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111-498: The Common Admission Test ( CAT ) is a computer based test for admission in graduate management programs. The test consists of three sections: Verbal Ability and Reading Comprehension, Data Interpretation and Logical Reasoning, and Quantitative Ability. The exam was taken online over a period of three hours, with one hour per section. In 2020, due to the COVID-19 precautions, Indian Institute of Management Indore decided to conduct

222-467: A book, article or media without properly citing the source. Individuals can be dishonest due to lack of time management skills, the pursuit of better grades, cultural behavior or a misunderstanding of plagiarism. Online classroom environments are no exception to the possibility of academic dishonesty. It can easily be seen from a student's perspective as an easy passing grade. Proper assignments types, meetings and projects can prevent academic dishonesty in

333-428: A collaborative learning model in which the learning is driven by the students and/or a cooperative learning model where tasks are assigned and the instructor is involved in decisions. Pre-testing – Prior to the teaching of a lesson or concept, a student can complete an online pretest to determine their level of knowledge. This form of assessment helps determine a baseline so that when a summative assessment or post-test

444-1117: A common denominator. This can be achieved by scaling the first number with the denominator of the second number while scaling the second number with the denominator of the first number. For instance, 1 3 + 1 2 = 1 ⋅ 2 3 ⋅ 2 + 1 ⋅ 3 2 ⋅ 3 = 2 6 + 3 6 = 5 6 {\displaystyle {\tfrac {1}{3}}+{\tfrac {1}{2}}={\tfrac {1\cdot 2}{3\cdot 2}}+{\tfrac {1\cdot 3}{2\cdot 3}}={\tfrac {2}{6}}+{\tfrac {3}{6}}={\tfrac {5}{6}}} . Two rational numbers are multiplied by multiplying their numerators and their denominators respectively, as in 2 3 ⋅ 2 5 = 2 ⋅ 2 3 ⋅ 5 = 4 15 {\displaystyle {\tfrac {2}{3}}\cdot {\tfrac {2}{5}}={\tfrac {2\cdot 2}{3\cdot 5}}={\tfrac {4}{15}}} . Dividing one rational number by another can be achieved by multiplying

555-548: A common scale or metric to ensure appropriate interpretation of the scores. This process is called 'scaling'. The change in the total number of questions and number of questions per section in CAT can vary by year. On the whole, there are 66 number of questions combining each section. The very first section which is the verbal ability and reading comprehension contains 24 questions, further bifurcating 16 questions of reading comprehension and 8 questions of verbal ability, then next section

666-442: A general identity element since 1 is not the neutral element for the base. Exponentiation and logarithm are neither commutative nor associative. Different types of arithmetic systems are discussed in the academic literature. They differ from each other based on what type of number they operate on, what numeral system they use to represent them, and whether they operate on mathematical objects other than numbers. Integer arithmetic

777-410: A limited amount of basic numerals, which directly refer to certain numbers. The system governs how these basic numerals may be combined to express any number. Numeral systems are either positional or non-positional. All early numeral systems were non-positional. For non-positional numeral systems, the value of a digit does not depend on its position in the numeral. The simplest non-positional system

888-493: A maximum score of 198 marks and 66 total questions in the CAT exam pattern. Candidates cannot jump between the three sections while taking the exam. The order of the sections is fixed: VARC -> DILR -> QA . The number of registrations in the past years are shown in the following chart: Registered Appeared Note: Data of candidates registered till 2012 are approximate. Computer based test Different types of online assessments contain elements of one or more of

999-464: A more complex non-positional numeral system . They have additional symbols for numbers like 10, 100, 1000, and 10,000. These symbols can be combined into a sum to more conveniently express larger numbers. For instance, the numeral for 10,405 uses one time the symbol for 10,000, four times the symbol for 100, and five times the symbol for 1. A similar well-known framework is the Roman numeral system . It has

1110-639: A number, it is also possible to multiply by its reciprocal . The reciprocal of a number is 1 divided by that number. For instance, 48 ÷ 8 = 48 × 1 8 {\displaystyle 48\div 8=48\times {\tfrac {1}{8}}} . The multiplicative identity element is 1 and the multiplicative inverse of a number is the reciprocal of that number. For example, 13 × 1 = 13 {\displaystyle 13\times 1=13} and 13 × 1 13 = 1 {\displaystyle 13\times {\tfrac {1}{13}}=1} . Multiplication

1221-490: A plane. Further branches of number theory are probabilistic number theory , which employs methods from probability theory , combinatorial number theory , which relies on the field of combinatorics , computational number theory , which approaches number-theoretic problems with computational methods, and applied number theory, which examines the application of number theory to fields like physics , biology , and cryptography . Influential theorems in number theory include

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1332-553: A positive number as its base. The same is true for the logarithm of positive real numbers as long as the logarithm base is positive and not 1. Irrational numbers involve an infinite non-repeating series of decimal digits. Because of this, there is often no simple and accurate way to express the results of arithmetic operations like 2 + π {\displaystyle {\sqrt {2}}+\pi } or e ⋅ 3 {\displaystyle e\cdot {\sqrt {3}}} . In cases where absolute precision

