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






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






3. An operation of arity k is called a






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






5. Is called the type or arity of the operation






6. 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






7. The operation of multiplication means _______________: a






8. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






9. 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.






10. 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






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






12. Is Written as ab or a^b






13. Operations can have fewer or more than






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






15. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.






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






17. May not be defined for every possible value.






18. 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)






19. If a < b and c < d






20. Is called the codomain of the operation






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






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






23. () 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.






24. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






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






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






27. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.






28. Not commutative a^b?b^a






29. If a < b and c < 0






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






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






32. Are called the domains of the operation






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






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






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






36. 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.






37. 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






38. 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).






39. The value produced is called






40. Is Written as a






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






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






43. A






44. Is algebraic equation of degree one






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






46. Is an equation involving integrals.






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. Applies abstract algebra to the problems of geometry






49. Include composition and convolution






50. 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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