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






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






3. If a < b and c < d






4. If a < b and c > 0






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






6. 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






7. 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)






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






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






10. Include composition and convolution






11. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






12. If a < b and c < 0






13. Is algebraic equation of degree one






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






15. 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






16. May not be defined for every possible value.






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






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






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






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






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






22. 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.






23. Division ( / )






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






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






26. Is an equation involving integrals.






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






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






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






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






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






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






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






34. Is Written as a + b






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






36. k-ary operation is a






37. 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.






38. If a < b and b < c






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






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






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






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






43. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






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






45. 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






46. The squaring operation only produces






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






48. An operation of arity k is called a






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






50. 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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