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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. Decreased by






2. A number is divisible by 2 if






3. 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






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






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






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






7. First axiom of equality






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






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






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






11. 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






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






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






14. 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






15. A number is divisible by 6 if it is






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






17. Are used to indicate sets






18. 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.






19. 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






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






21. The relative greatness of positive and negative numbers






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






23. Less than






24. 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






25. The number without a variable (5m+2). In this case - 2






26. 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.






27. Total






28. Sum






29. 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






30. 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.






31. A number is divisible by 8 if






32. Product






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






34. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -






35. The set of all complex numbers is denoted by






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






37. 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.






38. 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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39. 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.






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






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






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






43. 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






44. Remainder






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






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






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






48. 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.)






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






50. 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.







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