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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. Not associative

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

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

4. 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

5. 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.

6. Logarithm (Log)

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

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

9. 1 - which preserves numbers: a

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

11. If a < b and b < c

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

13. Operations can have fewer or more than

14. The value produced is called

15. If a < b and c < 0

16. 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).

17. Include composition and convolution

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

19. 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).

20. The values combined are called

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

22. An operation of arity k is called a

23. 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)

24. A

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

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

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

28. Is the claim that two expressions have the same value and are equal.

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

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

31. The inner product operation on two vectors produces a

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

33. 1 - which preserves numbers: a^1 = a

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

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

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

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

38. 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.

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

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

41. Not commutative a^b?b^a

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

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

44. (a

45. Division ( / )

46. k-ary operation is a

47. The operation of multiplication means _______________: a

48. 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.

49. Are called the domains of the operation

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