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






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






3. 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






4. A curve in the plane






5. 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






6. Increased by






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






8. First axiom of equality






9. Number X decreased by 12 divided by forty






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






11. A number is divisible by 4 if






12. 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.






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






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






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






16. Sum






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






18. 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.)






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






20. Plus






21. 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






22. A number is divisible by 6 if it is






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






24. 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.






25. 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






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






27. One term (5x or 4)






28. 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






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






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






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






32. 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.






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






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






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






36. A number is divisible by 5 if its






37. 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






38. 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






39. 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.






40. 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






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






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






43. Sixteen less than number Q






44. Total






45. Decreased by






46. 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.






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






48. A number is divisible by 3 if






49. 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






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