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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. 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






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






3. 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.






4. Not associative






5. Subtraction ( - )






6. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics






7. Applies abstract algebra to the problems of geometry






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






9. If a < b and c < d






10. Is Written as a






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






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






13. Division ( / )






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






15. 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






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






17. 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'.






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






19. The squaring operation only produces






20. 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.






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






22. A






23. 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






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






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






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






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






28. 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).






29. There are two common types of operations:






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






31. The operation of exponentiation means ________________: a^n = a






32. 1 - which preserves numbers: a






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






34. 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)






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






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






37. A unary operation






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






39. Logarithm (Log)






40. 0 - which preserves numbers: a + 0 = a






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






42. Operations can have fewer or more than






43. If a = b then b = a






44. Include composition and convolution






45. b = b






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






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






48. () 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.






49. The value produced is called






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