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






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






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






5. 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)






6. 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).






7. Is Written as ab or a^b






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






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






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






11. The inner product operation on two vectors produces a






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






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






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






15. A unary operation






16. A binary operation






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






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






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






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






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






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






23. 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).






24. If a < b and c > 0






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






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






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






28. (a






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






30. 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.






31. 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






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






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






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






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






36. 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






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






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






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






40. Can be added and subtracted.






41. b = b






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






43. If a < b and c < 0






44. 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.






45. A + b = b + a






46. 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






47. Not associative






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






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






50. 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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