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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. 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






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






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






4. 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.






5. 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.






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






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






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






9. The Arabic numerals from 0 through 9 are called






10. 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 -






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






12. 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






13. Subtraction






14. Implies a collection or grouping of similar - objects or symbols.






15. 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:






16. Any number that can be divided lnto a given number without a remainder is a






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






18. Number T increased by 9






19. Sum






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






21. 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






22. A number is divisible by 5 if its






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






24. 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.)






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






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






27. 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






28. 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.






29. Number symbols






30. A number is divisible by 6 if it is






31. 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






32. A curve in the plane






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


34. 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.






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






36. 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.






37. 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.






38. A number is divisible by 2 if






39. 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






40. 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






41. Less than






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






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






44. 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.






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






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. 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.






48. 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






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






50. 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.