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






2. A + b = b + a






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






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






6. k-ary operation is a






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






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






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






10. 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)






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






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






13. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.






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






15. 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






16. If a < b and c < 0






17. The value produced is called






18. A unary operation






19. An operation of arity k is called a






20. 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).






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






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






23. 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.






24. If a < b and b < c






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






26. 0 - which preserves numbers: a + 0 = a






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






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






29. The squaring operation only produces






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






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






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






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






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






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






36. Can be added and subtracted.






37. 1 - which preserves numbers: a^1 = a






38. 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)






39. 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






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






41. 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)






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






43. 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






44. 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






45. Is an equation involving integrals.






46. There are two common types of operations:






47. Applies abstract algebra to the problems of geometry






48. Can be defined axiomatically up to an isomorphism






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






50. If a < b and c < d






Can you answer 50 questions in 15 minutes?



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