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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.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. 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.






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






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






4. 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.






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






6. Decreased by






7. A number is divisible by 8 if






8. 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.)






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






10. 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.






11. 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






12. LAWS FOR COMBINING NUMBERS






13. One term (5x or 4)






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






15. A number is divisible by 5 if its






16. A number is divisible by 9 if






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






18. 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






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






20. 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 -






21. 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.






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. 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.






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






25. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.






26. Total






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






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






29. A number is divisible by 2 if






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






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






32. 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.






33. A number is divisible by 4 if






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






35. Sixteen less than number Q






36. Sum






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






38. Number T increased by 9






39. Does not have an equal sign (3x+5) (2a+9b)






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






41. 2 -3 -4 -5 -6






42. 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






43. 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.






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






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






46. Plus






47. 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:






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






49. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.






50. A curve in the plane