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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. The value produced is called






2. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi






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






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






5. 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






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






7. 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)






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






9. Not commutative a^b?b^a






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






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






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






13. Can be defined axiomatically up to an isomorphism






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






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






16. If a < b and b < c






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






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






19. 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).






20. The values combined are called






21. 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).






22. In which abstract algebraic methods are used to study combinatorial questions.






23. Is Written as a






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






25. 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






26. 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






27. If a = b then b = a






28. Applies abstract algebra to the problems of geometry






29. If a < b and c > 0






30. 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.






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






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






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






34. 1 - which preserves numbers: a^1 = a






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






36. The inner product operation on two vectors produces a






37. 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'.






38. 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.






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






40. Is Written as a + b






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






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






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






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






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






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






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






48. If a < b and c < 0






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






50. 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