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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. Number symbols






2. Since the elements of the set {2 - 4 - e} are the same as the elements of{4 - 2 - e} - these two sets are said to be






3. Remainder






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






5. 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






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






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






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






9. 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 -






10. The set of all complex numbers is denoted by






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






12. Number T increased by 9






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






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






15. 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






16. 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






17. 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.






18. The objects or symbols in a set are called Numerals - Lines - or Points






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






20. Sixteen less than number Q






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






22. 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.






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






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






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






26. 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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27. Increased by






28. 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.)






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






30. 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






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






32. Total






33. 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






34. 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.






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






36. 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.






37. A number is divisible by 4 if






38. A number is divisible by 8 if






39. Less than






40. Sum






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






42. More than






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






44. 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.






45. In particular - the square of the imaginary unit is -1: The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit. Indeed - if i is treated as a number so that di mean






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






47. Quotient






48. 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:






49. 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






50. 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