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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. 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.






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






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






4. 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 -






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






6. The finiteness or not of the number of rational or integer points on an algebraic curve






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






8. 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.






9. 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






10. LAWS FOR COMBINING NUMBERS






11. 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.






12. Plus






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






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






15. 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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16. More than






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






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. A number is divisible by 4 if






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






21. A number is divisible by 3 if






22. Remainder






23. Sum






24. Less than






25. 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






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






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. First axiom of equality






29. 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:






30. 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.






31. A curve in the plane






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






33. A number is divisible by 5 if its






34. One term (5x or 4)






35. 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.






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. Subtraction






38. Quotient






39. The Arabic numerals from 0 through 9 are called






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






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






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






43. A number is divisible by 8 if






44. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.






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






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






47. 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.






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






49. Decreased by






50. 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