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Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
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or
Call us at : 08263069601
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Arithmetic progression
For class 10.
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant
This PPT will clarify your all doubts in Arithmetic Progression.
Please download this PPT and if any doubt according to this PPT, please comment , then i will try to solve your problem.
Thank you :)
This document defines and provides examples of arithmetic progressions. An arithmetic progression is a sequence of numbers where each term is calculated by adding a fixed number, called the common difference, to the preceding term. The document provides formulas for calculating the nth term and sum of terms in an arithmetic progression. Examples are given for finding specific terms, number of terms, common differences, and sums of arithmetic progressions.
Arithmatic progression for Class 10 by G R AhmedMD. G R Ahmed
An arithmetic progression (AP) is a sequence of numbers where the difference between consecutive terms is constant. The constant difference is called the common difference. The sum of the first n terms of an AP can be calculated using the formula: Sum = n/2 * (first term + last term). Several word problems are presented involving finding sums, terms, or properties of AP sequences.
This document discusses arithmetic progressions (APs). Some key points:
- An AP is a sequence of numbers where each subsequent term is calculated by adding a fixed number (the common difference) to the previous term.
- The general term of an AP is expressed as an + (n-1)d, where a is the first term and d is the common difference.
- The sum of the first n terms of an AP is calculated as Sn = (n/2)(a + l), where a is the first term, l is the last term, and n is the number of terms being summed.
This document defines arithmetic progressions and provides examples to illustrate key concepts such as common difference, general term, and formulas to calculate the sum of terms. It includes 10 practice problems with solutions to find missing terms, sums of terms, and numbers in arithmetic progressions given information such as terms, sums, and products.
This document defines arithmetic progressions and provides formulas to calculate the nth term and sum of the first n terms of an arithmetic progression. It states that an arithmetic progression is a list of numbers where each subsequent term is obtained by adding a fixed number, called the common difference, to the preceding term. Formulas are derived to calculate the nth term as an = a + (n-1)d, where a is the first term and d is the common difference. The formula to calculate the sum of the first n terms is derived as Sn = n/2(a + an), where a is the first term, an is the nth term, and n is the number of terms. Some examples are provided to demonstrate using the
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )
Arithmetic progression
For class 10.
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant
This PPT will clarify your all doubts in Arithmetic Progression.
Please download this PPT and if any doubt according to this PPT, please comment , then i will try to solve your problem.
Thank you :)
This document defines and provides examples of arithmetic progressions. An arithmetic progression is a sequence of numbers where each term is calculated by adding a fixed number, called the common difference, to the preceding term. The document provides formulas for calculating the nth term and sum of terms in an arithmetic progression. Examples are given for finding specific terms, number of terms, common differences, and sums of arithmetic progressions.
Arithmatic progression for Class 10 by G R AhmedMD. G R Ahmed
An arithmetic progression (AP) is a sequence of numbers where the difference between consecutive terms is constant. The constant difference is called the common difference. The sum of the first n terms of an AP can be calculated using the formula: Sum = n/2 * (first term + last term). Several word problems are presented involving finding sums, terms, or properties of AP sequences.
This document discusses arithmetic progressions (APs). Some key points:
- An AP is a sequence of numbers where each subsequent term is calculated by adding a fixed number (the common difference) to the previous term.
- The general term of an AP is expressed as an + (n-1)d, where a is the first term and d is the common difference.
- The sum of the first n terms of an AP is calculated as Sn = (n/2)(a + l), where a is the first term, l is the last term, and n is the number of terms being summed.
This document defines arithmetic progressions and provides examples to illustrate key concepts such as common difference, general term, and formulas to calculate the sum of terms. It includes 10 practice problems with solutions to find missing terms, sums of terms, and numbers in arithmetic progressions given information such as terms, sums, and products.
