year expenditure) x 100 ii) A weighted average of relatives price index numbers: Pon= ∑WI/∑W where I=pn/po x 100 and W=poqo Read the full article

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Ncert solutions for class 3

Ncert solutions for class 3 English comprehensions are similar to Ncert solutions but differ in a few areas. The main difference between these two exams is that the former tests a person's understanding of the meaning of the terms used in the language. Whereas the latter focuses more on reading and writing skills. It is therefore important that when you prepare for these exams you consider how much you've progressed in both areas before looking at your English grammar scores.

Most NCERT textbooks cover issues from the current editions of all NCERT Class 3 Hindi texts. This includes the explanations of each topic and their corresponding practice examinations. The reality that Class 3 is such an important milestone in your educational career just adds to why you must pay special attention to every subject in your syllabus. In this guide, you will get tips and advice on preparing for the exams for each of the three classes included in the NCERT standard curriculum. Some of the topics you will study are as follows:

o Test preparation: When you choose to go through the reviews for the NCERT exam you will be asked to do several practice tests based on previously prepared material. Some of these review papers include questions based on a mix of previous exam papers and practice materials. As part of your preparation for the NCERT solutions for class 3 English comprehensions, you should also be preparing for a mock exam based on a sample exam. This will allow you to see how you are fair against the sample exam, as well as getting an idea of the kinds of questions you will face on the actual exam.

o Class 9 English fluency: When it comes to the NCERT exam, reading is not the only thing we learn. Not only do we have to be able to understand what we read, but we also have to be able to understand how we read it. In this class, you will learn about the different forms of literary language including the key constituents and differences between the various genres.

o Ncert solutions for class 4 maths: When you take the NCERT tests, you will be required to demonstrate your knowledge of arithmetic. This will involve answering a set of questions related to the subject matter, normally based on weekly issues. As part of your preparation, you will be expected to work through a range of practice questions that test both your understanding and basic skills. These will help you to build up what is known as speed reading' so that you can do well on the actual exam. One of the key things to remember about answering NCERT questions is to begin and finish answering them at the same time, completing your response before the other answers are displayed is one way of achieving this.

o Ncert solutions for class 8 maths: The syllabus for this test includes some topics that are covered not only in the main body of the course but in many of the sub-areas as well. One of these areas is Ncert solutions for class 8 maths which will include working through the quadratic equation and solving for the roots of the cubic boron polynomial. This is a key topic as it will help students to understand the inner workings of this integral and how to solve it for the purpose of finding out the answer using the right method. Another key area of this course is the quadratic formula which is used extensively in science and engineering and often found to be written off by students without being able to explain it in an understandable way. A good number of students will therefore look towards the use of a pre-algated solution for the problems when they cannot find an easy and clear answer on their own.

Ncert solutions for class 9 English. The syllabus for this test has some very standard Ncert solutions for class 9 English which will cover the basics of sentence structure, how to introduce a topic, and even how to give an explanation about a topic. The main topics covered are subject pronouns, demonstrative pronouns, question words, and prepositions. An important thing to remember when looking at the syllabus is that in every lesson there will be at least two or three topics that will be covered which will differ slightly from the rest of the lessons.

o Ncert solutions for class 6 science. The syllabus for this test includes quite a few standard Ncert solutions for class 6 science which are designed to test students’ understanding of properties of matter. These include topics such as atoms, molecules, matter, solid-state structures, electronic and optical properties, electromagnetic properties, and nuclear properties. Being able to understand the concepts behind each of these will allow students to grasp the material and therefore improve their grades.

[ncertsolutionsmath]

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. 

The responses to the inquiries present in the NCERT books are without a doubt the best examination material an understudy can get hold of. These CBSE NCERT Solutions of Class 10 Maths will likewise assist understudies with building a more profound comprehension of ideas canvassed in Class 10 Maths course reading. Rehearsing the course reading addresses will assist understudies with examining their degree of readiness and the information on ideas. The solutions to these inquiries present in the books can assist understudies with clearing their questions rapidly.

