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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. 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






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






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






4. Can be defined axiomatically up to an isomorphism






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






6. 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.






7. Is called the type or arity of the operation






8. 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






9. 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'.






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






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 an algebraic 'sentence' containing an unknown quantity.






13. Subtraction ( - )






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






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






16. Is Written as a + b






17. The squaring operation only produces






18. Is Written as ab or a^b






19. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an






20. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






21. May not be defined for every possible value.






22. 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






23. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






24. A + b = b + a






25. There are two common types of operations:






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






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






28. Is an equation involving derivatives.






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






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






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






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






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






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






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






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






37. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its






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






39. Is an action or procedure which produces a new value from one or more input values.






40. Division ( / )






41. The values of the variables which make the equation true are the solutions of the equation and can be found through






42. Not associative






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






44. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of






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






46. Are denoted by letters at the beginning - a - b - c - d - ...






47. 1 - which preserves numbers: a^1 = a






48. 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.






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






50. Is an equation in which the unknowns are functions rather than simple quantities.