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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. 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






2. Is an equation involving derivatives.






3. A + b = b + a






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






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






6. 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






7. 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)






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






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






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






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






12. Is Written as ab or a^b






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






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






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






16. Is Written as a






17. 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






18. 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.






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






20. Not commutative a^b?b^a






21. Can be added and subtracted.






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






23. The inner product operation on two vectors produces a






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






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






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






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






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






29. 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






30. Can be defined axiomatically up to an isomorphism






31. If a = b then b = a






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






33. 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






34. 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.






35. If a < b and c > 0






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






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. Include composition and convolution






39. 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.






40. A unary operation






41. The values combined are called






42. The value produced is called






43. 0 - which preserves numbers: a + 0 = a






44. If it holds for all a and b in X that if a is related to b then b is related to a.






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






46. A






47. Is called the type or arity of the operation






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






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






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