This document defines arithmetic progressions and provides formulas to calculate the nth term and sum of the first n terms of an arithmetic progression. It states that an arithmetic progression is a list of numbers where each subsequent term is obtained by adding a fixed number, called the common difference, to the preceding term. Formulas are derived to calculate the nth term as an = a + (n-1)d, where a is the first term and d is the common difference. The formula to calculate the sum of the first n terms is derived as Sn = n/2(a + an), where a is the first term, an is the nth term, and n is the number of terms. Some examples are provided to demonstrate using the
The document discusses arithmetic progressions (AP), which are lists of numbers where each subsequent term is calculated by adding a fixed number (the common difference) to the previous term. It provides examples of APs with positive, negative, and zero common differences. The general formula for the nth term and sum of the first n terms of an AP are defined. Examples are given to demonstrate calculating specific terms and sums using the formulas.
An arithmetic progression is a sequence of numbers where each term is calculated by adding a constant value, called the common difference, to the previous term. The common difference is the fixed amount subtracted between any two consecutive terms. The general formula for an arithmetic progression is an = a + (n-1)d, where a is the first term and d is the common difference. Some key points covered are:
- Sequences have a specific relation between consecutive terms
- Examples show calculating subsequent terms by adding the common difference
- The formula is used to find specific terms like the 5th term
- The sum of n terms can be calculated using a formula of n/2 * (2a + (n-1
This document provides information about getting fully solved assignments by emailing help.mbaassignments@gmail.com or calling 08263069601. It includes sample math assignment questions on sets, trigonometry, limits, probability, and solving systems of equations. The 6-question assignment covers topics like sets, radians, proof of trigonometric identities, continuity, probability, and solving 3 equations with 3 unknowns. Students are encouraged to email their semester and specialization to get solved assignments.
This document defines an arithmetic progression as a sequence of numbers where each term is calculated by adding a fixed number (the common difference) to the preceding term. It provides the formulas to calculate the nth term and the sum of the first n terms of an arithmetic progression given the first term, common difference, and n. It also works through examples of finding the 12th term when the 1st term is 2 and common difference is 2, and finding the sum of the first 10 terms when the 1st term is 5 and common difference is 3.
Arithmetic progression
For class 10.
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant
An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant. The document provides examples of arithmetic progressions and discusses formulas for calculating the nth term in a sequence, the sum of terms in a finite arithmetic progression, and solving problems involving finding the number of terms, first term, or common difference given values in the sequence.
This document provides a summary of concepts often seen on the JMET exam and includes example problems and solutions. Some key concepts covered include algebra, functions, equations, ratios and rates. Multiple choice problems are presented across various math and logic topics, followed by the solutions. Reviewing these types of problems and understanding the solutions can help prepare for exams like JMET, XAT and FMS that include quantitative reasoning sections.
The document discusses arithmetic progressions (AP), which are lists of numbers where each subsequent term is calculated by adding a fixed number (the common difference) to the previous term. It provides examples of APs and explains how to determine if a list is an AP based on having a common difference between terms. The key characteristics of an AP include the first term, common difference, a formula for calculating the nth term, and a formula for calculating the sum of the first n terms. Examples are provided to demonstrate how to use the formulas to find the 10th term or sum of terms in a given AP.
The document defines arithmetic mean and arithmetic series. Arithmetic mean is calculated by adding all terms of a sequence and dividing by the total number of terms. It provides examples of inserting arithmetic means between given terms. An arithmetic series is the sum of an arithmetic sequence. The sum is calculated by multiplying the number of terms by the average of the first and last terms. It provides examples of calculating the sum of arithmetic series.
The document discusses arithmetic progressions (AP), which are sequences where the difference between successive terms is constant. It defines an AP using the notation an = a + (n-1)d, where a is the first term, d is the common difference, and n indexes the terms. It provides examples and explains how to find individual terms, determine if a sequence is an AP, and calculate the sum of terms in an AP using the formula Sn = 1/2n(2a + (n-1)d). Various problems are worked through to demonstrate applying the concepts and formulas for APs.
pedagogy of mathematics part ii (numbers and sequence - ex 2.7), numbers and sequences, Std X samacheer Kalvi, Geometric progression, definition of geometric progression, general form of geometric progression, general term of geometric progression,
The document defines key polynomial vocabulary including:
- Terms are numbers or products of numbers and variables raised to powers. Coefficients are numerical factors of terms. Constants are terms that are only numbers.
