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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 number is divisible by 4 if






2. 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.






3. 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.






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






5. 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.






6. 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.






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






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






9. 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






10. Total






11. LAWS FOR COMBINING NUMBERS






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






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






14. 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.






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






16. Number T increased by 9






17. 2 -3 -4 -5 -6






18. A number is divisible by 6 if it is






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






20. 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






21. Decreased by






22. More than






23. 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






24. 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.






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






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






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






28. 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






29. The objects or symbols in a set are called Numerals - Lines - or Points






30. 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






31. 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 -






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. A number is divisible by 9 if






34. Less than






35. The relative greatness of positive and negative numbers






36. First axiom of equality






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






38. 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






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






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






41. 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






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






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






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






46. 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.






47. 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






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






49. The Arabic numerals from 0 through 9 are called






50. 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.)