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






2. The Arabic numerals from 0 through 9 are called






3. 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.






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






5. 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






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






7. 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:






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






9. Quotient






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






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






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






13. 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






14. 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.






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






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






17. 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






18. 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.






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






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






21. 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.






22. 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






23. Product






24. Total






25. A number is divisible by 8 if






26. A curve in the plane






27. 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.






28. LAWS FOR COMBINING NUMBERS






29. A number is divisible by 5 if its






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






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






32. A number is divisible by 9 if






33. Decreased by






34. 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






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. Increased by






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






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






39. 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.






40. Plus






41. 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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42. 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






43. 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.






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






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






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






47. A number is divisible by 3 if






48. One term (5x or 4)






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






50. 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.