1443-507: A range of values if one does not know the precise magnitude, for example, because of measurement errors . Interval arithmetic includes operations like addition and multiplication on intervals, as in [ 1 , 2 ] + [ 3 , 4 ] = [ 4 , 6 ] {\displaystyle [1,2]+[3,4]=[4,6]} and [ 1 , 2 ] × [ 3 , 4 ] = [ 3 , 8 ] {\displaystyle [1,2]\times [3,4]=[3,8]} . It

1554-608: A series of papers, including research specific to e-marking such as: Examining the impact of moving to on-screen marking on concurrent validity. In 2007, the International Baccalaureate implemented e-marking. In 2012, 66% of nearly 16 million exam scripts were "e-marked" in the United Kingdom. Ofqual reports that in 2015, all key stage 2 tests in the United Kingdom will be marked onscreen. In 2010, Mindlogicx implemented onscreen marking system for

1665-444: A series of two operations, it does not matter which operation is carried out first. This is the case for multiplication, for example, since ( 5 × 4 ) × 2 {\displaystyle (5\times 4)\times 2} is the same as 5 × ( 4 × 2 ) {\displaystyle 5\times (4\times 2)} . Addition is an arithmetic operation in which two numbers, called

1776-439: A special type of rational numbers since their denominator is a power of 10. For instance, 0.3 is equal to 3 10 {\displaystyle {\tfrac {3}{10}}} , and 25.12 is equal to 2512 100 {\displaystyle {\tfrac {2512}{100}}} . Every rational number corresponds to a finite or a repeating decimal . Irrational numbers are numbers that cannot be expressed through

1887-484: A wider sense, it also includes exponentiation , extraction of roots , and taking logarithms . Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers . Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers , which include both rational and irrational numbers . Another distinction

1998-556: Is exponentiation by squaring . It breaks down the calculation into a number of squaring operations. For example, the exponentiation 3 65 {\displaystyle 3^{65}} can be written as ( ( ( ( ( 3 2 ) 2 ) 2 ) 2 ) 2 ) 2 × 3 {\displaystyle (((((3^{2})^{2})^{2})^{2})^{2})^{2}\times 3} . By taking advantage of repeated squaring operations, only 7 individual operations are needed rather than

2109-406: Is 0 and the additive inverse of a number is the negative of that number. For instance, 13 + 0 = 13 {\displaystyle 13+0=13} and 13 + ( − 13 ) = 0 {\displaystyle 13+(-13)=0} . Addition is both commutative and associative. Multiplication is an arithmetic operation in which two numbers, called the multiplier and

2220-426: Is 0. 3 . Every repeating decimal expresses a rational number. Real number arithmetic is the branch of arithmetic that deals with the manipulation of both rational and irrational numbers. Irrational numbers are numbers that cannot be expressed through fractions or repeated decimals, like the root of 2 and π . Unlike rational number arithmetic, real number arithmetic is closed under exponentiation as long as it uses

2331-545: Is a prime number that has no other prime factorization. Euclid's theorem states that there are infinitely many prime numbers. Fermat's last theorem is the statement that no positive integer values can be found for a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} , to solve the equation a n + b n = c n {\displaystyle a^{n}+b^{n}=c^{n}} if n {\displaystyle n}

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2442-465: Is a relatively crude method, with some unintuitive subtleties; explicitly keeping track of an estimate or upper bound of the approximation error is a more sophisticated approach. In the example, the person's height might be represented as 1.62 ± 0.005 meters or 63.8 ± 0.2 inches . In performing calculations with uncertain quantities, the uncertainty should be propagated to calculated quantities. When adding or subtracting two or more quantities, add

2553-902: Is a similar process in which the last preserved digit is increased by one if the next digit is 5 or greater but remains the same if the next digit is less than 5, so that the rounded number is the best approximation of a given precision for the original number. For instance, if the number π is rounded to 4 decimal places, the result is 3.142 because the following digit is a 5, so 3.142 is closer to π than 3.141. These methods allow computers to efficiently perform approximate calculations on real numbers. In science and engineering, numbers represent estimates of physical quantities derived from measurement or modeling. Unlike mathematically exact numbers such as π or ⁠ 2 {\displaystyle {\sqrt {2}}} ⁠ , scientifically relevant numerical data are inherently inexact, involving some measurement uncertainty . One basic way to express

2664-450: Is an inverse of the operation " ∘ {\displaystyle \circ } " if it fulfills the following condition: t ⋆ s = r {\displaystyle t\star s=r} if and only if r ∘ s = t {\displaystyle r\circ s=t} . Commutativity and associativity are laws governing the order in which some arithmetic operations can be carried out. An operation

2775-436: Is applied to another element. For example, the identity element of addition is 0 since any sum of a number and 0 results in the same number. The inverse element is the element that results in the identity element when combined with another element. For instance, the additive inverse of the number 6 is -6 since their sum is 0. There are not only inverse elements but also inverse operations . In an informal sense, one operation

2886-492: Is assessment. Assessment is used to determine if learning is happening, to what extent and if changes need to be made. Most students will not complete assignments unless there is an assessment (i.e. motivation ). It is the instructor's role to catalyze student motivation. Appropriate feedback is the key to assessment, whether or not the assessment is graded. Students are often asked to work in groups . This brings on new assessment strategies. Students can be evaluated using

2997-526: Is at least thousands and possibly tens of thousands of years old. Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE. Starting in the 7th and 6th centuries BCE, the ancient Greeks initiated a more abstract study of numbers and introduced the method of rigorous mathematical proofs . The ancient Indians developed

