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

**2. 1 - which preserves numbers: a^1 = a**

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

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

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

**6. 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**

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

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

**9. 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)**

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

**11. The value produced is called**

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

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

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

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

**17. 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.**

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

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

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

**21. 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).**

**22. 0 - which preserves numbers: a + 0 = a**

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

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

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

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

**27. Is the claim that two expressions have the same value and are equal.**

**28. Can be added and subtracted.**

**29. Include composition and convolution**

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

**31. 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).**

**32. Division ( / )**

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

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

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

**36. Letters from the beginning of the alphabet like a - b - c... often denote**

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

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

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

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

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

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

**43. (a**

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

**45. 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)**

**46. A binary operation**

**47. A unary operation**

**48. 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.**

**49. 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**

**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)**