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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. 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)






2. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.






3. Is an equation involving derivatives.






4. 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






5. The value produced is called






6. In which abstract algebraic methods are used to study combinatorial questions.






7. Operations can have fewer or more than






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






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






10. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






11. 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'.






12. If a < b and c > 0






13. 1 - which preserves numbers: a






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






15. A






16. 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






17. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics






18. b = b






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






20. Can be combined using the function composition operation - performing the first rotation and then the second.






21. The inner product operation on two vectors produces a






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






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






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






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






26. If a < b and c < d






27. Is Written as a + b






28. May not be defined for every possible value.






29. Is Written as a






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






31. The operation of exponentiation means ________________: a^n = a






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






33. The values for which an operation is defined form a set called its






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






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






36. Is algebraic equation of degree one






37. If a < b and b < c






38. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.






39. Is an equation involving integrals.






40. Is the claim that two expressions have the same value and are equal.






41. Include the binary operations union and intersection and the unary operation of complementation.






42. The codomain is the set of real numbers but the range is the






43. Not associative






44. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:






45. 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.






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






47. Division ( / )






48. Subtraction ( - )






49. Not commutative a^b?b^a






50. A binary operation