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






2. The inner product operation on two vectors produces a






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






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






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






6. 1 - which preserves numbers: a






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






8. (a






9. 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)






10. A + b = b + a






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






12. 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






13. 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.






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






15. A






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






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






18. Is Written as a + b






19. An operation of arity zero is simply an element of the codomain Y - called a






20. k-ary operation is a






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






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






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






24. Operations can have fewer or more than






25. If a < b and b < c






26. If a < b and c > 0






27. 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)






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






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






30. 1 - which preserves numbers: a^1 = a






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






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






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






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






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






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






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






38. 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






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






40. 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






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






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






43. An operation of arity k is called a






44. 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






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






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






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






48. 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).






49. Involve only one value - such as negation and trigonometric functions.






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