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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. 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.






2. 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.






3. Are used to indicate sets






4. 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.






5. 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






6. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.






7. The objects in a set have at least






8. 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.






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






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






11. 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






12. A number is divisible by 6 if it is






13. A number is divisible by 2 if






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






15. A number is divisible by 9 if






16. 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






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






18. One term (5x or 4)






19. A number is divisible by 3 if






20. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract






21. 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






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






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






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






25. 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 -






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






27. Product






28. Total






29. 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.






30. 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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31. Implies a collection or grouping of similar - objects or symbols.






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






33. LAWS FOR COMBINING NUMBERS






34. 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.






35. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -






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






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






38. Decreased by






39. Since the elements of the set {2 - 4 - e} are the same as the elements of{4 - 2 - e} - these two sets are said to be






40. 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.






41. Number X decreased by 12 divided by forty






42. Number T increased by 9






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






44. 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.






45. 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.






46. 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.






47. Quotient






48. Remainder






49. 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






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