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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. 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.






2. 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






3. LAWS FOR COMBINING NUMBERS






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






5. The numbers which are used for counting in our number system are sometimes called






6. 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.)






7. Quotient






8. 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






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






10. Product






11. A number is divisible by 3 if






12. Decreased by






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






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






15. Number T increased by 9






16. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract






17. 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.






18. 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






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






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






21. A number is divisible by 6 if it is






22. More than






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






24. 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.






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






26. 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.






27. The set of all complex numbers is denoted by






28. 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 -






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






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. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.






32. Number X decreased by 12 divided by forty






33. 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






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






35. Are used to indicate sets






36. 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






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






38. 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






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






41. A number is divisible by 9 if






42. A number is divisible by 2 if






43. A curve in the plane






44. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive






45. 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:






46. One term (5x or 4)






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






48. No short method has been found for determining whether a number is divisible by






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






50. A number is divisible by 4 if