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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • 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. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract






2. 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






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






4. 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 -






5. Product






6. Sixteen less than number Q






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






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






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






10. 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






11. Number T increased by 9






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






13. 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.






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






15. One term (5x or 4)






16. A number is divisible by 3 if






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






18. 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






19. 2 -3 -4 -5 -6






20. Sum






21. 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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22. 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.






23. The objects in a set have at least






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






25. The numbers which are used for counting in our number system are sometimes called






26. 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






27. First axiom of equality






28. 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






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






30. 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






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






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






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






34. 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






35. 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.






36. Addition of two complex numbers can be done geometrically by






37. 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.






38. 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.)






39. Increased by






40. This law states that the sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.






41. 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:






42. 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.






43. The finiteness or not of the number of rational or integer points on an algebraic curve






44. A number is divisible by 9 if






45. 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






46. 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






47. 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.






48. A number is divisible by 6 if it is






49. Are used to indicate sets






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