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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. Is called the real part of z - and the real number b is often called the imaginary part. By this convention the imaginary part is a real number - not including the imaginary unit: hence b - not bi - is the imaginary part. (Others - however call bi th






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






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






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






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






7. 2 -3 -4 -5 -6






8. Product






9. 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.)






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






11. 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






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






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. Quotient






15. 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






16. A number is divisible by 5 if its






17. One term (5x or 4)






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






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






20. 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






21. Sum






22. 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.






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






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






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






26. Are used to indicate sets






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. 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.






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






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






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






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






33. A number is divisible by 9 if






34. More than






35. 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.






36. 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.






37. 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






38. First axiom of equality






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






40. 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.






41. Integers greater than zero and less than 5 form a set - as follows:






42. Number symbols






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. 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






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






46. A number is divisible by 3 if






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






48. The Arabic numerals from 0 through 9 are called






49. 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:






50. 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.