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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Indian Navy  Coaching in Chandigarh | NAVY SSR AA COACHING INSTITUTE IN CHANDIGARH- RN CAREER GROUP

Indian Navy Coaching in Chandigarh

RN Career Academy is that the best coaching centre for Defence & Navy Examination because it doesn't compromise with its quality and standard of teaching. it's tough being the simplest , but RN Career Academy team is usually up for a challenge of the very best magnitude. RN Career Academy is India’s best coaching institutefor Indian Navy Exam in Chandigarh that's offering quality educational service in several fields of study and examinations. Therefore, in reference to prominent Defence & Navy Exam entrance tests, our organization offers quality coaching for several subjects that fall therein.

Indian navy SSR AA exam coaching in chandigarh

Join best institute for Indian navy exam coaching in chandigarh. Here you get all best study material and best study environment.

• Join RN Career Academy Institute For – Indian Navy / Navy SSR Exam Coaching

Branches : Chandigarh

Teaching and Training on the Pattern of MILITARY SCHOOL

• Call Now for more information : 7399973929

APPLICATION FORM:

The application form is published within the important Newspapers which can be used. the shape within the prescribed format could also be typed on plain paper or downloaded from this website. the appliance forms are going to be available on this site from the date of advertisement for the respective batch and sort of entry. Candidates applying for quite one sort of entry are required to submit separate applications. However, just one form is to be filled for a specific entry. Choice of entry is to be clearly indicated on the appliance form.

You can apply just for one entry between MR Cook / MR Steward/ NMR Topass during a batch. All applications for AA and SSR, MR, MUS, NMR are to be addressed to the authority promulgated. Application sent through agent won't be accepted. Applications are received only through Ordinary Post. Applications received through speed post/ registered mail or couriers are rejected.

Navy SSR Eligibility Criteria:

Candidates must Passed 10+2 exams with Physics and Math and a minimum of one among these Subjects Chemistry/ Biology/ computing with recognized Board.

Age Limit for Navy SSR:

The required age of the candidates should be between 16 years and 20 years and their dates of birth. Candidates must change state between 1st February 2000 to 31st January 2003

Marital Status:

Unmarried candidates are eligible for Indian Navy SSR.

Candidates must be citizen of India.

Indian Navy SSR Exam Pattern 2020:

Indian Navy Senior Secondary Recruits (SSR) Exam Pattern is given below. Applicant who is applying for SSR Course released under Indian Navy SSR Recruitment 2020 are going to be selected supported the subsequent process.

• Written Exam.

• fitness test.

• Medical test.

Written Test for Indian Navy SSR Exam Pattern:

Exam Mode: English & Hindi

Exam Types: Objective Type

Exam Topics: English, Mathematics, public knowledge and Science.

Time Duration for the exam is hour

Applicant should have passed 10+2 class.

Medical Eligibility:

• Applicant must have minimum 157cm height.

• Weight and Chest should be proportionate.

• Ears should be cleaned and tartar faraway from teeth.

• The applicant must be in good physical and psychological state and free from any quite defect.

Visual Ability For Navy Exam:

• Without Glasses: Better Eyes – 6/6 and Worse Eyes- 6/9

• With Glasses: Better Eyes- 6/6 and Worse Eyes- 6/6

Navy SSR Exam Syllabus 2020:

There will be a four section: – General Awareness, Mathematics, Science, English

Navy SSR Syllabus for General Awareness:

Culture and Religion, Geography: Rivers, Soil, Ports, Mountains, Freedom Movement, Dance, Heritage and humanities , History, Languages, Capital and Currencies

Sports: Winners or championships or terms or No of Players, Defence, Current Affairs, Wars, Award and Authors, Diseases and Nutrition, National: Animals/ Birds/ Flower/ Sport/ Flag/ Monuments etc.

Navy SSR Syllabus for English:

This section question from Passage, Preposition, Correction of sentences, Change active to passive/passive to active , Change direct to indirect/indirect to direct, Verbs/Tense/Non Finites, Synonyms and Antonyms, Meanings of inauspicious words, Use of adjectives, Determiners(use of a, the, any, etc.)

