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






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






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






4. 0 - which preserves numbers: a + 0 = a






5. A unary operation






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






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






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






9. (a






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






11. Is Written as a + b






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






13. 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.






14. 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'.






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






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






17. 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






18. 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.






19. 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






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






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






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






23. 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).






24. 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






25. Is algebraic equation of degree one






26. Division ( / )






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






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






29. 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).






30. The inner product operation on two vectors produces a






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






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






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






34. If a < b and b < c






35. May not be defined for every possible value.






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






37. 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.






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






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






40. 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.






41. () 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.






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






43. A






44. If a < b and c > 0






45. 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






46. Applies abstract algebra to the problems of geometry






47. Is an equation involving derivatives.






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






49. A binary operation






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







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