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






2. In which the specific properties of vector spaces are studied (including matrices)






3. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called






4. Can be added and subtracted.






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






6. 1 - which preserves numbers: a^1 = a






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






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






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






10. 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'.






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






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






13. 1 - which preserves numbers: a






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






16. If a = b then b = a






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






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






19. Subtraction ( - )






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






21. Is Written as ab or a^b






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






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






24. Is an equation involving integrals.






25. Not associative






26. Is called the type or arity of the operation






27. 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.






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






29. 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.






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






31. Is algebraic equation of degree one






32. 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






33. 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






34. 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).






35. () 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.






36. Are called the domains of the operation






37. If a < b and c < d






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






39. Not commutative a^b?b^a






40. 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






41. There are two common types of operations:






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






43. Is Written as a






44. A






45. Is an equation involving derivatives.






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






47. If a < b and c < 0






48. Means repeated addition of ones: a + n = a + 1 + 1 +...+ 1 (n number of times) - has an inverse operation called subtraction: (a + b) - b = a - which is the same as adding a negative number - a - b = a + (-b)






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






50. 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)