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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.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. A number is divisible by 8 if






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






4. Is any complex number that is a solution to some polynomial equation with rational coefficients; for example - every solution x of (say) is an algebraic number. Fields of algebraic numbers are also called algebraic number fields - or shortly number f






5. Increased by






6. Number symbols






7. Number T increased by 9






8. Remainder






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






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






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






12. 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






13. 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.






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






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






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






17. First axiom of equality






18. Decreased by






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






20. 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 -






21. Product






22. 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:






23. 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.)






24. A letter tat represents a number that is unknown (usually X or Y)






25. 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.






26. A number is divisible by 3 if






27. 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.






28. One term (5x or 4)






29. 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.






30. Less than






31. 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.






32. A number is divisible by 9 if






33. 2 -3 -4 -5 -6






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






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






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






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






38. More than






39. The relative greatness of positive and negative numbers






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






41. Sum






42. The Arabic numerals from 0 through 9 are called






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






44. Are used to indicate sets






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






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






48. LAWS FOR COMBINING NUMBERS






49. 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.






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