3108-593: Is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers . Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the implementation of binary arithmetic on computers . Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix arithmetic. Arithmetic operations form

3219-583: Is both commutative and associative. Exponentiation is an arithmetic operation in which a number, known as the base, is raised to the power of another number, known as the exponent. The result of this operation is called the power. Exponentiation is sometimes expressed using the symbol ^ but the more common way is to write the exponent in superscript right after the base. Examples are 2 4 = 16 {\displaystyle 2^{4}=16} and 3 {\displaystyle 3} ^ 3 = 27 {\displaystyle 3=27} . If

3330-403: Is closed under division as long as the divisor is not 0. Both integer arithmetic and rational number arithmetic are not closed under exponentiation and logarithm. One way to calculate exponentiation with a fractional exponent is to perform two separate calculations: one exponentiation using the numerator of the exponent followed by drawing the nth root of the result based on the denominator of

3441-401: Is commutative if the order of the arguments can be changed without affecting the results. This is the case for addition, for instance, 7 + 9 {\displaystyle 7+9} is the same as 9 + 7 {\displaystyle 9+7} . Associativity is a rule that affects the order in which a series of operations can be carried out. An operation is associative if, in

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3552-440: Is given, quantitative evidence is provided showing that learning has occurred. Formative assessment – Formative assessment is used to provide feedback during the learning process. In online assessment situations, objective questions are posed, and feedback is provided to the student either during or immediately after the assessment. Summative assessment – Summative assessments provide a quantitative grade and are often given at

3663-431: Is greater than 2 {\displaystyle 2} . Rational number arithmetic is the branch of arithmetic that deals with the manipulation of numbers that can be expressed as a ratio of two integers. Most arithmetic operations on rational numbers can be calculated by performing a series of integer arithmetic operations on the numerators and the denominators of the involved numbers. If two rational numbers have

3774-439: Is infinite without repeating decimals. The set of rational numbers together with the set of irrational numbers makes up the set of real numbers. The symbol of the real numbers is R {\displaystyle \mathbb {R} } . Even wider classes of numbers include complex numbers and quaternions . A numeral is a symbol to represent a number and numeral systems are representational frameworks. They usually have

3885-427: Is not closed under division. This means that when dividing one integer by another integer, the result is not always an integer. For instance, 7 divided by 2 is not a whole number but 3.5. One way to ensure that the result is an integer is to round the result to a whole number. However, this method leads to inaccuracies as the original value is altered. Another method is to perform the division only partially and retain

3996-417: Is not required, the problem of calculating arithmetic operations on real numbers is usually addressed by truncation or rounding . For truncation, a certain number of leftmost digits are kept and remaining digits are discarded or replaced by zeros. For example, the number π has an infinite number of digits starting with 3.14159.... If this number is truncated to 4 decimal places, the result is 3.141. Rounding

4107-555: Is of data interpretation and logical reasoning which contains 20 questions and the last section is of quantitative ability which contains 22 questions making it to 66 questions in total. CAT is conducted in three slots/sessions (Morning Slot, Afternoon Slot, Evening Slot). Source: Three 40-minute sessions will be held to conduct the CAT 2024 exam. A total of 120 minutes will be given. The CAT exam pattern will consist of Multiple Choice Question and non-multiple-choice questions or TITA {Type In The Answer} questions. The three sections in

4218-437: Is often treated as a special case of addition: instead of subtracting a positive number, it is also possible to add a negative number. For instance 14 − 8 = 14 + ( − 8 ) {\displaystyle 14-8=14+(-8)} . This helps to simplify mathematical computations by reducing the number of basic arithmetic operations needed to perform calculations. The additive identity element

4329-428: Is one type of digital assessment tool that can engage students in a different way whilst gathering data that teachers can use to gain insight. In summative assessment, which could be described as 'assessment of learning', exam boards and awarding organisations delivering high-stakes exams often find the journey from paper-based exam assessment to fully digital assessment a long one. Practical considerations such as having

4440-930: Is restricted to the study of integers and focuses on their properties and relationships such as divisibility , factorization , and primality . Traditionally, it is known as higher arithmetic. Numbers are mathematical objects used to count quantities and measure magnitudes. They are fundamental elements in arithmetic since all arithmetic operations are performed on numbers. There are different kinds of numbers and different numeral systems to represent them. The main kinds of numbers employed in arithmetic are natural numbers , whole numbers, integers , rational numbers , and real numbers . The natural numbers are whole numbers that start from 1 and go to infinity. They exclude 0 and negative numbers. They are also known as counting numbers and can be expressed as { 1 , 2 , 3 , 4 , . . . } {\displaystyle \{1,2,3,4,...\}} . The symbol of

4551-517: Is the unary numeral system . It relies on one symbol for the number 1. All higher numbers are written by repeating this symbol. For example, the number 7 can be represented by repeating the symbol for 1 seven times. This system makes it cumbersome to write large numbers, which is why many non-positional systems include additional symbols to directly represent larger numbers. Variations of the unary numeral systems are employed in tally sticks using dents and in tally marks . Egyptian hieroglyphics had

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4662-462: Is the branch of arithmetic that deals with the manipulation of positive and negative whole numbers. Simple one-digit operations can be performed by following or memorizing a table that presents the results of all possible combinations, like an addition table or a multiplication table . Other common methods are verbal counting and finger-counting . For operations on numbers with more than one digit, different techniques can be employed to calculate