- Polynomials are sums of terms involving variables raised to whole number exponents, with no variables in denominators.
- Types of polynomials include monomials (1 term), binomials (2 terms), and trinomials (3 terms). Degree is the largest exponent of any term.
- Operations on polynomials include adding/subtracting like terms, multiplying using distribution and FOIL, dividing using long division, and special products like (a+b)2 and (a+b)(a
An arithmetic progression is a sequence of numbers where each term after the first is calculated by adding a fixed number, called the common difference, to the previous term. The nth term can be calculated as an = a + (n - 1)d, where a is the first term and d is the common difference. An arithmetic progression can be either finite, with a fixed number of terms, or infinite, with an unlimited number of terms. The sum of the first n terms of an arithmetic progression is given by Sn = n/2(2a + (n-1)d).
Algebra 1 commutative and associative properitesmathriot
The document provides examples of using properties of numbers and algebra to simplify expressions. It gives step-by-step workings for expressions like 11(10-8), 6(4x+5), and 3⋅5⋅3⋅4. It defines the commutative and associative properties. Later examples show how to write an algebraic expression from a word problem and then simplify it using the distributive property.
This document contains a 40 question mathematics exam with multiple choice questions covering topics like trigonometry, calculus, algebra, geometry, and complex numbers. The questions test concepts such as finding the resultant of forces, variances of populations, solving quadratic equations, evaluating integrals, solving trigonometric equations, properties of matrices, logarithmic functions, maxima and minima of functions, loci of points, differentiability of functions, areas of geometric shapes, combinations, Taylor series expansions, solutions to differential equations, and transformations of points and planes.
This document discusses arithmetic and geometric progressions. It defines arithmetic and geometric sequences as lists of numbers where each subsequent term is calculated using a common difference or ratio. It provides formulas to calculate the nth term and sum of the first n terms for both progressions. The document also discusses arithmetic and geometric means as the averages between two numbers in an arithmetic or geometric progression.
This document provides an introduction to number theory, covering divisibility, greatest common divisors, least common multiples, and modular arithmetic. It defines key concepts such as division, factors, multiples, and the division algorithm. It presents theorems about divisibility and the relationship between greatest common divisors and least common multiples. Examples are provided to illustrate divisibility, the division algorithm, greatest common divisors, least common multiples, and modular arithmetic. The document serves as an overview of fundamental topics in number theory.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
The document provides information about sets and operations on sets such as union, intersection, complement, difference, properties of these operations, counting theorems for finite sets, and the number of elements in power sets. It defines key terms like union, intersection, complement, difference of sets. It lists properties of union, intersection, and complement. It presents counting theorems for finite sets involving union, intersection. It states that the number of elements in the power set of a set with n elements is 2n and the number of proper subsets is 2n-2.
The document provides information about a seminar on excellence for the PMR examination, including its objectives to help students understand the exam requirements and marking scheme. It discusses key points about correctly writing answers and interpreting different types of questions. Examples of objective and subjective questions are also included to demonstrate the format and how to solve different math problems.
The document discusses arithmetic progressions (AP), which are lists of numbers where each subsequent term is calculated by adding a fixed number (the common difference) to the previous term. It provides examples of APs with positive, negative, and zero common differences. The general formula for the nth term and sum of the first n terms of an AP are defined. Examples are given to demonstrate calculating specific terms and sums using the formulas.
An arithmetic progression is a sequence of numbers where each term is calculated by adding a constant value, called the common difference, to the previous term. The common difference is the fixed amount subtracted between any two consecutive terms. The general formula for an arithmetic progression is an = a + (n-1)d, where a is the first term and d is the common difference. Some key points covered are:
- Sequences have a specific relation between consecutive terms
- Examples show calculating subsequent terms by adding the common difference
- The formula is used to find specific terms like the 5th term
- The sum of n terms can be calculated using a formula of n/2 * (2a + (n-1
This document provides information about getting fully solved assignments by emailing help.mbaassignments@gmail.com or calling 08263069601. It includes sample math assignment questions on sets, trigonometry, limits, probability, and solving systems of equations. The 6-question assignment covers topics like sets, radians, proof of trigonometric identities, continuity, probability, and solving 3 equations with 3 unknowns. Students are encouraged to email their semester and specialization to get solved assignments.
