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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. A






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






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






4. () 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.






5. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).






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






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






8. 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).






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






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






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






12. Subtraction ( - )






13. Division ( / )






14. An operation of arity k is called a






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






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






17. 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.






18. 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.






19. Is algebraic equation of degree one






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






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






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






23. Not associative






24. 1 - which preserves numbers: a^1 = a






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






26. Operations can have fewer or more than






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






28. 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)






29. Can be added and subtracted.






30. Is Written as a + b






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






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






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






34. Is Written as a






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






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






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






38. (a






39. If a < b and c < d






40. 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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41. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






42. Is called the codomain of the operation






43. The value produced is called






44. A binary operation






45. A unary operation






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






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






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






49. Applies abstract algebra to the problems of geometry






50. 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)







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