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






2. 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)






3. Is an equation of the form aX = b for a > 0 - which has solution






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






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






6. Subtraction ( - )






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






8. Not commutative a^b?b^a






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






10. Is called the codomain of the operation






11. Include composition and convolution






12. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






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






14. 1 - which preserves numbers: a






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






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






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






18. If a < b and c < 0






19. The value produced is called






20. 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.






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






22. 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






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






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






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






26. Is Written as a






27. There are two common types of operations:






28. Applies abstract algebra to the problems of geometry






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






30. If it holds for all a and b in X that if a is related to b then b is related to a.






31. The squaring operation only produces






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






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






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






35. Logarithm (Log)






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






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






38. 1 - which preserves numbers: a^1 = a






39. If a = b then b = a






40. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.






41. 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).






42. 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






43. k-ary operation is a






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 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'.






46. Is algebraic equation of degree one






47. 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






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






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






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