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






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






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






4. 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)






5. 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).






6. If a < b and b < c






7. Is Written as a






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






9. The squaring operation only produces






10. The values of the variables which make the equation true are the solutions of the equation and can be found through






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






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. The values for which an operation is defined form a set called its






14. Is an equation involving derivatives.






15. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s






16. The operation of multiplication means _______________: a






17. 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).






18. Not associative






19. 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






20. 0 - which preserves numbers: a + 0 = a






21. 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)






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






23. 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.






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






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






26. The values combined are called






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






28. k-ary operation is a






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






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






31. Include composition and convolution






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






33. 1 - which preserves numbers: a






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






35. 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.






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






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






38. If a < b and c < d






39. If a < b and c > 0






40. Subtraction ( - )






41. A






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






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






44. A + b = b + a






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






46. Is the claim that two expressions have the same value and are equal.






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






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






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






50. Not commutative a^b?b^a