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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. Is any complex number that is a solution to some polynomial equation with rational coefficients; for example - every solution x of (say) is an algebraic number. Fields of algebraic numbers are also called algebraic number fields - or shortly number f






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






3. Total






4. A letter tat represents a number that is unknown (usually X or Y)






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. 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






7. The relative greatness of positive and negative numbers






8. Increased by






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






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






11. As shown earlier - c - di is the complex conjugate of the denominator c + di.






12. 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.






13. Quotient






14. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract






15. Another way of encoding points in the complex plane other than using the x- and y-coordinates is to use the distance of a point P to O - the point whose coordinates are (0 - 0) (the origin) - and the angle of the line through P and O. This idea leads






16. The greatest of 3 consecutive whole numbers - the smallest of which is F






17. 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.






18. 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.)






19. First axiom of equality






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






21. The set of all complex numbers is denoted by






22. 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.






23. 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.






24. A number is divisible by 3 if






25. A number is divisible by 9 if






26. 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.






27. A number that has factors other than itself and 1 is a






28. The defining characteristic of a position vector is that it has






29. Are used to indicate sets






30. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.






31. 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.






32. Any number that is not a multiple of 2 is an






33. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the


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






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






36. 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.






37. 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.






38. The place value which corresponds to a given position in a number is determined by the






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






40. 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






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






42. 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






43. 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






44. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number






45. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative






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






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






48. The number touching the variable (in the case of 5x - would be 5)






49. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.






50. Sixteen less than number Q