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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. If a < b and c < 0






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






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






5. 1 - which preserves numbers: a^1 = a






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






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






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






9. Operations can have fewer or more than






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






11. An operation of arity k is called a






12. 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'.






13. The value produced is called






14. Logarithm (Log)






15. The operation of multiplication means _______________: a






16. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






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






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






19. Is called the type or arity of the operation






20. 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.






21. 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.






22. 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).






23. 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.


24. The values combined are called






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. 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






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






28. 0 - which preserves numbers: a + 0 = a






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






30. 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






31. A






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






33. If a = b then b = a






34. The inner product operation on two vectors produces a






35. A unary operation






36. (a






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






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






39. Can be added and subtracted.






40. 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






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






42. 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






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






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






45. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its






46. Can be defined axiomatically up to an isomorphism






47. 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)






48. Not associative






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






50. 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