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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. 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






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






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






4. Implies a collection or grouping of similar - objects or symbols.






5. A number is divisible by 9 if






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






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






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






9. LAWS FOR COMBINING NUMBERS






10. First axiom of equality






11. The relative greatness of positive and negative numbers






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






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






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






15. A number is divisible by 4 if






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






17. A number is divisible by 2 if






18. Number X decreased by 12 divided by forty






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






20. 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:






21. 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.)






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






23. 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.






24. 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






25. 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.






26. 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.






27. 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.






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






29. 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.






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






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






32. 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






33. Quotient






34. Sixteen less than number Q






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






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






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






39. 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.






40. 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






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






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






43. Number symbols






44. Less than






45. Remainder






46. The greatest of 3 consecutive whole numbers - the smallest of which is F






47. The Arabic numerals from 0 through 9 are called






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






49. The set of all complex numbers is denoted by






50. A curve in the plane