## 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. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).**

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

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

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

**5. Logarithm (Log)**

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

**7. 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**

**8. 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**

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

**10. Is an equation involving integrals.**

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

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

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

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

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

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

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

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

**21. The values for which an operation is defined form a set called its**

**22. 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)**

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

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

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

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

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

**28. 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.**

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

**30. 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)**

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

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

**34. Include composition and convolution**

**35. Is Written as a**

**36. A**

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

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

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

**40. 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.**

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

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

**43. 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.**

**44. May not be defined for every possible value.**

**45. The values combined are called**

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

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

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

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