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CLEP College Algebra: Algebra Principles

Subjects : clep, math, algebra
  • Answer 50 questions in 15 minutes.
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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. The values combined are called

2. 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

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

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

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

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

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

8. If a < b and c < 0

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

10. 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'.

11. Is called the codomain of the operation

12. 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.

13. 1 - which preserves numbers: a

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

15. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that

16. If a < b and c > 0

17. If a = b then b = a

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

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

20. The inner product operation on two vectors produces a

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

22. In an equation with a single unknown - a value of that unknown for which the equation is true is called

23. Is algebraic equation of degree one

24. Are called the domains of the operation

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

26. Is Written as ab or a^b

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

28. An operation of arity k is called a

29. If a < b and c < d

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

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

32. Subtraction ( - )

33. The squaring operation only produces

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

35. Can be added and subtracted.

36. 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.

37. Applies abstract algebra to the problems of geometry

38. A + b = b + a

39. A unary operation

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

41. 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)

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

43. There are two common types of operations:

44. b = b

45. 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.

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

47. () 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.

48. (a

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

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