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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. Allow the variables in f(x -y) = 0 to be complex numbers; then f(x -y) = 0 defines a 2-dimensional surface in (projective) 4-dimensional space (since two complex variables can be decomposed into four real variables - i.e. - four dimensions). Count th






2. Less than






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






4. Increased by






5. A number is divisible by 3 if






6. 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.






7. Product






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






9. Plus






10. 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.






11. 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






12. Number symbols






13. 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






14. 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.






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






16. Subtraction






17. 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






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






19. 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.






20. More than






21. LAWS FOR COMBINING NUMBERS






22. A number is divisible by 4 if






23. A curve in the plane






24. 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






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






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






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

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28. 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






29. 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






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






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. 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.






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






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






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






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






37. 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.)






38. A number is divisible by 9 if






39. The objects in a set have at least






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






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






42. The set of all complex numbers is denoted by






43. 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.






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






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






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






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






48. The Arabic numerals from 0 through 9 are called






49. 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






50. Are used to indicate sets