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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 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






3. 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.






4. 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.)






5. 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






6. Subtraction






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






8. The Arabic numerals from 0 through 9 are called






9. 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






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






11. The set of all complex numbers is denoted by






12. 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.






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






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






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






16. Sum






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






18. 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.






19. 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.






20. 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:






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






22. Quotient






23. 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.






24. 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.






25. Remainder






26. Are used to indicate sets






27. Number T increased by 9






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






29. 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






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






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






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. A number is divisible by 6 if it is






34. Total






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






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






37. 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






38. 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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39. 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.






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






41. A number is divisible by 4 if






42. 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.






43. A number is divisible by 8 if






44. 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






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






46. 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.






47. Less than






48. Decreased by






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






50. 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.