This document defines an arithmetic progression as a sequence of numbers where each term is calculated by adding a fixed number (the common difference) to the preceding term. It provides the formulas to calculate the nth term and the sum of the first n terms of an arithmetic progression given the first term, common difference, and n. It also works through examples of finding the 12th term when the 1st term is 2 and common difference is 2, and finding the sum of the first 10 terms when the 1st term is 5 and common difference is 3.
Arithmetic progression
For class 10.
In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant
An arithmetic progression is a sequence of numbers where the difference between consecutive terms is constant. The document provides examples of arithmetic progressions and discusses formulas for calculating the nth term in a sequence, the sum of terms in a finite arithmetic progression, and solving problems involving finding the number of terms, first term, or common difference given values in the sequence.
This document provides a summary of concepts often seen on the JMET exam and includes example problems and solutions. Some key concepts covered include algebra, functions, equations, ratios and rates. Multiple choice problems are presented across various math and logic topics, followed by the solutions. Reviewing these types of problems and understanding the solutions can help prepare for exams like JMET, XAT and FMS that include quantitative reasoning sections.
The document discusses arithmetic progressions (AP), which are lists of numbers where each subsequent term is calculated by adding a fixed number (the common difference) to the previous term. It provides examples of APs and explains how to determine if a list is an AP based on having a common difference between terms. The key characteristics of an AP include the first term, common difference, a formula for calculating the nth term, and a formula for calculating the sum of the first n terms. Examples are provided to demonstrate how to use the formulas to find the 10th term or sum of terms in a given AP.
The document defines arithmetic mean and arithmetic series. Arithmetic mean is calculated by adding all terms of a sequence and dividing by the total number of terms. It provides examples of inserting arithmetic means between given terms. An arithmetic series is the sum of an arithmetic sequence. The sum is calculated by multiplying the number of terms by the average of the first and last terms. It provides examples of calculating the sum of arithmetic series.
The document discusses arithmetic progressions (AP), which are sequences where the difference between successive terms is constant. It defines an AP using the notation an = a + (n-1)d, where a is the first term, d is the common difference, and n indexes the terms. It provides examples and explains how to find individual terms, determine if a sequence is an AP, and calculate the sum of terms in an AP using the formula Sn = 1/2n(2a + (n-1)d). Various problems are worked through to demonstrate applying the concepts and formulas for APs.
pedagogy of mathematics part ii (numbers and sequence - ex 2.7), numbers and sequences, Std X samacheer Kalvi, Geometric progression, definition of geometric progression, general form of geometric progression, general term of geometric progression,
The document defines key polynomial vocabulary including:
- Terms are numbers or products of numbers and variables raised to powers. Coefficients are numerical factors of terms. Constants are terms that are only numbers.
- Polynomials are sums of terms involving variables raised to whole number exponents, with no variables in denominators.
- Types of polynomials include monomials (1 term), binomials (2 terms), and trinomials (3 terms). Degree is the largest exponent of any term.
- Operations on polynomials include adding/subtracting like terms, multiplying using distribution and FOIL, dividing using long division, and special products like (a+b)2 and (a+b)(a
An arithmetic progression is a sequence of numbers where each term after the first is calculated by adding a fixed number, called the common difference, to the previous term. The nth term can be calculated as an = a + (n - 1)d, where a is the first term and d is the common difference. An arithmetic progression can be either finite, with a fixed number of terms, or infinite, with an unlimited number of terms. The sum of the first n terms of an arithmetic progression is given by Sn = n/2(2a + (n-1)d).
