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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. 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.






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






3. 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.






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






5. 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.






6. A curve in the plane






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 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






9. 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.






10. A number is divisible by 9 if






11. 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






12. The objects in a set have at least






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






14. Number X decreased by 12 divided by forty






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






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






17. Decreased by






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






19. A number is divisible by 2 if






20. 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.






21. Increased by






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






23. Subtraction






24. 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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25. 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.)






26. More than






27. The set of all complex numbers is denoted by






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






29. 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:






30. 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






31. 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.






32. 2 -3 -4 -5 -6






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






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






35. 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






36. Remainder






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






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






39. Sixteen less than number Q






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






41. 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.






42. The Arabic numerals from 0 through 9 are called






43. A number is divisible by 4 if






44. 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






45. 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






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






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






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






49. 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.






50. Integers greater than zero and less than 5 form a set - as follows: