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






2. 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.






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






4. Total






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






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






7. One term (5x or 4)






8. Are used to indicate sets






9. 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






10. More than






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. Number T increased by 9






13. A number is divisible by 4 if






14. 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.






15. Number X decreased by 12 divided by forty






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






17. A number is divisible by 9 if






18. 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






19. Number symbols






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






21. Remainder






22. 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






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






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






25. LAWS FOR COMBINING NUMBERS






26. 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.)






27. A number is divisible by 5 if its






28. Decreased by






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. 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.






31. The set of all complex numbers is denoted by






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






33. Plus






34. 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






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






36. 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






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






38. The relative greatness of positive and negative numbers






39. 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






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






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






42. 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.






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






44. 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






45. 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.






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






47. 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.






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






49. 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






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







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