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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 a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.






2. Is Written as a






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






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






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






6. 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).






7. If a < b and b < c






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






9. Division ( / )






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






12. 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.






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






14. Not associative






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






16. 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






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






18. Can be combined using logic operations - such as and - or - and not.






19. Subtraction ( - )






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






21. 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)






22. Logarithm (Log)






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






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






25. 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).






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






27. The squaring operation only produces






28. () 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.






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






30. Is Written as a + b






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






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






33. 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






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






35. k-ary operation is a






36. 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.






37. 1 - which preserves numbers: a






38. Are called the domains of the operation






39. 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






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






41. The operation of multiplication means _______________: a






42. 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






43. A unary operation






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






45. The values combined are called






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






47. Is called the type or arity of the operation






48. Include composition and convolution






49. The inner product operation on two vectors produces a






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