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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. 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.






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






3. Not commutative a^b?b^a






4. Division ( / )






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






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






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






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






9. Can be combined using the function composition operation - performing the first rotation and then the second.






10. Can be defined axiomatically up to an isomorphism






11. k-ary operation is a






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






14. 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)






15. b = b






16. Operations can have fewer or more than






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






18. Is called the codomain of the operation






19. An operation of arity k is called a






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






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






22. Logarithm (Log)






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






24. May not be defined for every possible value.






25. 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






26. If a = b then b = a






27. A






28. 0 - which preserves numbers: a + 0 = a






29. Not associative






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






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






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






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






34. The inner product operation on two vectors produces a






35. 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.






36. 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.






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






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






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






40. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






41. 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.

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42. Include composition and convolution






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






44. 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






45. Are called the domains of the operation






46. 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)






47. 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






48. 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.






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






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






Can you answer 50 questions in 15 minutes?



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