Algebra 1 commutative and associative properitesmathriot
The document provides examples of using properties of numbers and algebra to simplify expressions. It gives step-by-step workings for expressions like 11(10-8), 6(4x+5), and 3⋅5⋅3⋅4. It defines the commutative and associative properties. Later examples show how to write an algebraic expression from a word problem and then simplify it using the distributive property.
This document contains a 40 question mathematics exam with multiple choice questions covering topics like trigonometry, calculus, algebra, geometry, and complex numbers. The questions test concepts such as finding the resultant of forces, variances of populations, solving quadratic equations, evaluating integrals, solving trigonometric equations, properties of matrices, logarithmic functions, maxima and minima of functions, loci of points, differentiability of functions, areas of geometric shapes, combinations, Taylor series expansions, solutions to differential equations, and transformations of points and planes.
This document discusses arithmetic and geometric progressions. It defines arithmetic and geometric sequences as lists of numbers where each subsequent term is calculated using a common difference or ratio. It provides formulas to calculate the nth term and sum of the first n terms for both progressions. The document also discusses arithmetic and geometric means as the averages between two numbers in an arithmetic or geometric progression.
This document provides an introduction to number theory, covering divisibility, greatest common divisors, least common multiples, and modular arithmetic. It defines key concepts such as division, factors, multiples, and the division algorithm. It presents theorems about divisibility and the relationship between greatest common divisors and least common multiples. Examples are provided to illustrate divisibility, the division algorithm, greatest common divisors, least common multiples, and modular arithmetic. The document serves as an overview of fundamental topics in number theory.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
The document provides information about sets and operations on sets such as union, intersection, complement, difference, properties of these operations, counting theorems for finite sets, and the number of elements in power sets. It defines key terms like union, intersection, complement, difference of sets. It lists properties of union, intersection, and complement. It presents counting theorems for finite sets involving union, intersection. It states that the number of elements in the power set of a set with n elements is 2n and the number of proper subsets is 2n-2.
The document provides information about a seminar on excellence for the PMR examination, including its objectives to help students understand the exam requirements and marking scheme. It discusses key points about correctly writing answers and interpreting different types of questions. Examples of objective and subjective questions are also included to demonstrate the format and how to solve different math problems.
The document contains 6 problems related to algebra and numbers along with their solutions. Problem 1 involves a number guessing game between two players and determining the minimum number of rounds needed. Problem 2 examines properties of a polynomial where the polynomial equals certain values for distinct integer inputs. Problem 3 finds all integer solutions to a system of equations involving cubes of variables. Problem 4 determines the value of a polynomial of degree 8 at a particular input, given its values at other integers. Problems 5 and 6 involve finding the smallest integer greater than an expression and the minimum possible value of a product of variables, respectively, given an equation relating the variables.
This document provides notes and formulas for mathematics topics covered in Form 1 through Form 4 in Malaysian secondary schools. It includes formulas and explanations for topics like solid geometry, circle theorems, polygons, factorisation, expansion of algebraic expressions, indices, algebraic fractions, linear equations, simultaneous equations, quadratic expressions, sets, statistics, trigonometry, angles of elevation and depression, and lines and planes. The document is intended to serve as a single reference for key mathematics concepts and formulas for secondary school students.
enjoy the formulas and use it with convidence and make your PT3 AND SPM more easier..togrther we achieve the better:)
good luck guys and girls...simple and short ans also sweet formulas..
This document contains notes and formulas for mathematics from Form 1 to Form 5. It covers topics such as solid geometry, circle theorems, polygons, factorisation, indices, linear equations, trigonometry, statistics, and lines and planes. For each topic, key formulas and properties are listed. For example, under solid geometry it defines the formulas for calculating the areas and volumes of shapes like cubes, cuboids, cylinders, cones and spheres. Under statistics it explains how to calculate measures like the mean, mode, median, and introduces different types of graphs like histograms and frequency polygons.
This document contains notes and formulas for mathematics from Form 1 to Form 5. It covers topics such as solid geometry, circle theorems, polygons, factorisation, indices, linear equations, trigonometry, statistics, and lines and planes. For each topic, key formulas and properties are listed. For example, under solid geometry it defines the formulas for calculating the areas and volumes of shapes like cubes, cuboids, cylinders, cones and spheres. Under statistics it explains how to calculate measures like the mean, mode, median, and introduces different types of graphs like histograms and frequency polygons.
