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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. A number is divisible by 5 if its






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






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






4. 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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5. 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.






6. 2 -3 -4 -5 -6






7. 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






8. Sixteen less than number Q






9. 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






10. A number is divisible by 2 if






11. A number is divisible by 8 if






12. 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






13. 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.)






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






15. A number is divisible by 9 if






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






17. 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






18. Plus






19. 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.






20. 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






21. 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.






22. If z is a real number (i.e. - y = 0) - then r = |x|. In general - by Pythagoras' theorem - r is the distance of the point P representing the complex number z to the origin.






23. A form of coding in which the value of each digit of a number depends upon its position in relation to the other digits of the number. The convention used in our number system is that each digit has a higher place value than those digits to the right






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






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






26. 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 -






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






28. The relative greatness of positive and negative numbers






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






30. Total






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






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






33. 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






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






35. The smallest of four sonsecutive whole numbers - the biggest of which is K+6






36. A number is divisible by 4 if






37. 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.






38. 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






39. LAWS FOR COMBINING NUMBERS






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






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






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






43. Quotient






44. Number X decreased by 12 divided by forty






45. Subtraction






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






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






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






49. 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






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