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






2. 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.






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






4. 2 -3 -4 -5 -6






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






6. 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.






7. A number is divisible by 5 if its






8. 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






9. Subtraction






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






11. The objects in a set have at least






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






13. 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






14. 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.)






15. 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 -






16. LAWS FOR COMBINING NUMBERS






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






18. Less than






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






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






21. 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.






22. 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.






23. 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






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






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






26. Sixteen less than number Q






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






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






29. First axiom of equality






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. Number X decreased by 12 divided by forty






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






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






34. Are used to indicate sets






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






36. Increased by






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






38. 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:






39. 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.






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. 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






42. Decreased by






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






44. More than






45. Remainder






46. 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.






47. The relative greatness of positive and negative numbers






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






49. 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






50. 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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