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






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






3. 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






4. Is called the type or arity of the operation






5. A vector can be multiplied by a scalar to form another vector






6. If a < b and c > 0






7. Not associative






8. Is Written as a






9. Is called the codomain of the operation






10. Is an equation in which the unknowns are functions rather than simple quantities.






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






12. 0 - which preserves numbers: a + 0 = a






13. Are called the domains of the operation






14. Include composition and convolution






15. 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).






16. If a < b and c < d






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






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






19. 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)






20. May not be defined for every possible value.






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






22. (a






23. The squaring operation only produces






24. 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.






25. 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)






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






27. Logarithm (Log)






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






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






30. 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






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






32. Is Written as a + b






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






34. 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.






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






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






37. Is an equation in which a polynomial is set equal to another polynomial.






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






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






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






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






42. The inner product operation on two vectors produces a






43. 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






44. Division ( / )






45. Can be defined axiomatically up to an isomorphism






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






47. In which the specific properties of vector spaces are studied (including matrices)






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






50. Applies abstract algebra to the problems of geometry