## 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. The values combined are called**

**2. 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**

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

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

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

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

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

**8. If a < b and c < 0**

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

**10. 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'.**

**11. Is called the codomain of the operation**

**12. 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.**

**13. 1 - which preserves numbers: a**

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

**15. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that**

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

**17. If a = b then b = a**

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

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

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

**21. Is an equation where the unknowns are required to be integers.**

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

**23. Is algebraic equation of degree one**

**24. Are called the domains of the operation**

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

**26. Is Written as ab or a^b**

**27. An operation of arity zero is simply an element of the codomain Y - called a**

**28. An operation of arity k is called a**

**29. If a < b and c < d**

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

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

**32. Subtraction ( - )**

**33. The squaring operation only produces**

**34. Is an equation of the form log`a^X = b for a > 0 - which has solution**

**35. Can be added and subtracted.**

**36. 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.**

**37. Applies abstract algebra to the problems of geometry**

**38. A + b = b + a**

**39. A unary operation**

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

**41. 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)**

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

**43. There are two common types of operations:**

**44. b = b**

**45. 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.**

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

**47. () 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.**

**48. (a**

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

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