This document contains a mock CAT exam with multiple choice questions and explanations. It consists of two pages. The first page lists 60 multiple choice questions with answer options A-D. The second page provides explanations for the questions and solutions to problems. It discusses topics like probability, ratios, geometry, time/speed/distance word problems, and data interpretation from graphs.
The document provides information about a math exam including:
- It is divided into 4 sections with various question types and marks.
- Section A has 8 multiple choice 1-mark questions.
- Section B has 6 2-mark questions.
- Section C has 10 3-mark questions.
- Section D has 10 4-mark questions.
- Calculators are not permitted and additional time is given to read the paper.
The document contains 18 math word problems with their step-by-step solutions. The problems cover a range of topics including arithmetic sequences, geometric sequences, percentages, factorials, trigonometry, and more. The final problem asks to find the 12th term of a sequence where the first two terms are 3 and 2, and subsequent terms are the sum of all preceding terms. The solution shows this forms a geometric sequence and calculates the 12th term as 2,560.
This document provides instructions for a mathematics exam for Class X. It has the following key details:
- The exam has 4 sections (A, B, C, D) with a total of 40 questions. All questions are compulsory.
- Section A has 20 one-mark multiple choice questions. Section B has 6 two-mark questions. Section C has 8 three-mark questions. Section D has 6 four-mark questions.
- There is no overall choice but some questions provide an internal choice between alternatives. Students must attempt only one of the choices for those questions.
- Calculators are not permitted. The instructions provide details about the number and type of questions in each section and remind students
This document contains notes and formulas for SPM Mathematics for Forms 1-4. It covers topics such as solid geometry, circle theorems, polygons, factorisation, expansion of algebraic expressions, indices, algebraic fractions, linear equations, simultaneous linear equations, algebraic formulas, linear inequalities, statistics, quadratic expressions and equations, sets, mathematical reasoning, the straight line, trigonometry, angle of elevation and depression, lines and planes. Formulas and properties are provided for calculating areas and volumes of solids, solving different types of equations, and relationships in geometry, trigonometry and statistics. Examples are included to demonstrate solving problems and using the various formulas and concepts.
This document contains 10 math questions related to trigonometric functions, sets, relations and functions, complex numbers, sequences and series, straight lines, conic sections. The questions range from proving identities and equations to finding specific values based on given information. They require various trigonometric, algebraic and geometric problem solving skills at a higher-order thinking level.
This document contains 19 multiple choice questions with solutions. The questions cover a range of math and logic topics such as geometry, percentages, remainders, and inequalities. For each question, the correct multiple choice answers are indicated based on working through the logic presented in the short solutions. This provides a review of different types of multiple choice questions and reasoning through solutions in brief explanations.
1. The document provides an overview of the curriculum for 6th grade math including topics, pacing, and vocabulary for three units: Expressions and Equations, Solving Equations and Inequalities, and Decimals.
2. Key topics include exponents, order of operations, variables and expressions, translating between words and math, equations and solutions, adding/subtracting/multiplying/dividing decimals.
3. Each unit lists the corresponding textbook chapters and New York State Common Core Learning Standards addressed. Common assessments are also included.
The document contains a math exam for grade 9 with 7 questions. Question 1 involves graphing quadratic functions and finding their intersection point. Question 2 deals with the area of a soccer field if its dimensions change. Question 3 is about calculating a person's life expectancy based on smoking and drinking habits. Question 4 provides a taxi fare formula and calculates a fare. Questions 5 and 6 involve solving equations and using trigonometric ratios. Question 7 contains proofs about angles and similar triangles in a circle.
This document contains 23 math and logic problems with multiple choice answers. It provides the problems, possible answers, and brief explanations for the answers. The problems cover a range of topics including algebra, percentages, probability, geometry and logical reasoning. The explanations are 1-2 sentences and directly reference the numbers, variables or diagrams in the problems to justify the answers. The document is designed to help students practice and learn how to solve different types of math and logic problems.
