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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract






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. 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.






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






5. 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






6. 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.






7. 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






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






9. 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.






10. The Arabic numerals from 0 through 9 are called






11. 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.)






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






13. Number symbols






14. A number is divisible by 6 if it is






15. 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






16. 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.






17. A number is divisible by 3 if






18. A number is divisible by 9 if






19. Sum






20. 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






21. The relative greatness of positive and negative numbers






22. More than






23. Number X decreased by 12 divided by forty






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






25. 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 -






26. 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






27. A number is divisible by 4 if






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






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






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






31. Product






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






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






34. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.






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






36. 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.






37. 2 -3 -4 -5 -6






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. 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






40. Remainder






41. 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.






42. Increased by






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






44. Subtraction






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






46. 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






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






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






49. 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.






50. 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







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