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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. The operation of exponentiation means ________________: a^n = a






2. 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.






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






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






6. 1 - which preserves numbers: a






7. If a < b and c < 0






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






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






10. Not commutative a^b?b^a






11. If a < b and b < c






12. Applies abstract algebra to the problems of geometry






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






14. (a






15. The inner product operation on two vectors produces a






16. The squaring operation only produces






17. The values combined are called






18. 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






19. 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)






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






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






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






23. Is called the type or arity of the operation






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






25. A + b = b + a






26. 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)






27. 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.






28. Is called the codomain of the operation






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






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






31. The value produced is called






32. 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






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






34. A unary operation






35. Can be added and subtracted.






36. The operation of multiplication means _______________: a






37. Will have two solutions in the complex number system - but need not have any in the real number system.






38. Include composition and convolution






39. 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.






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






41. An operation of arity k is called a






42. Is algebraic equation of degree one






43. 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).






44. Is Written as a + b






45. 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






46. 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)






47. 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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48. 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).






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






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