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CLEP College Algebra: Algebra Principles

Subjects : clep, math, algebra
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).






2. An operation of arity k is called a






3. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






4. If a = b and c = d then a + c = b + d and ac = bd; that if a = b then a + c = b + c; that if two symbols are equal - then one can be substituted for the other.

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5. An operation of arity zero is simply an element of the codomain Y - called a






6. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.






7. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)






8. The operation of multiplication means _______________: a






9. Include composition and convolution






10. Can be added and subtracted.






11. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






12. Symbols that denote numbers - is to allow the making of generalizations in mathematics






13. Are called the domains of the operation






14. Is algebraic equation of degree one






15. Is Written as ab or a^b






16. The inner product operation on two vectors produces a






17. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:






18. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.






19. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






20. May not be defined for every possible value.






21. A vector can be multiplied by a scalar to form another vector






22. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.






23. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).






24. Is an algebraic 'sentence' containing an unknown quantity.






25. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.






26. Is Written as a






27. Will have two solutions in the complex number system - but need not have any in the real number system.






28. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.






29. The values combined are called






30. Is an equation in which a polynomial is set equal to another polynomial.






31. If a < b and b < c






32. Is an equation of the form aX = b for a > 0 - which has solution






33. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.






34. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym






35. Is called the type or arity of the operation






36. Not associative






37. Is called the codomain of the operation






38. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






39. If it holds for all a and b in X that if a is related to b then b is related to a.






40. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi






41. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






42. Operations can have fewer or more than






43. Is an equation of the form X^m/n = a - for m - n integers - which has solution






44. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).






45. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






46. A binary operation






47. Logarithm (Log)






48. Are true for only some values of the involved variables: x2 - 1 = 4.






49. That if a = b and c = d then a + c = b + d and ac = bd;that if a = b then a + c = b + c; that if two symbols are equal - then one can be substituted for the other.






50. Is a function of the form ? : V ? Y - where V ? X1