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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. 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






2. 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.






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






4. 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:






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






6. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative






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






8. 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






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






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






11. 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






12. 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.






13. 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






14. A number is divisible by 3 if






15. Quotient






16. 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.






17. A number is divisible by 4 if






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






19. A number is divisible by 2 if






20. The set of all complex numbers is denoted by






21. Number X decreased by 12 divided by forty






22. 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.






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






24. The place value which corresponds to a given position in a number is determined by the






25. Number symbols






26. Plus






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






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. 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






30. Are used to indicate sets






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






32. 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






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. 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.






35. 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.






36. Sixteen less than number Q






37. More than






38. Product






39. The finiteness or not of the number of rational or integer points on an algebraic curve






40. A number is divisible by 5 if its






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






42. Remainder






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






44. 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






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






46. 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.






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. A number is divisible by 8 if






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







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