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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. k-ary operation is a






2. The inner product operation on two vectors produces a






3. If a < b and c > 0






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






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






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






7. 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.






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






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






10. The squaring operation only produces






11. Can be added and subtracted.






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






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






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






15. 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).






16. If a = b then b = a






17. Subtraction ( - )






18. Is Written as a + b






19. Is called the type or arity of the operation






20. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.






21. The operation of multiplication means _______________: a






22. May not be defined for every possible value.






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






24. 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.






25. A binary operation






26. A + b = b + a






27. 1 - which preserves numbers: a






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






29. 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'.






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






31. A






32. 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






33. In which abstract algebraic methods are used to study combinatorial questions.






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






35. Not commutative a^b?b^a






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






37. 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)






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






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






41. 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






42. 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






43. Applies abstract algebra to the problems of geometry






44. 0 - which preserves numbers: a + 0 = a






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






46. Are called the domains of the operation






47. The value produced is called






48. Is an equation involving derivatives.






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






50. Logarithm (Log)