## 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. 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'.**

**2. 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.**

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

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

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

**6. Operations can have fewer or more than**

**7. 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**

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

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

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

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

**12. A binary operation**

**13. Not associative**

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

**15. May not be defined for every possible value.**

**16. (a**

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

**18. 1 - which preserves numbers: a^1 = a**

**19. The values of the variables which make the equation true are the solutions of the equation and can be found through**

**20. (a + b) + c = a + (b + c)**

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

**22. Is an algebraic 'sentence' containing an unknown quantity.**

**23. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction**

**24. 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).**

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

**26. 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)**

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

**28. Is called the type or arity of the operation**

**29. 1 - which preserves numbers: a**

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

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

**32. A + b = b + a**

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

**34. b = b**

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

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

**37. Logarithm (Log)**

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

**39. k-ary operation is a**

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

**41. 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.**

**42. Can be added and subtracted.**

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

**44. If a = b then b = a**

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

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

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

**48. In which properties common to all algebraic structures are studied**

**49. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym**

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