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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The objects in a set have at least






2. Are often studied as extensions of smaller number fields: a field L is said to be an extension of a field K if L contains K. (For example - the complex numbers C are an extension of the reals R - and the reals R are an extension of the rationals Q.)






3. Remainder






4. Sum






5. A number is divisible by 2 if






6. The objects or symbols in a set are called Numerals - Lines - or Points






7. Increased by






8. In particular - the square of the imaginary unit is -1: The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit. Indeed - if i is treated as a number so that di mean






9. Number symbols






10. A curve in the plane






11. 2 -3 -4 -5 -6






12. In terms of its tools - as the study of the integers by means of tools from real and complex analysis - in terms of its concerns - as the study within number theory of estimates on size and density - as opposed to identities.






13. More than one term (5x+4 contains two)






14. The set of all complex numbers is denoted by






15. If a factor of a number is prime - it is called a






16. These are emphasised in a complex number's polar form and it turns out notably that the operations of addition and multiplication take on a very natural geometric character when complex numbers are viewed as position vectors:






17. A number that has no factors except itself and 1 is a






18. The real and imaginary parts of a complex number can be extracted using the conjugate:






19. An equation - or system of equations - in two or more variables defines






20. Is called the real part of z - and the real number b is often called the imaginary part. By this convention the imaginary part is a real number - not including the imaginary unit: hence b - not bi - is the imaginary part. (Others - however call bi th






21. This law states that the sum of two or more addends is the same regardless of the order in which they are arranged. Means to change - substitute or move from place to place.






22. No short method has been found for determining whether a number is divisible by






23. A number is divisible by 8 if






24. This formula can be used to compute the multiplicative inverse of a complex number if it is given in






25. Any number that is exactly divisible by a given number is a






26. A number is divisible by 5 if its






27. The finiteness or not of the number of rational or integer points on an algebraic curve






28. The sum of two complex numbers A and B - interpreted as points of the complex plane - is the point X obtained by building a parallelogram three of whose vertices are O - A and B. Equivalently - X is the point such that the triangles with vertices O -






29. Total






30. The base which is most commonly used is ten - and the system with ten as a base is called the decimal system (decem is the Latin word for ten). Any number is assumed - unless indicated - to be a






31. A form of coding in which the value of each digit of a number depends upon its position in relation to the other digits of the number. The convention used in our number system is that each digit has a higher place value than those digits to the right






32. Begin by taking out the smallest factor If the number is even - take out all the 2's first - then try 3 as a factor






33. Product of 16 and the sum of 5 and number R






34. The number without a variable (5m+2). In this case - 2






35. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a






36. The numbers which are used for counting in our number system are sometimes called






37. Quotient






38. Integers greater than zero and less than 5 form a set - as follows:






39. Does not have an equal sign (3x+5) (2a+9b)






40. The Arabic numerals from 0 through 9 are called






41. LAWS FOR COMBINING NUMBERS






42. This law states that the product of three or more factors is the same regardless of the manner in which they are grouped. Negative signs require no special treatment in the application of this law.






43. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}






44. This law states that the sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.






45. A number is divisible by 3 if






46. Addition of two complex numbers can be done geometrically by






47. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.






48. The central problem of Diophantine geometry is to determine when a Diophantine equation has






49. Subtraction






50. Consists of all numbers of the form - where a and b are rational numbers and d is a fixed rational number whose square root is not rational.