Test your basic knowledge |

CLEP College Algebra: Algebra Principles

Subjects : clep, math, algebra
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. 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.






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






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






4. 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.






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






6. A + b = b + a






7. The operation of multiplication means _______________: a






8. 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)






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. Is Written as a + b






11. Applies abstract algebra to the problems of geometry






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






13. Not commutative a^b?b^a






14. The inner product operation on two vectors produces a






15. An operation of arity k is called a






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






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






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






19. Can be defined axiomatically up to an isomorphism






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






21. 1 - which preserves numbers: a






22. 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






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






24. The value produced is called






25. Is Written as ab or a^b






26. Include composition and convolution






27. If a < b and c > 0






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






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






30. A vector can be multiplied by a scalar to form another vector






31. 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)






32. The squaring operation only produces






33. A






34. 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






35. 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






36. Division ( / )






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






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






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






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






41. If a < b and b < c






42. There are two common types of operations:






43. 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






44. 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.






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






46. Logarithm (Log)






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






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






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






50. The codomain is the set of real numbers but the range is the