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






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






3. Is Written as a






4. Can be defined axiomatically up to an isomorphism






5. b = b






6. The operation of multiplication means _______________: a






7. A unary operation






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






9. 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.






10. If a < b and c > 0






11. 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






12. If a = b then b = a






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






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






15. Subtraction ( - )






16. Not associative






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






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






19. 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






20. Can be added and subtracted.






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






22. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)






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






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






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






26. () 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.






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






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






29. Division ( / )






30. Is Written as a + b






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






32. 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)






33. 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.






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






35. 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.






36. The values combined are called






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






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






39. If a < b and b < c






40. The value produced is called






41. 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'.






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






43. Not commutative a^b?b^a






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






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






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






47. The inner product operation on two vectors produces a






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






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






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