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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. Total






2. Sixteen less than number Q






3. More than






4. 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






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






6. 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






7. 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.)






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






9. Increased by






10. 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






11. One term (5x or 4)






12. 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






13. Number T increased by 9






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






15. 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






16. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a






17. Quotient






18. A number is divisible by 8 if






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






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






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






22. 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






23. A number is divisible by 3 if






24. Less than






25. Decreased by






26. 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.






27. The objects in a set have at least






28. The set of all complex numbers is denoted by






29. Remainder






30. 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






31. 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.






32. 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.






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






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






35. Number symbols






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






37. 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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38. 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.






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






40. 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






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






42. Subtraction






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






44. LAWS FOR COMBINING NUMBERS






45. A number is divisible by 6 if it is






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






47. A number is divisible by 9 if






48. 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






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






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