# CLEP College Algebra: Algebra Principles

Subjects : clep, math, algebra
Instructions:
• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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 mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).

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

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

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

5. Logarithm (Log)

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

7. 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

8. 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

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

10. Is an equation involving integrals.

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

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

14. Is called the codomain of the operation

15. Is Written as ab or a^b

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

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

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

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. 1 - which preserves numbers: a

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

22. 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)

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

24. If a < b and c < d

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

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

27. Operations can have fewer or more than

28. 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.

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

30. 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)

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

33. The operation of multiplication means _______________: a

34. Include composition and convolution

35. Is Written as a

36. A

37. Applies abstract algebra to the problems of geometry

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

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

40. 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.

41. There are two common types of operations:

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

43. 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.

44. May not be defined for every possible value.

45. The values combined are called

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

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

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. If a = b then b = a

50. If a < b and b < c