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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. Sum






2. 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






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






4. The Arabic numerals from 0 through 9 are called






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






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






7. A number is divisible by 2 if






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






9. 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.






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






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






12. First axiom of equality






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






14. 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.






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. 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. 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






18. 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






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






20. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.






21. More than






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






24. Total






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






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






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






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






29. 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






30. LAWS FOR COMBINING NUMBERS






31. A number is divisible by 8 if






32. Plus






33. 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.






34. If two equal quantities are divided by the same quantity - the resulting quotients are equal. If equals are divided by equals - the results 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. A number is divisible by 6 if it is






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






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






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






40. Subtraction






41. The defining characteristic of a position vector is that it has






42. 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.






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






44. 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






45. Increased by






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






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






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






49. 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.






50. 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.







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