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

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

3. 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

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

5. Are called the domains of the operation

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

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

8. If it holds for all a and b in X that if a is related to b then b is related to a.

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

10. Subtraction ( - )

11. Applies abstract algebra to the problems of geometry

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

13. The values combined are called

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

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

16. Not associative

17. The squaring operation only produces

18. There are two common types of operations:

19. Operations can have fewer or more than

20. If a = b then b = a

21. Is called the type or arity of the operation

22. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.

23. Can be added and subtracted.

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

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

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

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

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

29. (a

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

31. Is algebraic equation of degree one

32. Include composition and convolution

33. If a < b and c < 0

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

35. 0 - which preserves numbers: a + 0 = a

36. b = b

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

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

39. 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.

40. An operation of arity k is called a

41. 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.

42. The value produced is called

43. 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

44. 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)

45. If a < b and b < c

46. 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).

47. Not commutative a^b?b^a

48. 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

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

50. 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)