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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 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.






2. 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.






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






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






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






6. 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.






7. Division ( / )






8. Can be added and subtracted.






9. 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






10. 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






11. Is called the type or arity of the operation






12. The squaring operation only produces






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






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






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






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






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






18. Operations can have fewer or more than






19. A unary operation






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






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






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






23. 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.






24. Applies abstract algebra to the problems of geometry






25. (a






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






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






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






29. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






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






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






33. 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)






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






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






36. 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






37. Is Written as ab or a^b






38. k-ary operation is a






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






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






41. If a < b and c < 0






42. Is called the codomain of the operation






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






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






45. If a = b then b = a






46. 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).






47. If a < b and c < d






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






49. 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'.






50. Is algebraic equation of degree one