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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. 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.






2. The set of all complex numbers is denoted by






3. A number is divisible by 8 if






4. Plus






5. 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






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






7. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.






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






9. 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.






10. 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.






11. 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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12. 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.






13. The greatest of 3 consecutive whole numbers - the smallest of which is F






14. 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.






15. First axiom of equality






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






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. 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.






19. 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.






20. 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






21. Total






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






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






24. A number is divisible by 6 if it is






25. 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






26. Product of 16 and the sum of 5 and number R






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






28. Any number that la a multiple of 2 is an






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






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






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






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






34. 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.






35. One term (5x or 4)






36. A number is divisible by 9 if






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






38. The Arabic numerals from 0 through 9 are called






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






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






41. 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






42. A number is divisible by 5 if its






43. Number X decreased by 12 divided by forty






44. 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.






45. LAWS FOR COMBINING NUMBERS






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






47. Remainder






48. Less than






49. 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






50. 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.