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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 an algebraic 'sentence' containing an unknown quantity.






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






3. The inner product operation on two vectors produces a






4. 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.






5. () 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.






6. Not associative






7. Are called the domains of the operation






8. Is Written as a + b






9. 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






10. Not commutative a^b?b^a






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






12. Is called the codomain of the operation






13. 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.






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






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






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






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






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






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






20. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






21. 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)






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






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






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






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






26. Subtraction ( - )






27. A unary operation






28. Is Written as a






29. If a < b and c < d






30. (a






31. In which properties common to all algebraic structures are studied






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






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






34. 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






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






36. 0 - which preserves numbers: a + 0 = a






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






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






39. Include composition and convolution






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






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






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






43. 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)






44. Can be defined axiomatically up to an isomorphism






45. Can be added and subtracted.






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






47. 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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48. May not be defined for every possible value.






49. If a = b then b = a






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