4773-428: Is the inverse of another operation if it undoes the first operation. For example, subtraction is the inverse of addition since a number returns to its original value if a second number is first added and subsequently subtracted, as in 13 + 4 − 4 = 13 {\displaystyle 13+4-4=13} . Defined more formally, the operation " ⋆ {\displaystyle \star } "

4884-413: Is the inverse of exponentiation. The logarithm of a number x {\displaystyle x} to the base b {\displaystyle b} is the exponent to which b {\displaystyle b} must be raised to produce x {\displaystyle x} . For instance, since 1000 = 10 3 {\displaystyle 1000=10^{3}} ,

4995-436: Is the use of digital educational technology specifically designed for marking. The term refers to the electronic marking or grading of an exam. E-marking is an examiner led activity closely related to other e-assessment activities such as e-testing, or e-learning which are student led. E-marking allows markers to mark a scanned script or online response on a computer screen rather than on paper. There are no restrictions to

5106-423: Is used primarily to measure cognitive abilities, demonstrating what has been learned after a particular educational event has occurred, such as the end of an instructional unit or chapter. When assessing practical abilities or demonstrating learning that has occurred over a longer period of time an online portfolio (or ePortfolio ) is often used. The first element that must be prepared when teaching an online course

5217-667: The Association of Test Publishers (ATP) that focus specifically on Innovations in Testing , represent the growth in adoption of technology-enhanced assessment. In psychiatric and psychological testing, e-assessment can be used not only to assess cognitive and practical abilities but anxiety disorders, such as social anxiety disorder , i.e. SPAI-B . Widely in psychology. Cognitive abilities are assessed using e-testing software, while practical abilities are assessed using e-portfolios or simulation software. Online assessment

5328-591: The Hindu–Arabic numeral system , the radix is 10. This means that the first digit is multiplied by 10 0 {\displaystyle 10^{0}} , the next digit is multiplied by 10 1 {\displaystyle 10^{1}} , and so on. For example, the decimal numeral 532 stands for 5 ⋅ 10 2 + 3 ⋅ 10 1 + 2 ⋅ 10 0 {\displaystyle 5\cdot 10^{2}+3\cdot 10^{1}+2\cdot 10^{0}} . Because of

5439-428: The absolute uncertainties of each summand together to obtain the absolute uncertainty of the sum. When multiplying or dividing two or more quantities, add the relative uncertainties of each factor together to obtain the relative uncertainty of the product. When representing uncertainty by significant digits, uncertainty can be coarsely propagated by rounding the result of adding or subtracting two or more quantities to

5550-494: The fundamental theorem of arithmetic , Euclid's theorem , and Fermat's last theorem . According to the fundamental theorem of arithmetic, every integer greater than 1 is either a prime number or can be represented as a unique product of prime numbers. For example, the number 18 is not a prime number and can be represented as 2 × 3 × 3 {\displaystyle 2\times 3\times 3} , all of which are prime numbers. The number 19 , by contrast,

5661-589: The lattice method . Computer science is interested in multiplication algorithms with a low computational complexity to be able to efficiently multiply very large integers, such as the Karatsuba algorithm , the Schönhage–Strassen algorithm , and the Toom–Cook algorithm . A common technique used for division is called long division . Other methods include short division and chunking . Integer arithmetic

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5772-431: The quotient . The symbols of division are ÷ {\displaystyle \div } and / {\displaystyle /} . Examples are 48 ÷ 8 = 6 {\displaystyle 48\div 8=6} and 29.4 / 1.4 = 21 {\displaystyle 29.4/1.4=21} . Division is often treated as a special case of multiplication: instead of dividing by

5883-568: The remainder . For example, 7 divided by 2 is 3 with a remainder of 1. These difficulties are avoided by rational number arithmetic, which allows for the exact representation of fractions. A simple method to calculate exponentiation is by repeated multiplication. For instance, the exponentiation of 3 4 {\displaystyle 3^{4}} can be calculated as 3 × 3 × 3 × 3 {\displaystyle 3\times 3\times 3\times 3} . A more efficient technique used for large exponents

5994-452: The 64 operations required for regular repeated multiplication. Methods to calculate logarithms include the Taylor series and continued fractions . Integer arithmetic is not closed under logarithm and under exponentiation with negative exponents, meaning that the result of these operations is not always an integer. Number theory studies the structure and properties of integers as well as

6105-598: The CAT Exam in 2 hours with 40 minutes devoted to each section. The Indian Institutes of Management started this exam and use the test for selecting students for their business administration programs ( MBA or PGDM). The test is conducted every year by one of the Indian Institutes of Managements(IIMs) based on a policy of rotation. In August 2011, it was announced that Indian Institutes of Technology (IITs) and Indian Institute of Science (IISc) would also use

6216-548: The CAT scores, instead of the Joint Management Entrance Test (JMET), to select students for their management programmes starting with the 2012-15 batch. Before 2010, CAT was a paper based test conducted on a single day for all candidates. The pattern, number of questions and duration have seen considerable variations over the years. On 1 May 2009, it was announced that CAT would be a Computer Based Test starting from 2009. The American firm Prometric

