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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. 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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2. Are used to indicate sets






3. A number that has no factors except itself and 1 is a






4. 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






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






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






7. 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.






8. The relative greatness of positive and negative numbers






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






10. 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.






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






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






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






15. 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.






16. Sixteen less than number Q






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






18. 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 -






19. 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






20. 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.






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






22. First axiom of equality






23. 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.






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






25. 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.






26. Remainder






27. 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.






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






29. 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.






30. Number symbols






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






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






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






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






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






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






38. A curve in the plane






39. 2 -3 -4 -5 -6






40. Total






41. 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






42. 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.






43. 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






44. A number is divisible by 6 if it is






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






46. Decreased by






47. 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.






48. The set of all complex numbers is denoted by






49. The objects in a set have at least






50. 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







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