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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 an equation involving a transcendental function of one of its variables.

2. 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).

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

4. The inner product operation on two vectors produces a

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

6. The squaring operation only produces

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

8. 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

9. 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).

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

11. 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

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

13. 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.

14. 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

15. Logarithm (Log)

16. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.

17. 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.

18. Is called the codomain of the operation

19. A binary operation

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

21. 0 - which preserves numbers: a + 0 = a

22. 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)

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

24. A + b = b + a

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

26. The operation of multiplication means _______________: a

27. k-ary operation is a

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

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

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

31. Is called the type or arity of the operation

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

33. Subtraction ( - )

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

35. Is algebraic equation of degree one

36. Operations can have fewer or more than

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

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

39. (a

40. 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.

41. 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)

42. Applies abstract algebra to the problems of geometry

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

44. Include composition and convolution

45. The values combined are called

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

47. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s

48. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called

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

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