Navy SSR Syllabus for Mathematics:

In this exam question are asked from Relations and Functions, Logarithms, Complex Numbers, Quadratic Equations, Sequences and Series, Trigonometry, Circles, Conic Sections, Introduction to 3 Dimensional Geometry, Probability Function, Limits and Continuity, Differentiation, Applications of Derivatives, Indefinite Integrals theorem , etc.

Navy SSR Syllabus for Science:

Physical World and Measurement, Kinematics, Laws of Motion, Work, Energy, and Power, Motion of System of Particles and Rigid Body / Gravitation, Heat Thermodynamics, Oscillations, Magnetic Effect of Current and Magnetism, Electromagnetic, Atomic Nucleus / Solid and Semi-Conductor Devices, Metals and Non-Metals, chemistry , Food, Nutrition, and Health, Physiology and Human Diseases, computing etc.

Indian Navy SSR Exam Dates 2020:

Indian Navy has been released fresh notification for the recruitment of the new candidate for Indian Navy. Indian Navy invites online application from unmarried Indian Male candidates for enrolment as sailors for senior secondary Recruits (SSR) for August 2020 Batch. This test very tough to Crack, but if you properly specialise in the study then you'll easily crack the exam. In times competition is extremely high so got to do to clear SSR exam extra efforts.

Source : https://medium.com/@rncareergroup/indian-navy-coaching-in-chandigarh-navy-ssr-aa-coaching-institute-in-chandigarh-rn-career-group-a72d1666d5be

RN CAREER GROUP CHANDIGARH

Sco 54 55 fourth floor near mukat hospital sector 34A Chandigarh.

7399973929

#navycoachingchandigarh #best indian navy coaching institute in Chandigarh #navy ssr aa written exam coaching centre in Chandigarh #navy exam coaching centre in Chandigarh

[studyinginstyle]

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±√​b​2​​−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!

#studyinginstyle #study tips #SAT #SAT study tips #SAT studying #SAT resources #studyblr #studying #mine

[sciencespies]

Math genius has come up with a wildly simple new way to solve quadratic equations

https://sciencespies.com/humans/math-genius-has-come-up-with-a-wildly-simple-new-way-to-solve-quadratic-equations/

Math genius has come up with a wildly simple new way to solve quadratic equations

If you studied algebra in high school (or you’re learning it right now), there’s a good chance you’re familiar with the quadratic formula. If not, it’s possible you repressed it.

By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations, but according to mathematician Po-Shen Loh from Carnegie Mellon University, there’s actually been an easier and better way all along, although it’s remained almost entirely hidden for thousands of years.

In a 2019 research paper, Loh celebrates the quadratic formula as a “remarkable triumph of early mathematicians” dating back to the beginnings of the Old Babylonian Period around 2000 BCE, but also freely acknowledges some of its ancient shortcomings.

“It is unfortunate that for billions of people worldwide, the quadratic formula is also their first (and perhaps only) experience of a rather complicated formula which they must memorise,” Loh writes.

That arduous task – performed by approximately four millennia worth of maths students, no less – may not have been entirely necessary, as it happens. Of course, there have always been alternatives to the quadratic formula, such as factoring, completing the square, or even breaking out the graph paper.

But the quadratic formula is generally regarded as the most comprehensive and reliable method for solving quadratic problems, even if it is a bit inscrutable. This is what it looks like:

That formula can be used to solve standard form quadratic equations, where ax2 + bx + c = 0.

In September 2019, Loh was brainstorming the mathematics behind quadratic equations when he struck upon a new, simplified way of deriving the same formula – an alternative method which he describes in his paper as a “computationally-efficient, natural, and easy-to-remember algorithm for solving general quadratic equations”.

“I was dumbfounded,” Loh says of the discovery. “How can it be that I’ve never seen this before, and I’ve never seen this in any textbook?”

