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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 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.






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






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






4. Letters from the beginning of the alphabet like a - b - c... often denote






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






6. A + b = b + a






7. If a < b and c < 0






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






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






10. The squaring operation only produces






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. 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.






13. May not be defined for every possible value.






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






15. 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.






16. Is algebraic equation of degree one






17. Can be added and subtracted.






18. An operation of arity k is called a






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






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






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






22. (a






23. If a < b and c < d






24. A






25. Is an equation involving integrals.






26. Can be defined axiomatically up to an isomorphism






27. 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






28. Is an equation involving derivatives.






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






30. k-ary operation is a






31. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.






32. Are called the domains of the operation






33. The inner product operation on two vectors produces a






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






35. A unary operation






36. Is Written as a






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






38. Is called the type or arity of the operation






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






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






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






42. Applies abstract algebra to the problems of geometry






43. Division ( / )






44. 1 - which preserves numbers: a^1 = a






45. 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






46. 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.






47. 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






48. 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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49. If a < b and b < c






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







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