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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. If a < b and b < c






3. 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)






4. 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'.






5. Is called the codomain of the operation






6. If a = b then b = a






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






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






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






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






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






12. The values combined are called






13. A unary operation






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






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






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






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






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






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






20. An operation of arity k is called a






21. Can be defined axiomatically up to an isomorphism






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






23. 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






24. A + b = b + a






25. Is Written as ab or a^b






26. 1 - which preserves numbers: a






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






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






29. Is Written as a






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






31. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






32. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






33. Is called the type or arity of the operation






34. 0 - which preserves numbers: a + 0 = a






35. Is an equation involving derivatives.






36. 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






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






38. 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)






39. Is algebraic equation of degree one






40. Can be added and subtracted.






41. 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.






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






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






44. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left






45. 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.






46. The value produced is called






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






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






49. Applies abstract algebra to the problems of geometry






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