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






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






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






4. The value produced is called






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






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






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






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






9. (a + b) + c = a + (b + c)






10. Is Written as a + b






11. Is an equation involving integrals.






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






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






15. Is an action or procedure which produces a new value from one or more input values.






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






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






18. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called






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






20. k-ary operation is a






21. 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






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






23. Not associative






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






25. Operations can have fewer or more than






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






27. Include composition and convolution






28. Is called the codomain of the operation






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






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






31. A unary operation






32. Can be defined axiomatically up to an isomorphism






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






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. 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






36. 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.






37. If a < b and c > 0






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






39. 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






40. Not commutative a^b?b^a






41. 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)






42. 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'.






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






44. Applies abstract algebra to the problems of geometry






45. 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






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






47. An operation of arity k is called a






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






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






50. Is Written as ab or a^b