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






2. 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






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






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






5. k-ary operation is a






6. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.






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






8. 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'.






9. If a < b and c < d






10. If a < b and c > 0






11. Not associative






12. A binary operation






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






14. 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






15. The inner product operation on two vectors produces a






16. 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






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






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






19. b = b






20. If a = b then b = a






21. If a < b and c < 0






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






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






24. 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






25. A unary operation






26. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






27. (a






28. 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.






29. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






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






31. Is algebraic equation of degree one






32. Applies abstract algebra to the problems of geometry






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






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






35. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






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






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






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






39. 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).






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






41. Is an equation involving derivatives.






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






43. A






44. Operations can have fewer or more than






45. 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.






46. Not commutative a^b?b^a






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






48. 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)






49. 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.






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







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