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






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






3. Total






4. The Arabic numerals from 0 through 9 are called






5. Any number that can be divided lnto a given number without a remainder is a






6. 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.






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






8. 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






9. 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






10. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.






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






12. A number is divisible by 2 if






13. 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






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






15. Product






16. 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.






17. 2 -3 -4 -5 -6






18. 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.






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






20. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.






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






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






23. 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.






24. More than






25. LAWS FOR COMBINING NUMBERS






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






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






28. 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.






29. 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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30. A number is divisible by 8 if






31. 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






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






33. The set of all complex numbers is denoted by






34. 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






35. 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






36. 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.






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






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






39. Number X decreased by 12 divided by forty






40. The relative greatness of positive and negative numbers






41. Plus






42. Subtraction






43. 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






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






45. A number is divisible by 9 if






46. 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.






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






48. 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.)






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






50. A number is divisible by 4 if