In Loh’s new method, he starts from the standard method of trying to factor the quadratic x² + bx + c as (x −   )(x −   ), which amounts to looking for two numbers to put in the blanks with sum −b and product c. He uses an averaging technique that concentrates on the sum, as opposed to the more commonly taught way of focusing on the product of two numbers that make up c, which requires guesswork to solve problems.

“The sum of two numbers is 2 when their average is 1.” Loh explains on his website.

“So, we can try to look for numbers that are 1 plus some amount, and 1 minus the same amount. All we need to do is to find if there exists a u such that 1 + u and 1 − u work as the two numbers, and u is allowed to be 0.”

According to Loh, a valid value for u can always be determined per Loh’s alternative quadratic method, in an intuitive way, making it possible to solve any quadratic equation.

In Loh’s paper, he admits he would “be very surprised if this approach has entirely eluded human discovery until the present day, given the 4,000 years of history on this topic”, but says the alternative technique – which combines steps pioneered by Babylonian, Greek, and French mathematicians – is “certainly not widely taught or known (the author could find no evidence of it in English sources)”.

However, since first sharing his pre-print paper describing the simple proof online in October, Loh says his attention has been drawn to a 1989 research article that is the most similar previous work he has found – going some way to justify his disbelief that this alternative method had not been identified before now.

“The other work overlapped in almost all calculations, with an apparent logical difference in assuming that every quadratic can be factored, and a pedagogical difference in choice of sign,” Loh explained to ScienceAlert in an email.

All that remains to be solved then, is the mystery of why this technique hasn’t become more widely known previous to this, since it gives us, in Loh’s words, “a delightful alternative approach for solving quadratic equations, which is practical for integration into all mainstream curricula”.

(Not to mention, of course, that it might just mean that nobody need ever again memorise the quadratic formula.)

We still don’t know how this escaped wider notice for millennia, but if Loh’s instincts are right, maths textbooks could be on the verge of a historic rewriting – and we don’t take textbook-changing discoveries lightly.

“I wanted to share it as widely as possible with the world,” Loh says, “because it can demystify a complicated part of maths that makes many people feel that maybe maths is not for them.”

The research paper is available at pre-print website arXiv.org, and you can read Po-Shen Loh’s generalised explanation of the simple proof here.

A version of this article was first published in December 2019.

#Humans

#Humans

[etutorworld123]

Strategies To Ace SAT Math Questions

In less than a month from now, you are going to write your SAT test, by this time, you must have studied and understood the SAT test format thoroughly. Now, it is more crucial than ever to give it your best shot- make use of all the resources at your disposal. Solving innumerable SAT practice test is not enough to get a high score; it demands right planning and strategies.

Set a target score!!! Have a clear picture of where you want to land.

You have heretofore, a clear vision of your desired college or colleges and the subject you want to study. Thus, you are aware of the degree of score flexibility you can afford in your SAT math section. For example, if your target is a math or science major in schools like MIT, Caltech or any other technical school, then your SAT math target score should be no less than 800. Do not be overwhelmed and know that it is absolutely achievable. In fact, only math section allows you the opportunity of scoring a perfect 800.

Even if math wasn’t your forte, with smart SAT prep, 800 SAT math score is definitely attainable.

The math questions in SAT test may appear like you have never seen anything like this before. However, the SAT math test is not composed to check advanced math skills. In reality, SAT math section is designed to test only the concepts that you have studied in high school like Basic and advanced algebra, geometry and basic statistics.

Here’s the complete list of  concepts tested in SAT math-

·          Basic Algebra

o         Linear functions

o         Single variable equations

o         Systems of linear equations

o         Absolute value

·          Advanced Algebra

o         Manipulating polynomials

o         Quadratic equations

o         Dividing polynomials

o         Exponential functions

o         Function notation

o         Solving exponential equations

o         Systems of equations with nonlinear  equations

·          Problem Solving and Data Analysis

o         Ratios and proportions

o         Scatterplots and graphs

o         Categorical data and probabilities

o         Experimental interpretation

o         Mean, median, mode, standard deviation

·          Additional Topics

o         Coordinate geometry—lines and slopes

o         Coordinate  geometry—nonlinear functions

o         Geometry—circles

o         Geometry—lines  and angles

o         Geometry—solid  geometry

o         Geometry—triangles  and polygons

o         Trigonometry

o         Complex numbers

To maintain the difficulty level, the SAT test is designed to test high school math concepts in unconventional ways. So, scoring perfect 800 does not depend on how skilled you are in math, it actually depends on hard you work to polish the already learnt concepts.

