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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. 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






2. Remainder






3. 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.






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






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






6. Quotient






7. 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.






8. The Arabic numerals from 0 through 9 are called






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






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






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






12. A number is divisible by 3 if






13. 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






14. First axiom of equality






15. A number is divisible by 4 if






16. 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 -






17. Sixteen less than number Q






18. Number X decreased by 12 divided by forty






19. 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






20. Number symbols






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






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






23. 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:






24. One term (5x or 4)






25. Increased by






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






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






28. Number T increased by 9






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






30. 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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31. 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.






32. 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






33. 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






34. A curve in the plane






35. Product






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. 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.)






38. 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






39. Less than






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






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






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. The set of all complex numbers is denoted by






44. More than






45. A number is divisible by 5 if its






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






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






48. 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.






49. 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.






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