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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. 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






2. 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.






3. Quotient






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






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






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






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






8. 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






9. A number is divisible by 8 if






10. 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






11. A number is divisible by 5 if its






12. A number is divisible by 4 if






13. 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.






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






15. 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






16. Remainder






17. 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






18. Decreased by






19. A number is divisible by 9 if






20. 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.)






21. 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






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






23. A number is divisible by 6 if it is






24. The number without a variable (5m+2). In this case - 2






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






26. Number symbols






27. 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.






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






29. Are used to indicate sets






30. 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.






31. 2 -3 -4 -5 -6






32. 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.






33. Plus






34. 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






35. The relative greatness of positive and negative numbers






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






37. 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.






38. Number T increased by 9






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






40. 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






41. Less than






42. 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






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






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






45. 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.






46. 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.






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






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






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






50. 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