Time yourself- for your SAT test math section, you will get a little over a minute per question, it is therefore, paramount to practice working against the clock.

·Consider hiring a SAT math tutor instead of wasting time in finding free study material online. Your tutor will provide all the material you need while you invest your precious time where it should be invested i.e. preparation.

·Confidence comes from practice and preparation; solve as many SAT math practice tests as you can. Confidence equals to less exam anxiety and thus a better score.

·While solving practice test questions pay utmost attention to repeated errors; understanding your mistakes is as an important aspect of practice.

·Fill the concept gap! This is where your SAT prep tutor could be of great help; take a diagnostic test to gauge your weaknesses and overcome them with your tutor’s help.

Must know EQUATION-SOLVING TECHNIQUES to pace your SAT prep-

1.Cardinal rule of equations—apply the same condition to both sides of the equation. For example, if you divide the left side of the equation by 2, divide the equation on the right side with the same.

2.Solve a system of two equations with two variables—practice how to use substitution and combination/elimination

· Substitution method- solve an equation to get one variable and apply that in the other equation

·Combination/elimination method- multiply both sides of one equation by a number that will allow you to remove a variable when you add the two equations together.

3.Factor and solve quadratics—to solve a quadratic equation, you must first get it to the form ax2 + bx + c = 0, then factor, and finally set each factor equal to 0. If an equation is not easily factored, you can use the quadratic formula:

4.Clearing fractions—a fraction heavy equation becomes easier to work with after eliminating fractions; find the lowest common denominator (LCD) of all fractions, and multiply the entire equation by this LCD.

5.Cross multiplying—when you have an equation with a single fraction on each side, multiply the denominator of the left side by the numerator of the right and vice-versa. Set these two results equal to each other to have a simpler equation to solve.

For more such tips and tricks hire an expert SAT math tutor at https://www.etutorworld.com/. Remember SAT test demands practice; it is therefore crucial that you invest your time wisely and let your tutor take care of the rest. Unlike other tuition services available online, your trust and investment in etutor is secured by a money back guarantee.

#SAT practice test

[ss1986us]

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.

 Chapter 11 – Construction

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.

 Chapter 12 - Areas related to Circles

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.

 Chapter 14 – Statistics

Here you will be calculating mean, median and mode to grouped data. The problems related to cumulative frequency will also be worked upon.

Chapter 15 – Probability

Students will be made acquainted with the values of probability lying between zero and one.

 Why Entrancei

The expert team at Entrancei has created some awesome content as presented in the form of ncert solutions for class 10 maths. We believe in providing a complete solution to students.

#https://www.entrancei.com/cbse-sample-paper-class-10-maths

[wiskwa-en]

A `mathematical’ problem

The following `mathematical’ problem is doing the rounds on the internet.

Personally I am not a big fan of this kind of `problem’ because the purpose is not to determine the system behind the data, because there is no unique law that governs it, but whatever it was that was in the head of the poser of the problem.

My standard reply to such a question is: 0 (or sometimes 42, the universal answer from The Hitch-hikers Guide to the Galaxy). Can we say something sensible about a problem like this?

Let us see. For starters: the function of + is clearly not that of addition (if = is supposed to mean equality); this suggested to many people to replace it by some other symbol, @ say. The question then is: is there an operation @ that produces for every pair of natural numbers m and n a natural number m@n and in such a way that 1@4=5, 2@5=12 and 3@6=21? And if yes then what is 5@8?

