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






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






3. 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:






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






5. A number is divisible by 8 if






6. 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.






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






8. Plus






9. Number symbols






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






11. A number is divisible by 3 if






12. A number is divisible by 2 if






13. 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






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






15. A number is divisible by 4 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. 2 -3 -4 -5 -6






18. The objects in a set have at least






19. 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






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






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






22. Quotient






23. Are used to indicate sets






24. 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






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






26. 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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27. 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.






28. 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 -






29. 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.






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






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






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






33. 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.






34. 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






35. A curve in the plane






36. LAWS FOR COMBINING NUMBERS






37. 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.






38. Number T increased by 9






39. Increased by






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






41. Sixteen less than number Q






42. 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.






43. 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.






44. A number is divisible by 5 if its






45. First axiom of equality






46. 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.)






47. 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.






48. The number without a variable (5m+2). In this case - 2






49. 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.






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







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