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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. 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






2. 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.)






3. 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.






4. A number is divisible by 6 if it is






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






6. 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






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






8. A number is divisible by 2 if






9. 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






10. This law states that the sum of two or more addends is the same regardless of the order in which they are arranged. Means to change - substitute or move from place to place.






11. 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






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






13. 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.






14. Quotient






15. 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.






16. More than






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






18. Product






19. Number X decreased by 12 divided by forty






20. Number T increased by 9






21. The relative greatness of positive and negative numbers






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






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






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






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






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






28. 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.






29. Sum






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






31. 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






32. 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.






33. 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






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






35. Sixteen less than number Q






36. 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.






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






38. 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.






39. 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:






40. 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






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






42. 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.






43. A number is divisible by 8 if






44. Are used to indicate sets






45. Less than






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






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






48. A number is divisible by 4 if






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






50. 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 -