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






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






3. 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.






4. A number is divisible by 6 if it is






5. 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.






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






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






8. A number is divisible by 3 if






9. The set of all complex numbers is denoted by






10. 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






11. Are used to indicate sets






12. The relative greatness of positive and negative numbers






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. Number X decreased by 12 divided by forty






15. 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






16. Less than






17. 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






18. 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 -






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






20. 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






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






22. 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.






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






24. 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






25. 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.






26. 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






27. 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.






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






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






30. 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.)






31. 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:






32. A curve in the plane






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






34. Plus






35. Product






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






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






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






39. 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.






40. One term (5x or 4)






41. Number symbols






42. Number T increased by 9






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






44. A number is divisible by 8 if






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






46. 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.






47. 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






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






49. 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






50. Quotient