## 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. Include composition and convolution**

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

**3. Is Written as a**

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

**5. The squaring operation only produces**

**6. A + b = b + a**

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

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

**9. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.**

**10. 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.**

**11. Is Written as a + b**

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

**13. A**

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

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

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

**17. 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**

**18. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.**

**19. 0 - which preserves numbers: a + 0 = a**

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

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

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

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

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

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

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

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

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

**29. A unary operation**

**30. Is an equation of the form log`a^X = b for a > 0 - which has solution**

**31. 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)**

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

**33. Subtraction ( - )**

**34. A binary operation**

**35. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym**

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

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

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

**39. 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).**

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

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

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

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

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

**45. 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.**

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

**47. Not associative**

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

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

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