For a mathematician the answer is clear: apart from the three demands we are free to do as we please, so the answer is “yes” and 5@8 is not determined it can be what we want it to be. For eaxample: define m@n=0, except in the three prescribed cases; that justifies my standard answer. If we separately define 5@8=42 then Deep Thought’s universal answer becomes correct.

Most people do not expect an answer like the two given above but rather a `formula’; some expression with m and n in it that `predicts’ what 5@8 should be. Formulas like that are plentiful. If you look at the data then the three equations are of the form m@(m+3)=x, so it could very well be that the operation simply works with the first coordinate only.

We have three values and these can be fitted by a quadratic polynomial in m alone. You can check that m@n=m2+4m meets our three requirements (plug in m=1, 2, 3). That will produce the answer given by most of the internet: 5@8=45.

With a little twist you can make infinitely many formulas that give the three desired outcomes all produce different results for 5@8. The trick is to find something that produces the value 0 when you substitute 1, 2, or 3 for m and only then. You can take (m-1)(m-2)(m-3). Using that we can produce infinitely many formulas: for every natural number k define m@kn=m2+4m+k(m-1)(m-2)(m-3).

With some tinkering it should be possible to make formulas that have 5@8 take on any value you like; I’d say: get to work. Here’s an example.

It produces 5@8=4754660328285.

To those who want to know if the sequence 5, 12 21 has any `natural’ extensions I recommend the On-line Encyclopedia of Integer Sequences; put the sequence in the search box to see what’s available.

#sequence #iq-test #interpolation

[toppersexam]

NDA 2020 Age Limit, Syllabus, Online Free Mock Test, MCQ, Books

NDA 2020 Age Limit, Syllabus, Online Free Mock Test, MCQ, Books NDA (II) 2020 Rejected applicants list has been published due to non-payment of exam fee. Admit Card is releasing soon. The exam will be conducted by Union Public Service Commission (UPSC). UPSC NDA entrance exam is a gateway for the aspirants who want to make their career in Indian Army, Navy and Air Force. NDA Age Limit It should be clearly noted that only unmarried male candidates, who are not born earlier than July 2, 2001 and not later than July 1, 2004 are eligible to appear for NDA 1 Exam. For NDA 2 2020, candidates must be born between January 2, 2002 and January 1, 2005.

