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






2. Decreased by






3. 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 -






4. 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






5. Subtraction






6. 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.






7. 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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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. Sixteen less than number Q






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






11. 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






12. Product






13. The objects in a set have at least






14. The relative greatness of positive and negative numbers






15. 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.






16. This formula can be used to compute the multiplicative inverse of a complex number if it is given in






17. 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.






18. Remainder






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






20. A number is divisible by 9 if






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






22. 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






23. 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






24. A number is divisible by 8 if






25. Number T increased by 9






26. A number is divisible by 5 if its






27. Total






28. More than






29. LAWS FOR COMBINING NUMBERS






30. Less than






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






32. 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.






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






34. 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.






35. Plus






36. A number is divisible by 3 if






37. Are used to indicate sets






38. 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






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






40. 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






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






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






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






44. A number is divisible by 4 if






45. The Arabic numerals from 0 through 9 are called






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






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






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






49. A curve in the plane






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







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