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






3. First axiom of equality






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






5. The set of all complex numbers is denoted by






6. 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.)






7. 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






8. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag






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. The Arabic numerals from 0 through 9 are called






11. 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.






12. Quotient






13. 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.






14. 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






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






16. 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.






17. One term (5x or 4)






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






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






20. Increased by






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






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






23. 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.






24. Less than






25. A number is divisible by 4 if






26. 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.






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






28. The relative greatness of positive and negative numbers






29. 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.






30. A number is divisible by 2 if






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






32. Total






33. 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.






34. 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.






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






36. 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






37. 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






38. The objects in a set have at least






39. 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






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. A number is divisible by 8 if






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






43. Plus






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






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






46. A number is divisible by 3 if






47. More than






48. Decreased by






49. 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






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