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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. 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:






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






3. A number is divisible by 9 if






4. 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.






5. Number symbols






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






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






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






9. 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.






10. Total






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






12. 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






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






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






16. 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.






17. More than






18. 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.






19. The set of all complex numbers is denoted by






20. The number touching the variable (in the case of 5x - would be 5)






21. A number is divisible by 4 if






22. 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






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






24. Product






25. Quotient






26. Remainder






27. Sum






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






29. The relative greatness of positive and negative numbers






30. 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






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






32. 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.






33. 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






34. 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.






35. 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






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






37. Plus






38. 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.






39. The square roots of a + bi (with b ? 0) are - where and where sgn is the signum function. This can be seen by squaring to obtain a + bi.






40. Number X decreased by 12 divided by forty






41. A number is divisible by 5 if its






42. One term (5x or 4)






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






44. 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






45. If a factor of a number is prime - it is called a






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






47. A number is divisible by 6 if it is






48. Are used to indicate sets






49. 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






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







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