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






2. 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.






3. If a < b and b < c






4. Is Written as ab or a^b






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






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






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






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






9. () 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.






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






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






12. 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






13. 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.






14. A binary operation






15. Can be defined axiomatically up to an isomorphism






16. If a < b and c > 0






17. 0 - which preserves numbers: a + 0 = a






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






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






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






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






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






24. Not commutative a^b?b^a






25. 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).






26. Is Written as a + b






27. Is the claim that two expressions have the same value and are equal.






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






29. If a < b and c < d






30. 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






31. Referring to the finite number of arguments (the value k)






32. The values combined are called






33. 1 - which preserves numbers: a^1 = a






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






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






36. 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






37. 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).






38. 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.






39. 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)






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






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






42. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)






43. May not be defined for every possible value.






44. Is called the codomain of the operation






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






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






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






48. Are called the domains of the operation






49. Logarithm (Log)






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