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






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






3. If a < b and c > 0






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






5. If a < b and c < 0






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






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






8. Is Written as a + b






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






10. Is called the type or arity of the operation






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






12. May not be defined for every possible value.






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






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






15. Is algebraic equation of degree one






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






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






18. 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






19. 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)






20. There are two common types of operations:






21. A






22. 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.






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






25. If a = b then b = a






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






27. Logarithm (Log)






28. 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.






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






30. 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).






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






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






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






34. 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






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






36. Is an equation where the unknowns are required to be integers.






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






38. 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.






39. Are denoted by letters at the beginning - a - b - c - d - ...






40. Can be defined axiomatically up to an isomorphism






41. 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






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






43. Not commutative a^b?b^a






44. A unary operation






45. 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






46. The inner product operation on two vectors produces a






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






48. The process of expressing the unknowns in terms of the knowns is called






49. 1 - which preserves numbers: a






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