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






2. Applies abstract algebra to the problems of geometry






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






4. (a






5. 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.






6. 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






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






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






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






10. Can be added and subtracted.






11. 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).






12. A unary operation






13. 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.






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






15. 1 - which preserves numbers: a^1 = a






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






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






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






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






20. The process of expressing the unknowns in terms of the knowns is called






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






22. An operation of arity k is called a






23. Can be defined axiomatically up to an isomorphism






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






25. 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).






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






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






28. Is algebraic equation of degree one






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






30. A binary operation






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






32. The operation of multiplication means _______________: a






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






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






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






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






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






38. 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'.






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






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






41. Division ( / )






42. 0 - which preserves numbers: a + 0 = a






43. 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.






44. Are called the domains of the operation






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






46. 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






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






48. The values combined are called






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






50. If a = b then b = a







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