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






2. 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






3. Product






4. 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






5. Increased by






6. A number is divisible by 2 if






7. 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






8. 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






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






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






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






12. 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.






13. Number symbols






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






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






16. Are used to indicate sets






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






18. 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






19. LAWS FOR COMBINING NUMBERS






20. 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.






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






22. More than






23. A number is divisible by 9 if






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. Plus






26. The number of digits in an integer indicates its rank; that is - whether it is 'in the hundreds -' 'in the thousands -' etc. The idea of ranking numbers in terms of tens - hundreds - thousands - etc. - is based on the






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






28. 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






29. A number is divisible by 3 if






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






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






32. 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






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






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






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






36. 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






37. The set of all complex numbers is denoted by






38. Quotient






39. 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






40. A number is divisible by 6 if it is






41. Less than






42. 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.






43. Number T increased by 9






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






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






46. 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






47. One term (5x or 4)






48. 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.






49. Subtraction






50. 2 -3 -4 -5 -6