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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. 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






2. 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)






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






4. 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).






5. () 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.






6. If a = b then b = a






7. Can be defined axiomatically up to an isomorphism






8. 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






9. Is an equation involving integrals.






10. A + b = b + a






11. (a






12. The values combined are called






13. Can be added and subtracted.






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






15. 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)






16. 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






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






18. 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).






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






20. A






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






22. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






23. Include composition and convolution






24. 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.






25. Not commutative a^b?b^a






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






27. The inner product operation on two vectors produces a






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






29. Are called the domains of the operation






30. May not be defined for every possible value.






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






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






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






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






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






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






38. 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.






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






40. Is Written as ab or a^b






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






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






43. Is algebraic equation of degree one






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






45. Subtraction ( - )






46. 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






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






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






49. Division ( / )






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