NDA Free Online Mock Test Crack NDA Recruitment exam with the help of online mock test Series or Free Mock Test. Every Sample Paper in NDA Exam has a designated weightage so do not miss out any Paper. Prepare and Practice Mock for NDA exam and check your test scores. You can get an experience by doing the Free Online Test or Sample Paper of NDA Exam. Free Mock Test will help you to analysis your performance in the Examination. NDA Free Online Mock Test : Available Now NDA MCQs Buy the question bank or online quiz of NDA Exam Going through the NDA Exam Question Bank is a must for aspirants to both understand the exam structure as well as be well prepared to attempt the exam. The first step towards both preparation as well as revision is to practice from NDA Exam with the help of Question Bank or Online quiz. We will provide you the questions with detailed answer. NDA MCQs : Available Now NDA 2020 Syllabus Paper-1 : Mathematics Algebra 1. relation, Logarithms and their applications. 2. equivalence relation. 3. Representation of real numbers on a line. 4. Complex numbers—basic properties, 5. modulus, argument,  Binomial theorem and its applications 6. cube roots of unity. 7. Solution of linear inequations of two variables by graphs.   8. Binary system of numbers. 9. Conversion of a number in decimal system to binary system and      vice-versa. 10. Arithmetic, Permutation and Combination. 11. Geometric and Harmonic progressions. 12. Quadratic equations with real coefficients. 13. Solution of linear inequations of two variables by graphs. Matrices and Determinants 1. Types of matrices, Adjoint and inverse of a square matrix, 2. operations on matrices.basic properties of determinants. 3. Determinant of a matrix, 4. Applications-Solution of a system of linear equations in two or three    unknowns by Cramer’s rule and by Matrix Method. Trigonometry 1. Angles and their measures in degrees and in radians. 2. Trigonometrical ratios. 3. Trigonometric identities Sum and difference formulae. 4. Multiple and Sub-multiple angles. 5. Inverse trigonometric functions. 6. Applications-Height and distance, 7. properties of triangles. Analytical Geometry of Two and Three Dimensions 1. Rectangular Cartesian Coordinate system. 2. Distance formula.Direction Cosines and direction ratios.   3. Equation of a line in various forms. 4. Angle between two lines. 5. Distance of a point from a line. 6. Equation of a circle in standard and in general form. 7. Standard forms of parabola,Equation of a sphere. 8. ellipse and hyperbola.Equation two points.   9. Eccentricity and axis of a conic. 10. Point in a three dimensional space, 11. distance between two points. 12. Direction Cosines and direction ratios. 15. Equation of a plane and a line in various forms. 16. Angle between two lines and angle between two planes. Differential Calculus 1. Concept of a real valued function–domain, 2. range and graph of a function. 3. Composite functions, Derivatives of sum, 4. one to one, Increasing and decreasing functions. 5. onto and inverse functions. 6. Notion of limit, Second order derivatives. 7. Standard limits—examples. 8. Continuity of functions - examples, 9. algebraic operations on continuous functions. 10. Derivative of function at a point, 11. geometrical and physical interpretation of a derivative-application. 12. derivative of a function with respect to another function, 13. product and quotient of functions, 15. derivative of a composite function. 16. Application of derivatives in problems of maxima and minima Integral Calculus and Differential Equations 1. Integration as inverse of differentiation, 2. integration by substitution and by parts, 3. standard integrals involving algebraic expressions, 4. trigonometric,  Application in problems of growth and decay. 5. exponential and hyperbolic functions. 6. Evaluation of definite integrals—determination of areas of plane regions     bounded by curves—applications. 7. Definition of order and degree of a differential equation, 8. formation of a differential equation by examples. 9. General and particular solution of a differential equations, 10. solution of first order and first degree differential equations      of various types—examples. Victor Algebra 1. Vectors in two and three dimensions, 2. magnitude and direction of a vector. 3. Unit and null vectors,  addition of vectors, 4. Applications—work done by a force and moment of a force and in    geometrical problems. 5. scalar multiplication of a vector, 6. scalar product or dot product of two vectors. 7. Vector product or cross product of two vectors. Statistics and Probability 1. Statistics: Classification of data, 2. Frequency distribution,  Conditional probability,   3. cumulative frequency distribution - examples. 4. Graphical representation - Histogram, 5. Pie Chart, frequency polygon—examples. Measures of Central tendency—     Mean, median and mode. 6. Variance and standard deviation determination and comparison. 7. Correlation and regression.Probability: Random experiment, 8. outcomes and associated sample space, events, 9. mutually exclusive and exhaustive events, impossible and certain events. 