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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. Decreased by






2. Number T increased by 9






3. More than one term (5x+4 contains two)






4. 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.






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






6. 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 -






7. 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.






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






9. 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






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






11. Product






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






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. 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






15. A number is divisible by 8 if






16. 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






17. 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.)






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






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






20. 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






21. A number is divisible by 3 if






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






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






24. 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.






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






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






27. 2 -3 -4 -5 -6






28. 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.






29. First axiom of equality






30. Increased by






31. 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.






32. A number is divisible by 6 if it is






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






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






35. If a factor of a number is prime - it is called a






36. A number is divisible by 5 if its






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






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






39. In the Rectangular Coordinate System - the direction to the left along the horizontal line is






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






41. 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






42. 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






43. Number X decreased by 12 divided by forty






44. 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.






45. 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.






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






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






48. Subtraction






49. 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.






50. 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.







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