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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. 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






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






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






4. Are used to indicate sets






5. The set of all complex numbers is denoted by






6. 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






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






8. 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






9. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number






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






11. A curve in the plane






12. A number is divisible by 8 if






13. Allow for solutions to certain equations that have no real solution: the equation has no real solution - since the square of a real number is 0 or positive.






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






15. A number is divisible by 6 if it is






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






17. 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.






18. 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






19. 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






20. 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.






21. 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






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






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






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






25. Quotient






26. A number is divisible by 5 if its






27. 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.)






28. 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.






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. A number is divisible by 9 if






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






32. 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.






33. 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.






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






35. 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 -






36. Remainder






37. 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






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






39. 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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40. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.






41. The relative greatness of positive and negative numbers






42. Total






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






44. More than






45. A number that has factors other than itself and 1 is a






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. Number T increased by 9






48. Number X decreased by 12 divided by forty






49. One term (5x or 4)






50. 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.