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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 called the domains of the operation






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






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






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






5. May not be defined for every possible value.






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






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






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






9. 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






10. 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.






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






12. k-ary operation is a






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






14. If a < b and c < 0






15. In which properties common to all algebraic structures are studied






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






17. If a < b and c < d






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






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






20. Can be defined axiomatically up to an isomorphism






21. () 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.






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






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






24. Division ( / )






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






26. 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.






27. 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'.






28. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






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






30. 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)






31. 0 - which preserves numbers: a + 0 = a






32. 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)






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






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






35. Is called the codomain of the operation






36. 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






37. Can be added and subtracted.






38. Not commutative a^b?b^a






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






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






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






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






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






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






45. 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.






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






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






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






49. 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






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