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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. 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






2. Has an equal sign (3x+5 = 14)






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






4. 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






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






6. 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.






7. 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.






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






9. LAWS FOR COMBINING NUMBERS






10. 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 -






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. 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






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






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






16. The objects in a set have at least






17. Product






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






19. Quotient






20. Decreased by






21. Number X decreased by 12 divided by forty






22. 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






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






24. Increased by






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






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






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






28. Less than






29. A number is divisible by 2 if






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






31. Number symbols






32. 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






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






34. Sum






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






36. 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






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






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






39. Remainder






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






41. 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.






42. 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






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






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






45. 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.






46. 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






47. Total






48. 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.






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






50. Number T increased by 9