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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.
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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. 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.






2. 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.






3. A number is divisible by 8 if






4. 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.






5. 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






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






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






8. 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.)






9. 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






10. A number is divisible by 3 if






11. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the

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12. Number X decreased by 12 divided by forty






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






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






15. 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






16. 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.






17. 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.






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






19. 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






20. 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.






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






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






23. 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 -






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






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






26. The set of all complex numbers is denoted by






27. A number is divisible by 2 if






28. Quotient






29. 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






30. Number symbols






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






32. One term (5x or 4)






33. Number T increased by 9






34. 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






35. 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






36. A number is divisible by 6 if it is






37. The number without a variable (5m+2). In this case - 2






38. 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






39. Product






40. 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.






41. 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.






42. 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






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






44. 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.






45. 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.






46. LAWS FOR COMBINING NUMBERS






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






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






49. Total






50. 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.







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