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






2. 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:






3. Number T increased by 9






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






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






6. Sixteen less than number Q






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






8. Remainder






9. 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






10. 2 -3 -4 -5 -6






11. 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






12. 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.






13. The set of all complex numbers is denoted by






14. Number symbols






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






16. A number is divisible by 9 if






17. A number is divisible by 5 if its






18. 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






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






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






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






22. 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.






23. 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






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






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






26. 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.






27. Number X decreased by 12 divided by forty






28. 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






29. 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.






30. 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






31. A number is divisible by 3 if






32. A number is divisible by 8 if






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






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






35. Quotient






36. 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






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






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






39. 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.






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






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






42. 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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43. 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.






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






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






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






47. No short method has been found for determining whether a number is divisible by






48. 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






49. 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.






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







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