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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. In an equation with a single unknown - a value of that unknown for which the equation is true is called






2. 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)






3. 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






4. Can be defined axiomatically up to an isomorphism






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






6. Is an equation involving a transcendental function of one of its variables.






7. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.






8. An operation of arity k is called a






9. Division ( / )






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






11. 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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12. Is Written as a






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






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






15. Is Written as a + b






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






17. Can be combined using logic operations - such as and - or - and not.






18. Referring to the finite number of arguments (the value k)






19. May not be defined for every possible value.






20. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the






21. Is an equation involving derivatives.






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






23. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po






24. Is an equation where the unknowns are required to be integers.






25. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






26. (a + b) + c = a + (b + c)






27. 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.






28. Not associative






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






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






31. Is an equation of the form log`a^X = b for a > 0 - which has solution






32. The inner product operation on two vectors produces a






33. Involve only one value - such as negation and trigonometric functions.






34. If a = b and b = c then a = c






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






36. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)






37. 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.






38. There are two common types of operations:






39. A binary operation






40. Is called the type or arity of the operation






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






42. Letters from the beginning of the alphabet like a - b - c... often denote






43. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






44. Is an equation involving integrals.






45. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






46. The process of expressing the unknowns in terms of the knowns is called






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






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






49. 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






50. Not commutative a^b?b^a