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






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






4. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






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






6. 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).






7. Not associative






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






9. 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)






10. 1 - which preserves numbers: a






11. 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






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






13. Is called the codomain of the operation






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






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






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






17. Subtraction ( - )






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






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






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






21. Not commutative a^b?b^a






22. (a






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. 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)






25. Are called the domains of the operation






26. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.






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






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






29. A unary operation






30. The values combined are called






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






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






33. Is an equation where the unknowns are required to be integers.






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






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






36. A






37. 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'.






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






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






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






41. 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






42. If a < b and c < 0






43. 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






44. (a + b) + c = a + (b + c)






45. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym






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






47. 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






48. The squaring operation only produces






49. Is Written as a + b






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