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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 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






2. Sixteen less than number Q






3. A number is divisible by 8 if






4. 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.






5. The relative greatness of positive and negative numbers






6. 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






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






8. Quotient






9. Subtraction






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






11. 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.






12. 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






13. Number symbols






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






15. 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:






16. The set of all complex numbers is denoted by






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






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






19. Product






20. 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






21. The objects in a set have at least






22. 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






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






24. Plus






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






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






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






28. 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.






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






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






31. The objects or symbols in a set are called Numerals - Lines - or Points






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






33. 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.






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






35. 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.)






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






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. In terms of its tools - as the study of the integers by means of tools from real and complex analysis - in terms of its concerns - as the study within number theory of estimates on size and density - as opposed to identities.






39. A number is divisible by 2 if






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






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






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






43. 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






44. 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.






45. 2 -3 -4 -5 -6






46. Number X decreased by 12 divided by forty






47. 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






48. Sum






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






50. First axiom of equality







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