6327-658: The Latin term " arithmetica " which derives from the Ancient Greek words ἀριθμός (arithmos), meaning "number", and ἀριθμητική τέχνη (arithmetike tekhne), meaning "the art of counting". There are disagreements about its precise definition. According to a narrow characterization, arithmetic deals only with natural numbers . However, the more common view is to include operations on integers , rational numbers , real numbers , and sometimes also complex numbers in its scope. Some definitions restrict arithmetic to

6438-772: The United Kingdom include A levels and GCSE exams, and in the US includes the SAT test for college admissions. Ofqual reports that e-marking is the main type of marking used for general qualifications in the United Kingdom. Early adopters include the University of Cambridge Local Examinations Syndicate , (which operates under the brand name Cambridge Assessment ) which conducted its first major test of e-marking in November 2000. Cambridge Assessment has conducted extensive research into e-marking and e-assessment. The syndicate has published

6549-457: The accuracy and speed with which arithmetic calculations could be performed. Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition , subtraction , multiplication , and division . In a wider sense, it also includes exponentiation , extraction of roots , and logarithm . The term "arithmetic" has its root in

6660-435: The addends, are combined into a single number, called the sum. The symbol of addition is + {\displaystyle +} . Examples are 2 + 2 = 4 {\displaystyle 2+2=4} and 6.3 + 1.26 = 7.56 {\displaystyle 6.3+1.26=7.56} . The term summation is used if several additions are performed in a row. Counting is a type of repeated addition in which

6771-510: The base can be understood from context. So, the previous example can be written log 10 ⁡ 1000 = 3 {\displaystyle \log _{10}1000=3} . Exponentiation and logarithm do not have general identity elements and inverse elements like addition and multiplication. The neutral element of exponentiation in relation to the exponent is 1, as in 14 1 = 14 {\displaystyle 14^{1}=14} . However, exponentiation does not have

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6882-504: The basis of many branches of mathematics, such as algebra , calculus , and statistics . They play a similar role in the sciences , like physics and economics . Arithmetic is present in many aspects of daily life , for example, to calculate change while shopping or to manage personal finances . It is one of the earliest forms of mathematics education that students encounter. Its cognitive and conceptual foundations are studied by psychology and philosophy . The practice of arithmetic

6993-440: The claim that every even number is a sum of two prime numbers . Algebraic number theory employs algebraic structures to analyze the properties of and relations between numbers. Examples are the use of fields and rings , as in algebraic number fields like the ring of integers . Geometric number theory uses concepts from geometry to study numbers. For instance, it investigates how lattice points with integer coordinates behave in

7104-502: The concept of zero and the decimal system , which Arab mathematicians further refined and spread to the Western world during the medieval period. The first mechanical calculators were invented in the 17th century. The 18th and 19th centuries saw the development of modern number theory and the formulation of axiomatic foundations of arithmetic. In the 20th century, the emergence of electronic calculators and computers revolutionized

7215-640: The course or experience needs justification or improvement. Performance testing – The user shows what they know and what they can do. This type of testing is used to show technological proficiency, reading comprehension , math skills, etc. This assessment is also used to identify gaps in student learning. New technologies, such as the Web , digital video, sound, animations , and interactivity , are providing tools that can make assessment design and implementation more efficient, timely, and sophisticated. Electronic marking, also known as e-marking and onscreen marking,

7326-488: The decimal fraction notation. Modified versions of integer calculation methods like addition with carry and long multiplication can be applied to calculations with decimal fractions. Not all rational numbers have a finite representation in the decimal notation. For example, the rational number 1 3 {\displaystyle {\tfrac {1}{3}}} corresponds to 0.333... with an infinite number of 3s. The shortened notation for this type of repeating decimal

7437-522: The degree of certainty about each number's value and avoid false precision is to round each measurement to a certain number of digits, called significant digits , which are implied to be accurate. For example, a person's height measured with a tape measure might only be precisely known to the nearest centimeter, so should be presented as 1.62 meters rather than 1.6217 meters. If converted to imperial units, this quantity should be rounded to 64 inches or 63.8 inches rather than 63.7795 inches, to clearly convey

7548-576: The desired level of accuracy. The Taylor series or the continued fraction method can be utilized to calculate logarithms. The decimal fraction notation is a special way of representing rational numbers whose denominator is a power of 10. For instance, the rational numbers 1 10 {\displaystyle {\tfrac {1}{10}}} , 371 100 {\displaystyle {\tfrac {371}{100}}} , and 44 10000 {\displaystyle {\tfrac {44}{10000}}} are written as 0.1, 3.71, and 0.0044 in

7659-652: The distinction between the natural and the whole numbers by including 0 in the set of natural numbers. The set of integers encompasses both positive and negative whole numbers. It has the symbol Z {\displaystyle \mathbb {Z} } and can be expressed as { . . . , − 2 , − 1 , 0 , 1 , 2 , . . . } {\displaystyle \{...,-2,-1,0,1,2,...\}} . Based on how natural and whole numbers are used, they can be distinguished into cardinal and ordinal numbers . Cardinal numbers, like one, two, and three, are numbers that express

7770-475: The effect of the digits' positions, the numeral 532 differs from the numerals 325 and 253 even though they have the same digits. Another positional numeral system used extensively in computer arithmetic is the binary system , which has a radix of 2. This means that the first digit is multiplied by 2 0 {\displaystyle 2^{0}} , the next digit by 2 1 {\displaystyle 2^{1}} , and so on. For example,

