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






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






3. 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






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






5. In the Rectangular Coordinate System - the direction to the right along the horizontal line is






6. Increased by






7. This law states that the product of three or more factors is the same regardless of the manner in which they are grouped. Negative signs require no special treatment in the application of this law.






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






9. First axiom of equality






10. 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.






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






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






13. 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






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






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






16. 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.






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






18. A number is divisible by 4 if






19. 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






20. 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.






21. Plus






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






23. 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.






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






25. Product






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






27. The relative greatness of positive and negative numbers






28. 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






29. 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






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






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






32. 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






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






34. The objects in a set have at least






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






36. Quotient






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


38. No short method has been found for determining whether a number is divisible by






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






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






41. Are used to indicate sets






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






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






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. 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.






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






47. A number is divisible by 2 if






48. A number is divisible by 5 if its






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






50. 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.