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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. (a

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

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

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

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

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

7. b = b

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

9. The inner product operation on two vectors produces a

10. May not be defined for every possible value.

11. If a < b and b < c

12. The values combined are called

13. If a < b and c < 0

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

15. Is an equation in which a polynomial is set equal to another polynomial.

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

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

18. Applies abstract algebra to the problems of geometry

19. Operations can have fewer or more than

20. Is Written as a + b

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

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

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

24. Division ( / )

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

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

27. 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.

28. 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)

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

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

31. 1 - which preserves numbers: a

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

33. 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

34. k-ary operation is a

35. Is Written as ab or a^b

36. The value produced is called

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

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

39. Is an equation involving integrals.

40. Can be combined using logic operations - such as and - or - and not.

41. Are called the domains of the operation

42. 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.

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

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

45. 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.

46. 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

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

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

49. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in

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