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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. 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






2. A number is divisible by 2 if






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






4. If the same quantity is subtracted from each of two equal quantities - the resulting quantities are equal. If equals are subtracted from equals - the results are equal.






5. 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






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






7. A number is divisible by 5 if its






8. Implies a collection or grouping of similar - objects or symbols.






9. Has an equal sign (3x+5 = 14)






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






11. The smallest of four sonsecutive whole numbers - the biggest of which is K+6






12. Product






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






14. Quotient






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






16. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive






17. 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






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






20. A number is divisible by 3 if






21. 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.






22. 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.






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






24. 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






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






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






27. 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






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






29. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.






30. 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






31. Less than






32. 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






33. 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.






34. More than






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






36. 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






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. LAWS FOR COMBINING NUMBERS






39. Number T increased by 9






40. Increased by






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






42. The objects in a set have at least






43. Sixteen less than number Q






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






45. 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.






46. 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.






47. Are used to indicate sets






48. Sum






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






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