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






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






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






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






5. The squaring operation only produces






6. Is an equation involving integrals.






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






8. Is algebraic equation of degree one






9. If a = b then b = a






10. b = b






11. 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'.






12. Subtraction ( - )






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






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






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






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






17. Logarithm (Log)






18. Not associative






19. 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






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






21. May not be defined for every possible value.






22. 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.






23. Include composition and convolution






24. There are two common types of operations:






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






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






27. If a < b and c < d






28. The operation of exponentiation means ________________: a^n = 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 a function of the form ? : V ? Y - where V ? X1






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






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






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






34. A unary operation






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






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






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






38. Can be defined axiomatically up to an isomorphism






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






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






41. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.






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






43. 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






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






45. 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)






46. Is Written as a






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






48. Not commutative a^b?b^a






49. A






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