## 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 an equation involving a transcendental function of one of its variables.**

**2. 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).**

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

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

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

**6. The squaring operation only produces**

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

**8. 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**

**9. 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).**

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

**11. 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**

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

**13. 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.**

**14. 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**

**15. Logarithm (Log)**

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

**17. 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.**

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

**19. A binary operation**

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

**21. 0 - which preserves numbers: a + 0 = a**

**22. 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)**

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

**24. A + b = b + a**

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

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

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

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

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

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

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

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

**33. Subtraction ( - )**

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

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

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

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

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

**39. (a**

**40. 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.**

**41. 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)**

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

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

**44. Include composition and convolution**

**45. The values combined are called**

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

**47. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s**

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

**49. Is an equation in which the unknowns are functions rather than simple quantities.**

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