7881-675: The end of a unit or lesson to determine that the learning objectives have been met. Practice Testing – With the ever-increasing use of high-stakes testing in the educational arena, online practice tests are used to give students an edge. Students can take these types of assessments multiple times to familiarize themselves with the content and format of the assessment. Surveys – Online surveys may be used by educators to collect data and feedback on student attitudes, perceptions or other types of information that might help improve instruction. Evaluations – This type of survey allows facilitators to collect data and feedback on any type of situation where

7992-553: The exact wordage, but the thought or idea. It is important to learn to properly cite a source when using someone else's work. To assist sharing of assessment items across disparate systems, standards such as the IMS Global Question and Test Interoperability specification ( QTI ) have emerged. Arithmetic Arithmetic is an elementary branch of mathematics that studies numerical operations like addition , subtraction , multiplication , and division . In

8103-771: The exam are as follows: -> 24 questions are asked in VARC out which 8 questions are of VA (Para jumble - 2 TITA questions, Para summary - 2 MCQ questions, Odd one out - 2 TITA questions, Sentence Placement - 2 MCQ questions) 16 questions of RC are asked by 4 passages with 4 questions in each passage (all questions are of MCQ type). -> 20 questions are asked in DILR, questions are asked in 4 sets with 6-6-4-4 or 5-5-5-5 pattern. -> 22 questions are asked in QA, 22 independent questions are asked from topics such as Arithmetic , Algebra , Geometry , Number System & Modern Math. There will be

8214-405: The exam duration has been reduced to two hours, with 40 minutes allotted per section. The candidate must satisfy the below specified criteria: The Common Admission Test (CAT), like virtually all large-scale exams, utilises multiple forms, or versions, of the test. Hence there are two types of scores involved: a raw score and a scaled score. The raw score is calculated for each section based on

8325-408: The exponent is a natural number then exponentiation is the same as repeated multiplication, as in 2 4 = 2 × 2 × 2 × 2 {\displaystyle 2^{4}=2\times 2\times 2\times 2} . Roots are a special type of exponentiation using a fractional exponent. For example, the square root of a number is the same as raising the number to

8436-458: The exponent. For example, 5 2 3 = 5 2 3 {\displaystyle 5^{\frac {2}{3}}={\sqrt[{3}]{5^{2}}}} . The first operation can be completed using methods like repeated multiplication or exponentiation by squaring. One way to get an approximate result for the second operation is to employ Newton's method , which uses a series of steps to gradually refine an initial guess until it reaches

8547-421: The field of numerical calculations. When understood in a wider sense, it also includes the study of how the concept of numbers developed, the analysis of properties of and relations between numbers, and the examination of the axiomatic structure of arithmetic operations. Arithmetic is closely related to number theory and some authors use the terms as synonyms. However, in a more specific sense, number theory

8658-483: The first number with the reciprocal of the second number. This means that the numerator and the denominator of the second number change position. For example, 3 5 : 2 7 = 3 5 ⋅ 7 2 = 21 10 {\displaystyle {\tfrac {3}{5}}:{\tfrac {2}{7}}={\tfrac {3}{5}}\cdot {\tfrac {7}{2}}={\tfrac {21}{10}}} . Unlike integer arithmetic, rational number arithmetic

8769-1067: The first time in India at Anna University enabling easy operations and efficient conduction of high stakes examination. In 2014, the Scottish Qualifications Authority (SQA) announced that most of the National 5 question papers would be e-marked. In June 2015, the Odisha state government in India announced that it planned to use e-marking for all Plus II papers from 2016. E-marking can be used to mark examinations that are completed on paper and then scanned and uploaded as digital images, as well as online examinations. Multiple-choice exams can be either marked by examiners online or be automarked where appropriate. When marking written script exams, e-marking applications provide markers with online tools and resources to mark as they go and can add up marks as they progress without exceeding

8880-545: The following components, depending on the assessment's purpose: formative, summative and diagnostic. Instant and detailed feedback may (or may not) be enabled. In formative assessment, often defined as 'assessment for learning', digital tools are increasingly being adopted by schools, higher education institutions and professional associations to measure where students are in their skills or knowledge. This can make it easier to provide tailored feedback, interventions or action plans to improve learning and attainment. Gamification

8991-502: The integer 1, called the numerator, by the integer 2, called the denominator. Other examples are 3 4 {\displaystyle {\tfrac {3}{4}}} and 281 3 {\displaystyle {\tfrac {281}{3}}} . The set of rational numbers includes all integers, which are fractions with a denominator of 1. The symbol of the rational numbers is Q {\displaystyle \mathbb {Q} } . Decimal fractions like 0.3 and 25.12 are

9102-493: The left. This process is repeated until all digits have been added. Other methods used for integer additions are the number line method, the partial sum method, and the compensation method. A similar technique is utilized for subtraction: it also starts with the rightmost digit and uses a "borrow" or a negative carry for the column on the left if the result of the one-digit subtraction is negative. A basic technique of integer multiplication employs repeated addition. For example,

9213-458: The leftmost last significant decimal place among the summands, and by rounding the result of multiplying or dividing two or more quantities to the least number of significant digits among the factors. (See Significant figures § Arithmetic .) More sophisticated methods of dealing with uncertain values include interval arithmetic and affine arithmetic . Interval arithmetic describes operations on intervals . Intervals can be used to represent

