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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. Are called the domains of the operation






2. If a = b then b = a






3. A binary operation






4. Symbols that denote numbers - is to allow the making of generalizations in mathematics






5. 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.






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






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






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






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






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






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






13. Is an equation involving derivatives.






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






15. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).






16. 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'.






17. Is Written as ab or a^b






18. Operations can have fewer or more than






19. 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).






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






21. 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)






22. Division ( / )






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






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






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






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






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






28. Not commutative a^b?b^a






29. 1 - which preserves numbers: a






30. Is an equation involving a transcendental function of one of its variables.






31. 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.






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






33. There are two common types of operations:






34. If a < b and c < d






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






36. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its






37. 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.






38. A unary operation






39. May not be defined for every possible value.






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






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. () 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.






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






44. Is Written as a + b






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






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






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






48. The value produced is called






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






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