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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 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).






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






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






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






6. (a






7. Can be defined axiomatically up to an isomorphism






8. 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






9. Subtraction ( - )






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






11. 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.






12. 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






13. Is an equation involving integrals.






14. May not be defined for every possible value.






15. The inner product operation on two vectors produces a






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






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






18. If a < b and c < d






19. An operation of arity k is called a






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






21. Are called the domains of the operation






22. 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






23. 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'.






24. 0 - which preserves numbers: a + 0 = a






25. Is an equation involving derivatives.






26. Division ( / )






27. Is an algebraic 'sentence' containing an unknown quantity.






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






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






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






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






32. If a < b and c > 0






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






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






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






36. 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.






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






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






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






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






41. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.






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






43. Can be added and subtracted.






44. 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






45. The squaring operation only produces






46. () 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.






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






48. Not commutative a^b?b^a






49. Is Written as ab or a^b






50. b = b







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