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

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

**3. 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**

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

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

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

**7. If a = b and b = c then a = c**

**8. If it holds for all a and b in X that if a is related to b then b is related to a.**

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

**10. Subtraction ( - )**

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

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

**13. The values combined are called**

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

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

**16. Not associative**

**17. The squaring operation only produces**

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

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

**20. If a = b then b = a**

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

**22. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.**

**23. Can be added and subtracted.**

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

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

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

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

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

**29. (a**

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

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

**32. Include composition and convolution**

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

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

**35. 0 - which preserves numbers: a + 0 = a**

**36. b = b**

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

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

**39. 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.**

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

**41. 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.**

**42. The value produced is called**

**43. 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**

**44. 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)**

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

**46. 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).**

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

**48. 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**

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

**50. 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)**