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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. A unary operation






2. 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






3. 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.






4. Are denoted by letters at the beginning - a - b - c - d - ...






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






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






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






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






9. Is an equation in which the unknowns are functions rather than simple quantities.






10. The inner product operation on two vectors produces a






11. 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.






12. Can be defined axiomatically up to an isomorphism






13. If a < b and c > 0






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






15. The value produced is called






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






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






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






19. Include composition and convolution






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






21. 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






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






23. If a = b then b = a






24. 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).






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






26. If a < b and c < d






27. Applies abstract algebra to the problems of geometry






28. Is the claim that two expressions have the same value and are equal.






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






30. Is called the codomain of the operation






31. The values combined are called






32. May not be defined for every possible value.






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






34. Not commutative a^b?b^a






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






36. A






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






38. 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






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






40. An operation of arity k is called a






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






42. b = b






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






44. 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).






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






46. 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)






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






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






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