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






2. k-ary operation is a






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






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






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






6. Is Written as a






7. The process of expressing the unknowns in terms of the knowns is called






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






9. Logarithm (Log)






10. Letters from the beginning of the alphabet like a - b - c... often denote






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






12. Operations can have fewer or more than






13. Can be added and subtracted.






14. 0 - which preserves numbers: a + 0 = a






15. Is Written as ab or a^b






16. Not commutative a^b?b^a






17. 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.






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






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






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






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






22. There are two common types of operations:






23. 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)






24. If a < b and c < d






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






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






27. Applies abstract algebra to the problems of geometry






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






29. May not be defined for every possible value.






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






31. Is called the type or arity of the operation






32. The value produced is called






33. 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.






34. The inner product operation on two vectors produces a






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






36. 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).






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






38. 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






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






40. Not associative






41. 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






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






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






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






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






46. Include composition and convolution






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






48. 1 - which preserves numbers: a^1 = a






49. 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)






50. The values combined are called