10. Union and Intersection of events. Complementary, 11. elementary and composite events. Definition of probability—classical      and statistical—examples. 12 .Elementary theorems on probability—simple problems. 13 .Bayes’ theorem—simple problems. Random variable as       function on a sample space. 14 .Binomial distribution, 15. examples of random experiments giving rise to Binominal distribution. Paper-2 : General Ability Test English 1. Grammar and usage, vocabulary, comprehension General Knowledge Physics 1. Physical Properties and States of Matter, 2. Mass, Weight, Volume, 3. Density and Specific Gravity, Principle of Archimedes, 4. Pressure Barometer. Motion of objects, 5. Velocity and Acceleration, Newton’s Laws of Motion, 6. Force and Momentum, Parallelogram of Forces, 7. Stability and Equilibrium of bodies, Gravitation, 8. elementary ideas of work, Power and Energy. 9. Effects of Heat, Measurement of Temperature and Heat, 10. change of State and Latent Heat, Modes of transference of Heat. 11. Sound waves and their properties, Simple musical instruments. 12. Rectilinear propagation of Light, Reflection and refraction. 13. Spherical mirrors and Lenses, Human Eye. 14. Natural and Artificial Magnets, Properties of a Magnet, 15. Earth as a Magnet.Static and Current Electricity, 16. conductors and Non-conductors,Ohm’s Law, 17. Simple Electrical Circuits, Heating, 18. Lighting and Magnetic effects of Current, 19. Measurement of Electrical Power, 20. Primary and Secondary Cells, Use of X-Rays. 21. General Principles in the working of the following: 22. Simple Pendulum, Simple Pulleys, Siphon, 23. Levers, Balloon,Pumps, Hydrometer, 24. Pressure Cooker, Thermos Flask, Gramophone, 25. Telegraphs, Telephone, Periscope, Telescope, 26. Microscope, Mariner’s Compass; 27. Lightening Conductors, Safety Fuses Chemistry 1. Physical and Chemical changes. 2. Elements, Carbon - different forms. 3. Mixtures and Compounds, 4. Symbols, Fertilizers—Natural and Artificial. 5. Formulae and simple Chemical Equations, 6. Law of Chemical Combination (excluding problems). 7. Properties of Air and Water. 8. Preparation and Properties of Hydrogen, 9. Oxygen,Glass, Ink, Paper, Cement, 10. Nitrogen and Carbondioxide, 11. Oxidation and Reduction. 12. Acids, bases and salts. 13. Material used in the preparation of substances like Soap, 14. Paints, Safety Matches and Gun-Powder. 15. Elementary ideas about the structure of Atom,      Atomic Equivalent and Molecular Weights, Valency. General Science 1. Difference between the living and non-living. Basis of Life—Cells, 2. Protoplasms and Tissues. Growth and Reproduction in    Plants and Animals. 3. Elementary knowledge of Human Body and its important organs. 4. Common Epidemics, their causes and prevention. 5. Food—Source of Energy for man. Constituents of food, 6. Balanced Diet. The Solar System—Meteors and Comets, 7. Eclipses. Achievements of Eminent Scientists. History Freedom Movement 1. A broad survey of Indian History, with emphasis on    Culture and Civilisation. 2. Freedom Movement in India. Elementary study of Indian    Constitution and Administration. 3. Elementary knowledge of Five Year Plans of India. 4. Panchayati Raj, Co-operatives and Community Development. 5. Bhoodan, Sarvodaya, National Integration and Welfare State, 6. Basic Teachings of Mahatma Gandhi.Exploration and Discovery; 7. Forces shaping the modern world; Renaissance,   8. War of American Independence. French Revolution, 9. Industrial Revolution and Russian Revolution. 10. Impact of Science and Technology on Society. 11. Concept of one World, United Nations, Panchsheel, 12. Democracy, Socialism and Communism. Role of      India in the present world. Geography 1. The Earth, its shape and size. Lattitudes and Longitudes, 2. Concept of time. International Date Line. . 3. Origin of Earth. Rocks and their classification; 4. Weathering-Mechanical and Chemical, 5. Earthquakes and Volcanoes.Movements of Earth and their effects. 6. Ocean Currents and Tides Atmosphere and its composition; 7. Temperature and Atmospheric Pressure, 8. Planetary Winds, Cyclones and Anti-cyclones; 9. Humidity; Condensation and Precipitation; 10. Types of Climate, Major Natural regions of the World. 11. Regional Geography of India—Climate, Natural vegetation. 12. Mineral and Power resources; 13. location and distribution of agricultural and Industrial activities. 14. Important Sea ports and main sea, 15. land and air routes of India. Main items of Imports and Exports of India. Current Events 1. Knowledge of Important events that have happened in    India in the recent years. 2. Current important world events. 3. Prominent personalities—both Indian and International including those connected with cultural activities and sports. NDA Exam Pattern 2020 Negative Marking : Mathematics : 0.83 General Abilities : 1.33 PaperSubjectNo. of QuestionMarksDuration Paper -1 Mathematics120300150 Minutes Paper - IIGeneral Ability Test (English & General Knowledge)

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