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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.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. 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






2. A number is divisible by 3 if






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






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






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






6. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number






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






8. 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






9. 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.






10. 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






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






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






13. 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.






14. A letter tat represents a number that is unknown (usually X or Y)






15. 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.






16. Plus






17. Remainder






18. The Arabic numerals from 0 through 9 are called






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






20. 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






21. Any number that la a multiple of 2 is an






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






23. More than






24. 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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25. 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






26. Quotient






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






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






29. The set of all complex numbers is denoted by






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






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






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






33. 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.






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






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






36. Increased by






37. 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






38. A number is divisible by 8 if






39. 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






40. 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






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






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






43. 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






44. 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






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






46. 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






47. One term (5x or 4)






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






49. 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.






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







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