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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • 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. Integers greater than zero and less than 5 form a set - as follows:






2. A number is divisible by 8 if






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






4. 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 -






5. 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.)






6. 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






7. 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.






8. 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






9. 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






10. 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:






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






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






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






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






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






16. 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.






17. 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






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






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






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






21. LAWS FOR COMBINING NUMBERS






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






23. 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






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






25. 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.






26. More than






27. 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






28. Total






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






30. The Arabic numerals from 0 through 9 are called






31. A number is divisible by 6 if it is






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






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






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






35. A number is divisible by 2 if






36. 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






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






38. One term (5x or 4)






39. 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.






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






41. Plus






42. 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.






43. 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.






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






45. Quotient






46. Number T increased by 9






47. 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.






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






49. Any number that is exactly divisible by a given number is a






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