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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. LAWS FOR COMBINING NUMBERS






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






3. 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






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






5. Subtraction






6. 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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7. 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






8. 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.






9. One term (5x or 4)






10. 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






11. 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.






12. 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:






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






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






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






16. 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






17. A number is divisible by 2 if






18. First axiom of equality






19. Total






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






21. 2 -3 -4 -5 -6






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






23. 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






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






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






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






27. 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.






28. 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.






29. The Arabic numerals from 0 through 9 are called






30. Remainder






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. Increased by






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






34. 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






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






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






37. A number is divisible by 9 if






38. A number is divisible by 6 if it is






39. Number T increased by 9






40. 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






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






42. Number symbols






43. 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.






44. 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.






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






46. 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






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






48. 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.






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






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







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