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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. Is an equation in which the unknowns are functions rather than simple quantities.






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






3. 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






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






5. 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)






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






7. If a < b and b < c






8. Not associative






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






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






11. The squaring operation only produces






12. May not be defined for every possible value.






13. The values combined are called






14. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






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






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






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. 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.






19. Are called the domains of the operation






20. Logarithm (Log)






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






22. 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






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 Written as a






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






26. Is an equation involving integrals.






27. 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)






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






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






30. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






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






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






33. The inner product operation on two vectors produces a






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






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






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






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






38. Subtraction ( - )






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






40. 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






41. A binary operation






42. 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






43. 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.

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44. Can be added and subtracted.






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






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






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






48. If a < b and c < 0






49. 1 - which preserves numbers: a^1 = a






50. 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.