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

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

**3. Is Written as a**

**4. Can be defined axiomatically up to an isomorphism**

**5. b = b**

**6. The operation of multiplication means _______________: a**

**7. A unary operation**

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

**9. 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.**

**10. If a < b and c > 0**

**11. 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**

**12. If a = b then b = a**

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

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

**15. Subtraction ( - )**

**16. Not associative**

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

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

**19. 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**

**20. Can be added and subtracted.**

**21. Involve only one value - such as negation and trigonometric functions.**

**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. A vector can be multiplied by a scalar to form another vector**

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

**25. The codomain is the set of real numbers but the range is the**

**26. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.**

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

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

**29. Division ( / )**

**30. Is Written as a + b**

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

**32. 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)**

**33. 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.**

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

**35. 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.**

**36. The values combined are called**

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

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

**39. If a < b and b < c**

**40. The value produced is called**

**41. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.**

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

**43. Not commutative a^b?b^a**

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

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

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

**47. The inner product operation on two vectors produces a**

**48. Can be combined using the function composition operation - performing the first rotation and then the second.**

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

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