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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. 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.






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






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






5. 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.






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






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






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






9. Are used to indicate sets






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. 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.






12. Product






13. 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:






14. 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.






15. The set of all complex numbers is denoted by






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






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






18. 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.






19. Remainder






20. Number symbols






21. A number is divisible by 9 if






22. 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.






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






24. 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.






25. 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.)






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






27. 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






28. Less than






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






30. 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.






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






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






33. 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 -






34. 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






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






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






37. 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






38. Subtraction






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






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






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






42. Number T increased by 9






43. Number X decreased by 12 divided by forty






44. More than






45. 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






46. 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






47. 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.






48. 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






49. 2 -3 -4 -5 -6






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







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