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






2. Applies abstract algebra to the problems of geometry






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






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






5. Is algebraic equation of degree one






6. A binary operation






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






8. Is called the codomain of the operation






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






10. Not associative






11. 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).






12. There are two common types of operations:






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






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






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






16. Is called the type or arity of the operation






17. The inner product operation on two vectors produces a






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






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






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






21. 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'.






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






23. 0 - which preserves numbers: a + 0 = a






24. 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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25. 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






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






27. The value produced is called






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






29. Is an equation of the form log`a^X = b for a > 0 - which has solution






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






31. 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.






32. 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.






33. 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






34. A unary operation






35. The squaring operation only produces






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






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






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






39. 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.






40. 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)






41. 1 - which preserves numbers: a






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






43. Is Written as a






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






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






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






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






48. May not be defined for every possible value.






49. Operations can have fewer or more than






50. Are called the domains of the operation