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






2. Applies abstract algebra to the problems of geometry






3. Not commutative a^b?b^a






4. The operation of multiplication means _______________: a






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






6. Can be added and subtracted.






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






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






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






10. A + b = b + a






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






12. May not be defined for every possible value.






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






14. The inner product operation on two vectors produces a






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






16. Are called the domains of the operation






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






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






19. A unary operation






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






21. 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






22. 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.






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






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






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






26. Is Written as ab or a^b






27. 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.






28. A






29. 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






30. 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).






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






32. 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.






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






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






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






36. 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.






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






38. 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)






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






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






41. There are two common types of operations:






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






43. Include composition and convolution






44. Is a function of the form ? : V ? Y - where V ? X1






45. If a < b and c > 0






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






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






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






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






50. 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)