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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. A number is divisible by 9 if






2. 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






3. 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






4. A curve in the plane






5. The set of all complex numbers is denoted by






6. A number is divisible by 3 if






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






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






9. A number that has factors other than itself and 1 is a






10. First axiom of equality






11. 2 -3 -4 -5 -6






12. A number is divisible by 2 if






13. 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






14. 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.






15. 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






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






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






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






19. Sum






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






21. Less than






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






23. More than






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






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






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






27. 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.)






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. 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






30. 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:






31. 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.






32. 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.






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






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






35. 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.






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






37. A number is divisible by 8 if






38. 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






39. Number X decreased by 12 divided by forty






40. 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.






41. The relative greatness of positive and negative numbers






42. Product






43. 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.






44. Sixteen less than number Q






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






46. Decreased by






47. 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






48. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.






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






50. 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