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

2. 1 - which preserves numbers: a^1 = a

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

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

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

6. 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

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

8. Is Written as ab or a^b

9. 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)

10. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.

11. The value produced is called

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. 1 - which preserves numbers: a

14. In an equation with a single unknown - a value of that unknown for which the equation is true is called

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

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

17. 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.

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

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

20. k-ary operation is a

21. 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).

22. 0 - which preserves numbers: a + 0 = a

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

24. Operations can have fewer or more than

25. Is algebraic equation of degree one

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

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

28. Can be added and subtracted.

29. Include composition and convolution

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

31. 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).

32. Division ( / )

33. There are two common types of operations:

34. If a < b and c < d

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

36. Letters from the beginning of the alphabet like a - b - c... often denote

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

38. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an

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

40. If a < b and c < 0

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

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

43. (a

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

45. 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)

46. A binary operation

47. A unary operation

48. 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.

49. 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

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)