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






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






3. A






4. 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






5. Is Written as ab or a^b






6. Is Written as a + b






7. Is called the codomain of the operation






8. The inner product operation on two vectors produces a






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






10. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).






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






12. 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






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






14. Is Written as a






15. 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






16. If a < b and c < d






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






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






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






20. Operations can have fewer or more than






21. 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).






22. Include composition and convolution






23. Subtraction ( - )






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






25. Division ( / )






26. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






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






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






29. May not be defined for every possible value.






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






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






32. A binary operation






33. A unary operation






34. () 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.






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






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






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






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






39. 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.






40. 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.






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






42. 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.






43. 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'.






44. Is an equation involving integrals.






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






46. There are two common types of operations:






47. 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)






48. The operation of multiplication means _______________: a






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






50. Applies abstract algebra to the problems of geometry