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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. 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.)






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






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






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






5. If two equal quantities are divided by the same quantity - the resulting quotients are equal. If equals are divided by equals - the results are equal.






6. Since the elements of the set {2 - 4 - e} are the same as the elements of{4 - 2 - e} - these two sets are said to be






7. Allow for solutions to certain equations that have no real solution: the equation has no real solution - since the square of a real number is 0 or positive.






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






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






10. A number is divisible by 4 if






11. One term (5x or 4)






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






13. Number T increased by 9






14. 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






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






16. 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 -






17. 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.






18. A number is divisible by 8 if






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






20. In the Rectangular Coordinate System - the direction to the right along the horizontal line is






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






22. 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






23. Plus






24. Any number that can be divided lnto a given number without a remainder is a






25. 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






26. Remainder






27. One asks whether there are any rational points (points all of whose coordinates are rationals) or integral points (points all of whose coordinates are integers) on the curve or surface. If there are any such points - the next step is to ask how many






28. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.






29. The Arabic numerals from 0 through 9 are called






30. The number of digits in an integer indicates its rank; that is - whether it is 'in the hundreds -' 'in the thousands -' etc. The idea of ranking numbers in terms of tens - hundreds - thousands - etc. - is based on the






31. If z is a real number (i.e. - y = 0) - then r = |x|. In general - by Pythagoras' theorem - r is the distance of the point P representing the complex number z to the origin.






32. 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






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






34. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.






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






36. Product






37. The square roots of a + bi (with b ? 0) are - where and where sgn is the signum function. This can be seen by squaring to obtain a + bi.






38. A number is divisible by 6 if it is






39. Sum






40. Are used to indicate sets






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






42. 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






43. More than






44. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag






45. A number is divisible by 2 if






46. Any number that la a multiple of 2 is an






47. Number symbols






48. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -






49. The objects in a set have at least






50. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.