## Test your basic knowledge |

# CLEP College Algebra: Algebra Principles

**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**

**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.**