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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. 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






2. Plus






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






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






5. The objects in a set have at least






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






8. A number is divisible by 6 if it is






9. 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






10. 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






11. Product






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






13. Are used to indicate sets






14. 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






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






16. Subtraction






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






18. 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.






19. 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






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






21. 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






22. 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






23. Quotient






24. A number is divisible by 8 if






25. One term (5x or 4)






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






27. 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:






28. 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.)






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






30. 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.






31. 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.






32. Total






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






34. 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.






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






36. A curve in the plane






37. 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






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






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






40. 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.






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






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






43. 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






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






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






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






47. A number is divisible by 9 if






48. Number X decreased by 12 divided by forty






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






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