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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. b = b






2. 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).






3. 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.






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






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






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






7. 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.






8. 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.






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






10. Is called the codomain of the operation






11. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of






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






13. Is an equation of the form aX = b for a > 0 - which has solution






14. Not commutative a^b?b^a






15. 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.






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






17. If a < b and c < d






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






19. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).






20. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






21. 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.






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






23. Can be defined axiomatically up to an isomorphism






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






25. Include composition and convolution






26. Is Written as ab or a^b






27. If a < b and c > 0






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






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






30. Is Written as a + b






31. 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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32. 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






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






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






35. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.






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






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






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






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






40. Is algebraic equation of degree one






41. () 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.






42. A






43. The operation of multiplication means _______________: a






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






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






46. Division ( / )






47. 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






48. Is an equation involving integrals.






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






50. Operations can have fewer or more than