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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. 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.)






2. 2 -3 -4 -5 -6






3. A number is divisible by 4 if






4. Number X decreased by 12 divided by forty






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






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






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






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






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






10. One term (5x or 4)






11. A number is divisible by 2 if






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






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






14. 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.






15. 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






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






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






18. 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






19. A number is divisible by 5 if its






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






21. Less than






22. 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






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






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






25. Plus






26. 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






27. 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






28. Increased by






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






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






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






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






33. 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






34. 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 -






35. A curve in the plane






36. 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.






37. 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.






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






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






40. Subtraction






41. 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.






42. 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






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






44. Remainder






45. The Arabic numerals from 0 through 9 are called






46. A number is divisible by 9 if






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. 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.






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






50. 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.