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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. 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.






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






3. 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.






4. If a < b and c > 0






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






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






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






8. 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.






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






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






11. 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






12. 1 - which preserves numbers: a^1 = a






13. 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






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






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






16. Can be added and subtracted.






17. If a = b then b = a






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






19. The inner product operation on two vectors produces a






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






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






22. (a






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






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






25. Is called the codomain of the operation






26. A






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






28. Subtraction ( - )






29. Logarithm (Log)






30. Are called the domains of the operation






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






32. 1 - which preserves numbers: a






33. Is an equation involving integrals.






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






35. 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)






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






37. Is Written as a + b






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






39. 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)






40. An operation of arity k is called a






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






42. The value produced is called






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






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






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






46. The operation of multiplication means _______________: a






47. A unary operation






48. The values combined are called






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






50. 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).