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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 Written as ab or a^b






2. 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






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






4. A binary operation






5. 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'.






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






7. Is called the codomain of the operation






8. Involve only one value - such as negation and trigonometric functions.






9. 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






10. Subtraction ( - )






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






12. 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.






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






14. 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






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






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






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






18. Include composition and convolution






19. 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






20. There are two common types of operations:






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






22. May not be defined for every possible value.






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






24. 0 - which preserves numbers: a + 0 = a






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






26. Can be added and subtracted.






27. Is an equation involving integrals.






28. Not commutative a^b?b^a






29. Is algebraic equation of degree one






30. If a < b and c < d






31. 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).






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






33. The inner product operation on two vectors produces a






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






35. 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)






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






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






38. If a < b and c < 0






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






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






41. Is an equation involving derivatives.






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






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






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






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






46. Is called the type or arity of the operation






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






48. 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.






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






50. An operation of arity k is called a