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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. Not commutative a^b?b^a






2. Include composition and convolution






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






4. 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.






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






6. 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).






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






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






9. If a < b and c < 0






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






11. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






12. Can be defined axiomatically up to an isomorphism






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






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






15. The inner product operation on two vectors produces a






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






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






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






19. 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






20. 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)






21. The process of expressing the unknowns in terms of the knowns is called






22. Operations can have fewer or more than






23. Logarithm (Log)






24. Is Written as ab or a^b






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






26. A unary operation






27. If a = b then b = a






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






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






30. The operation of multiplication means _______________: a






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






32. The squaring operation only produces






33. Not associative






34. 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






35. If a < b and c < d






36. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.






37. Applies abstract algebra to the problems of geometry






38. Is Written as a + b






39. There are two common types of operations:






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






41. Division ( / )






42. k-ary operation is a






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






44. An operation of arity zero is simply an element of the codomain Y - called a






45. If a < b and c > 0






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






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






48. 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






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






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