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






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






3. An operation of arity zero is simply an element of the codomain Y - called a






4. A unary operation






5. The value produced is called






6. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in






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






8. Division ( / )






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.

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






12. Can be added and subtracted.






13. There are two common types of operations:






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






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






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






17. k-ary operation is a






18. The values combined are called






19. If a < b and c < d






20. 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.






21. 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)






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






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






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






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






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






27. 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.






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






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






30. b = b






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






32. An operation of arity k is called a






33. A + b = b + a






34. In an equation with a single unknown - a value of that unknown for which the equation is true is called






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. Subtraction ( - )






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






38. 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)






39. 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






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






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






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






43. 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.






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






45. The operation of multiplication means _______________: a






46. 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






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






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






49. (a






50. May not be defined for every possible value.