9324-817: The literature regarding advantages and disadvantages of E-assessment for different types of tests for different types of students in different educational environment from childhood through young adulthood was completed in 2010. In higher education settings, there is variation in the ways academics perceive the benefits of e-assessment. While some perceive e-assessment processes as integral to teaching, others think of e-assessment in isolation from teaching and their students' learning. Academic dishonesty , commonly known as cheating, occurs at all levels of educational institutions. In traditional classrooms, students cheat in various forms such as hidden prepared notes not permitted to be used or looking at another student's paper during an exam, copying homework from one another, or copying from

9435-492: The logarithm base 10 of 1000 is 3. The logarithm of x {\displaystyle x} to base b {\displaystyle b} is denoted as log b ⁡ ( x ) {\displaystyle \log _{b}(x)} , or without parentheses, log b ⁡ x {\displaystyle \log _{b}x} , or even without the explicit base, log ⁡ x {\displaystyle \log x} , when

9546-563: The marking of examinations. In some cases, e-marking can be combined with electronic examinations, whilst in other cases students will still hand-write their exam responses on paper scripts which are then scanned and uploaded to an e-marking system for examiners to mark on-screen. E-assessment is becoming more widely used by exam awarding bodies, particularly those with multiple or international study centres and those which offer remote study courses. Industry bodies such as The e-Assessment Association (eAA), founded in 2008, as well as events run by

9657-407: The multiplicand is a natural number then multiplication is the same as repeated addition, as in 2 × 3 = 2 + 2 + 2 {\displaystyle 2\times 3=2+2+2} . Division is the inverse of multiplication. In it, one number, known as the dividend, is split into several equal parts by another number, known as the divisor. The result of this operation is called

9768-433: The multiplicand, are combined into a single number called the product . The symbols of multiplication are × {\displaystyle \times } , ⋅ {\displaystyle \cdot } , and *. Examples are 2 × 3 = 6 {\displaystyle 2\times 3=6} and 0.3 ⋅ 5 = 1.5 {\displaystyle 0.3\cdot 5=1.5} . If

9879-484: The natural numbers is N {\displaystyle \mathbb {N} } . The whole numbers are identical to the natural numbers with the only difference being that they include 0. They can be represented as { 0 , 1 , 2 , 3 , 4 , . . . } {\displaystyle \{0,1,2,3,4,...\}} and have the symbol N 0 {\displaystyle \mathbb {N} _{0}} . Some mathematicians do not draw

9990-459: The necessary IT hardware to enable large numbers of student to sit an electronic examination at the same time, as well as the need to ensure a stringent level of security (for example, see: Academic dishonesty ) are among the concerns that need to resolved to accomplish this transition. E-marking is one way that many exam assessment and awarding bodies, such as Cambridge International Examinations , are utilizing innovations in technology to expedite

10101-512: The number 1 is continuously added. Subtraction is the inverse of addition. In it, one number, known as the subtrahend, is taken away from another, known as the minuend. The result of this operation is called the difference. The symbol of subtraction is − {\displaystyle -} . Examples are 14 − 8 = 6 {\displaystyle 14-8=6} and 45 − 1.7 = 43.3 {\displaystyle 45-1.7=43.3} . Subtraction

10212-430: The number 13 is written as 1101 in the binary notation, which stands for 1 ⋅ 2 3 + 1 ⋅ 2 2 + 0 ⋅ 2 1 + 1 ⋅ 2 0 {\displaystyle 1\cdot 2^{3}+1\cdot 2^{2}+0\cdot 2^{1}+1\cdot 2^{0}} . In computing, each digit in the binary notation corresponds to one bit . The earliest positional system

10323-459: The number of questions one answered correctly, incorrectly, or left unattempted. Candidates are given +3 points for each correct answer and -1 point for each incorrect answer, no negative marking for TITA (Type in the Answer) questions. No points are given for questions that are not answered. The raw scores are then adjusted through a process called equating. Equated raw scores are then placed on

10434-426: The online classroom. However, online assessment may provide additional possibilities for cheating, such as hacking. Two common types of academic dishonesty are identity fraud and plagiarism . Identity fraud can occur in the traditional or online classroom. There is a higher chance in online classes due to the lack of proctored exams or instructor-student interaction. In a traditional classroom, instructors have

10545-543: The opportunity to get to know the students, learn their writing styles or use proctored exams. To prevent identity fraud in an online class, instructors can use proctored exams through the institutions testing center or require students to come in at a certain time for the exam. Correspondence through phone or video conferencing techniques can allow an instructor to become familiar with a student through their voice and appearance. Another option would be personalize assignments to students backgrounds or current activities. This allows

10656-547: The power of 1 2 {\displaystyle {\tfrac {1}{2}}} and the cube root of a number is the same as raising the number to the power of 1 3 {\displaystyle {\tfrac {1}{3}}} . Examples are 4 = 4 1 2 = 2 {\displaystyle {\sqrt {4}}=4^{\frac {1}{2}}=2} and 27 3 = 27 1 3 = 3 {\displaystyle {\sqrt[{3}]{27}}=27^{\frac {1}{3}}=3} . Logarithm

10767-418: The precision of the measurement. When a number is written using ordinary decimal notation, leading zeros are not significant, and trailing zeros of numbers not written with a decimal point are implicitly considered to be non-significant. For example, the numbers 0.056 and 1200 each have only 2 significant digits, but the number 40.00 has 4 significant digits. Representing uncertainty using only significant digits

