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






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






3. There are two common types of operations:






4. 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






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






6. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)






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






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






9. The inner product operation on two vectors produces a






10. 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).






11. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






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






13. Logarithm (Log)






14. 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).






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






16. 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.






17. b = b






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






19. 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)






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






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






22. 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)






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






24. Letters from the beginning of the alphabet like a - b - c... often denote






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






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






27. Can be added and subtracted.






28. 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






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. 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.






31. If a < b and b < c






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






33. The value produced is called






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






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






36. 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.






37. If a < b and c < 0






38. Not associative






39. An operation of arity k is called a






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






41. The values combined are called






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






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






44. (a + b) + c = a + (b + c)






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






46. If a = b then b = a






47. Operations can have fewer or more than






48. Is an equation of the form aX = b for a > 0 - which has solution






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






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