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

2. Operations can have fewer or more than

3. Is Written as a

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

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

6. Division ( / )

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

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

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

10. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the

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

12. If a < b and c < d

13. Is an equation involving integrals.

14. Is called the codomain of the operation

15. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)

16. 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).

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

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

19. 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

20. 1 - which preserves numbers: a^1 = a

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

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

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

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

25. Can be added and subtracted.

26. 0 - which preserves numbers: a + 0 = a

27. 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).

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

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

30. The operation of multiplication means _______________: a

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

32. 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.

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

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

35. A binary operation

36. Applies abstract algebra to the problems of geometry

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

38. 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

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

40. Is called the type or arity of the operation

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

42. The squaring operation only produces

43. An operation of arity k is called a

44. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.

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

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

47. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left

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

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

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