10878-632: The prescribed total for each question. All candidate details are hidden from the work being marked to ensure anonymity during the marking process. Once marking is complete, results can be uploaded immediately, reducing both the time spent by examiners posting results and the wait time for students. The e-marking FAQ is a comprehensive list of answers to frequently asked questions surrounding e-marking. It has also been noted that in regards to university level work, providing electronic feedback can be more time-consuming than traditional assessments, and therefore more expensive. In 1986, Lichtenwald investigated

10989-414: The product of 3 × 4 {\displaystyle 3\times 4} can be calculated as 3 + 3 + 3 + 3 {\displaystyle 3+3+3+3} . A common technique for multiplication with larger numbers is called long multiplication . This method starts by writing the multiplier above the multiplicand. The calculation begins by multiplying the multiplier only with

11100-411: The quantity of objects. They answer the question "how many?". Ordinal numbers, such as first, second, and third, indicate order or placement in a series. They answer the question "what position?". A number is rational if it can be represented as the ratio of two integers. For instance, the rational number 1 2 {\displaystyle {\tfrac {1}{2}}} is formed by dividing

11211-441: The ratio of two integers. They are often required to describe geometric magnitudes. For example, if a right triangle has legs of the length 1 then the length of its hypotenuse is given by the irrational number 2 {\displaystyle {\sqrt {2}}} . π is another irrational number and describes the ratio of a circle 's circumference to its diameter . The decimal representation of an irrational number

11322-534: The relations and laws between them. Some of the main branches of modern number theory include elementary number theory , analytic number theory , algebraic number theory , and geometric number theory . Elementary number theory studies aspects of integers that can be investigated using elementary methods. Its topics include divisibility , factorization , and primality . Analytic number theory, by contrast, relies on techniques from analysis and calculus. It examines problems like how prime numbers are distributed and

11433-404: The result by using several one-digit operations in a row. For example, in the method addition with carries , the two numbers are written one above the other. Starting from the rightmost digit, each pair of digits is added together. The rightmost digit of the sum is written below them. If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to

11544-406: The rightmost digit of the multiplicand and writing the result below, starting in the rightmost column. The same is done for each digit of the multiplicand and the result in each case is shifted one position to the left. As a final step, all the individual products are added to arrive at the total product of the two multi-digit numbers. Other techniques used for multiplication are the grid method and

11655-418: The same denominator then they can be added by adding their numerators and keeping the common denominator. For example, 2 7 + 3 7 = 5 7 {\displaystyle {\tfrac {2}{7}}+{\tfrac {3}{7}}={\tfrac {5}{7}}} . A similar procedure is used for subtraction. If the two numbers do not have the same denominator then they must be transformed to find

11766-408: The student to apply it to their personal life and gives the instructor more assurance the actual student is completing the assignment. Lastly, an instructor may not make the assignments heavily weighted so the students do not feel as pressured. Plagiarism is the misrepresentation of another person's work. It is easy to copy and paste from the internet or retype directly from a source. It is not only

11877-437: The symbols I, V, X, L, C, D, M as its basic numerals to represent the numbers 1, 5, 10, 50, 100, 500, and 1000. A numeral system is positional if the position of a basic numeral in a compound expression determines its value. Positional numeral systems have a radix that acts as a multiplicand of the different positions. For each subsequent position, the radix is raised to a higher power. In the common decimal system, also called

11988-535: The test validity and test reliability of either personal computer administration or a paper and pencil administration of the Peabody Picture Vocabulary Test-Revised (PPVT-R). His project report included a review and analysis of the literature of pre-mid 1980s E-assessment systems. A review of the literature of E-assessment from the 1970s until 2000 examined the advantages and disadvantages of E-assessments. A detailed review of

12099-414: The types of tests that can use e-marking, with e-marking applications designed to accommodate multiple choice, written, and even video submissions for performance examinations. E-marking software is used by individual educational institutions and can also be rolled out to the participating schools of awarding exam organizations. e-marking has been used to mark many well-known high stakes examinations, which in

12210-735: Was developed by ancient Babylonians and had a radix of 60. Arithmetic operations are ways of combining, transforming, or manipulating numbers. They are functions that have numbers both as input and output. The most important operations in arithmetic are addition , subtraction , multiplication , and division . Further operations include exponentiation , extraction of roots , and logarithm . If these operations are performed on variables rather than numbers, they are sometimes referred to as algebraic operations . Two important concepts in relation to arithmetic operations are identity elements and inverse elements . The identity element or neutral element of an operation does not cause any change if it

12321-762: Was entrusted with the responsibility of conducting the test from 2009 to 2013. The first computer based CAT was marred with technical snags. The issue was so serious that it prompted the Government of India to seek a report from the convenor. The trouble was diagnosed as ' Conficker ' and 'W32 Nimda' , the two viruses that attacked the system display of the test, causing server slow down. Since 2014 onward, CAT has been conducted by Tata Consultancy Services (TCS) . CAT 2015 and CAT 2016 were 180-minute tests consisting of 100 questions (34 from Quantitative Ability, 34 from Verbal Ability and Reading Comprehension, and 32 from Data Interpretation and Logical Reasoning. CAT 2020 onwards,

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