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






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






3. Are used to indicate sets






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






5. 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






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






7. A number is divisible by 9 if






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






9. The relative greatness of positive and negative numbers






10. 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.






11. A number is divisible by 2 if






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






13. 2 -3 -4 -5 -6






14. First axiom of equality






15. The objects in a set have at least






16. 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.






17. 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.)






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






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






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






21. 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.






22. 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






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






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






25. 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






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






27. The Arabic numerals from 0 through 9 are called






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






29. 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






30. 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






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






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






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






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. 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






36. 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






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






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






39. 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.






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






41. 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






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






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






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






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






46. 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.






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 that has factors other than itself and 1 is a






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






50. Subtraction







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