## 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. Not associative**

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

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

**4. Is a way of solving a functional equation of two polynomials for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas in**

**5. 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.**

**6. Logarithm (Log)**

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

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

**9. 1 - which preserves numbers: a**

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

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

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

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

**14. The value produced is called**

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

**16. 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).**

**17. Include composition and convolution**

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

**19. 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).**

**20. The values combined are called**

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

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

**23. 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)**

**24. A**

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

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

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

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

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

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

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

**32. Can be combined using logic operations - such as and - or - and not.**

**33. 1 - which preserves numbers: a^1 = a**

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

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

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

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

**38. 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.**

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

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

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

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

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

**44. (a**

**45. Division ( / )**

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

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

**48. 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.**

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

**50. Is an equation in which a polynomial is set equal to another polynomial.**