## 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 of the variables which make the equation true are the solutions of the equation and can be found through**

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

**3. Is Written as a**

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

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

**6. Division ( / )**

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

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

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

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

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

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

**13. Is an equation involving integrals.**

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

**15. 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)**

**16. 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).**

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

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

**19. 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**

**20. 1 - which preserves numbers: a^1 = a**

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

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

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

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

**25. Can be added and subtracted.**

**26. 0 - which preserves numbers: a + 0 = a**

**27. 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).**

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

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

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

**31. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics**

**32. 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.**

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

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

**35. A binary operation**

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

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

**38. 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**

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

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

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

**42. The squaring operation only produces**

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

**44. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.**

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

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

**47. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left**

**48. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity**

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

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