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






2. 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






3. Is an equation involving integrals.






4. An operation of arity k is called a






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






6. 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'.






7. A unary operation






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






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. Can be defined axiomatically up to an isomorphism






12. The squaring operation only produces






13. 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.






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






15. 1 - which preserves numbers: a






16. Is an equation involving derivatives.






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






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






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






20. Is an action or procedure which produces a new value from one or more input values.






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






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






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






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






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






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






27. In which the specific properties of vector spaces are studied (including matrices)






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






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






30. 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).






31. Can be added and subtracted.






32. Is Written as ab or a^b






33. 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






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






35. 0 - which preserves numbers: a + 0 = a






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






37. 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)






38. Division ( / )






39. Operations can have fewer or more than






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






41. Not commutative a^b?b^a






42. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






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






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






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






46. Subtraction ( - )






47. Is algebraic equation of degree one






48. 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.






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






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