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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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 sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.






2. Are used to indicate sets






3. One term (5x or 4)






4. 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.






5. 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.






6. Decreased by






7. 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.






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






9. The place value which corresponds to a given position in a number is determined by the






10. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag






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






12. 2 -3 -4 -5 -6






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






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






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






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






17. 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.






18. Number symbols






19. 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






20. 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






21. 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






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






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






24. 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.






25. A number is divisible by 4 if






26. Plus






27. 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






28. 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






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






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






32. 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






33. 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.






34. Number T increased by 9






35. Allow for solutions to certain equations that have no real solution: the equation has no real solution - since the square of a real number is 0 or positive.






36. The sum of two complex numbers A and B - interpreted as points of the complex plane - is the point X obtained by building a parallelogram three of whose vertices are O - A and B. Equivalently - X is the point such that the triangles with vertices O -






37. 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






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






39. The set of all complex numbers is denoted by






40. Product






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






42. More than






43. A number is divisible by 6 if it is






44. A number is divisible by 5 if its






45. 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.






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






47. 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.)






48. A number is divisible by 2 if






49. 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






50. Remainder







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