This document contains 26 math and logic problems with multiple choice answers. It provides the problems, possible answers, and explanations for the answers. The problems cover a range of topics including algebra, arithmetic, geometry, probability, factoring, and word problems. The explanations for the answers clearly show the step-by-step work and logic used to arrive at the correct solution for each problem.
The document contains instructions for a mathematics exam consisting of 3 sections (A, B, C). Section A has 10 1-mark questions. Section B has 12 4-mark questions. Section C has 7 6-mark questions. Calculators are not permitted. Questions can have either internal choice or no choice. The document provides 10 sample 1-mark questions from Section A to illustrate the format and difficulty level.
1. Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
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(Prefer mailing. Call in emergency )
ASSIGNMENT
SUMMER 2014
PROGRAM BCA
SEMESTER 1
SUBJECT CODE & NAME BCA 1030- BASIC MATHEMATICS
CREDIT 4
BK ID B0950
MAX. MARKS 60
Q.1 (i) Let A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8}. Find A – B and B – A.
Answer: A-B = {1, 3, 5} , B-A = {8}
(ii) In a group of 50 people, 35 speak Hindi, 25 speak both English and Hindi and all the people speak
at least one of the two languages. How many people speak only English and not Hindi?
How many people speak English?
Answer: n (A U B )= people who speak in either Hindi and English.
Given people speak at least one of the languages.
n (A U B) = 50.
2. Q.2 (i) Express 7920 in radians and (7π/12) c in degrees.
(ii) Prove that (tan θ + sec θ – 1)/ (tan θ + sec θ +1) = Cos θ / (1-sin θ) = (1+sin θ)/ Cos θ
Answer: (i) The conversion is 180O= π radian
So 79200 = (7920*3.14)/180 = 138.247 radians
(7π/12) c in degrees:-
1radian = 57.29577795
Degrees = radians * (180/pi)
= (7π/12)*180/pi = 105
(ii). Solution:-
(tan θ + sec θ – 1)/ (tan θ + sec θ +1) =(1+sin θ)/ Cos θ
If (tan θ + sec θ – 1)/ (tan θ + sec θ +1) = (1/cosθ)+(sinθ/cosθ)
If (tan θ + sec θ – 1)/ (tan
Q.3 (i) Define continuity of a point
(ii) Test the continuity of the function f where f is defined by f(x) = {x-2/|x-2| if x ≠ 2, 7 if x = 2.
Answer: (i) Definition of Continuity
Let a be a point in the domain of the function f(x). Then f is continuous at x=a if and only if
lim f(x) = f(a)
x --> a
A function f(x) is continuous on a set
Q.4 Solve dy/dx = (y+x-2)/(y-x-4).
3. Answer:dy/dx = (y+x-2)/(y-x-4) -------------------------------- (i)
Put y = vx
Diff w.r.t “x”
dy/dx = v.1+x.dx/dx
dy/dx = v+xdy/dx
Q.5 (i) a bag contains two red balls, three blue balls and five green balls.
Three balls are drawn at random. Find the probability that
a) The three balls are of different colors’.
b) Two balls are of the same color.
Let nCk = number of ways to pick up k items from a set of n items.
Of course you should already know that nCk+=+n%21%2F%28k%21%2A%28n-k%29%21%29 (*)
Bag consists of 2 red balls (R), 3 blue
Q.6 Solve: 2x + 3y + 4z = 20, x + y + 2z = 9, 3x + 2y + z = 10.
Answer: These equations are written as
[2 3 4 [20
1 1 2 = 9
3 2 1] 10]
AX = B
Where A = [2 3 4 , 1 1 2 , 3 2 1 ] X =[ X,Y,Z] ,B= [20,9,30]
Therefore |A| = Determinant of |A| = 5
Now we have to find the value of Δ1. So replace first column of A with the values of B and find
Determinant.
Therefore Δ1 = 5
4. Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
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Call us at : 08263069601
(Prefer mailing. Call in emergency )