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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. Division ( / )






2. 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.






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






4. Is Written as a






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






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






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






8. 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






9. Is an equation involving derivatives.






10. A






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






12. Is called the type or arity of the operation






13. 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.






14. There are two common types of operations:






15. The value produced is called






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






17. 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.






18. If a < b and c > 0






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






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






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






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






23. 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)






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






25. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






26. The inner product operation on two vectors produces a






27. The squaring operation only produces






28. Is Written as ab or a^b






29. 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.


30. 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'.






31. (a






32. Are called the domains of the operation






33. 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).






34. Is an equation involving integrals.






35. Is an equation of the form X^m/n = a - for m - n integers - which has solution






36. k-ary operation is a






37. A binary operation






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






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






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






41. Not associative






42. A unary operation






43. 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






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






46. 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.






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






48. () 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.






49. Is called the codomain of the operation






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