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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 of the form aX = b for a > 0 - which has solution






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






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






4. An operation of arity k is called a






5. Logarithm (Log)






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






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






8. If a = b then b = a






9. May not be defined for every possible value.






10. () 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.






11. 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






12. A binary operation






13. 0 - which preserves numbers: a + 0 = a






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






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






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






17. If a < b and b < c






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






19. Applies abstract algebra to the problems of geometry






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






21. Is an equation involving integrals.






22. 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.






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






24. 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






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






26. A unary operation






27. 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






28. Can be added and subtracted.






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






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






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






32. 1 - which preserves numbers: a^1 = a






33. Are called the domains of the operation






34. 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)






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






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






37. Operations can have fewer or more than






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






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






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






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






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






43. 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)






44. A + b = b + a






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






46. 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'.






47. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po






48. A






49. (a






50. Is Written as a + b