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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. 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.






2. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the






3. (a






4. May not be defined for every possible value.






5. k-ary operation is a






6. Is algebraic equation of degree one






7. The values for which an operation is defined form a set called its






8. Is Written as a + b






9. Include composition and convolution






10. Operations can have fewer or more than






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






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






13. 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






14. 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






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






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






17. Not associative






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






19. () 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.






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






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






22. A






23. The inner product operation on two vectors produces a






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






25. 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.






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






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






28. b = b






29. The squaring operation only produces






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






31. Is called the codomain of the operation






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






33. The codomain is the set of real numbers but the range is the






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






35. 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'.






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






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






38. A binary operation






39. Is an equation involving derivatives.






40. A + b = b + a






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






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






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






44. 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.






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






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






47. 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.






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. 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






50. 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)