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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 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.






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






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






4. If a < b and c < 0






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






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






7. The inner product operation on two vectors produces a






8. The squaring operation only produces






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






10. If a < b and c < d






11. A binary operation






12. 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






13. The operation of multiplication means _______________: a






14. Not associative






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






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






18. 1 - which preserves numbers: a^1 = a






19. Not commutative a^b?b^a






20. A + b = b + a






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






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






23. Can be added and subtracted.






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






25. 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).






26. Is an equation involving integrals.






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






28. 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)






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






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






31. There are two common types of operations:






32. Is called the codomain of the operation






33. 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.






34. 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.






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






36. (a






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






38. Logarithm (Log)






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






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






41. 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






42. Can be defined axiomatically up to an isomorphism






43. 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






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






45. May not be defined for every possible value.






46. Applies abstract algebra to the problems of geometry






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






48. The values combined are called






49. () 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.






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