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CLEP College Algebra: Algebra Principles

Subjects : clep, math, algebra
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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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. 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'.

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

4. The operation of multiplication means _______________: a

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

6. Operations can have fewer or more than

7. 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

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

9. Can be defined axiomatically up to an isomorphism

10. An operation of arity k is called a

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

12. A binary operation

13. Not associative

14. Not commutative a^b?b^a

15. May not be defined for every possible value.

16. (a

17. If a < b and c < 0

18. 1 - which preserves numbers: a^1 = a

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

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

21. The inner product operation on two vectors produces a

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

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

24. 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).

25. Is called the codomain of the operation

26. 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)

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

28. Is called the type or arity of the operation

29. 1 - which preserves numbers: a

30. Applies abstract algebra to the problems of geometry

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

32. A + b = b + a

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

34. b = b

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

36. There are two common types of operations:

37. Logarithm (Log)

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

39. k-ary operation is a

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

41. 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.

42. Can be added and subtracted.

43. Can be combined using the function composition operation - performing the first rotation and then the second.

44. If a = b then b = a

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

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

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

48. In which properties common to all algebraic structures are studied

49. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym

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