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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. Can be added and subtracted.






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






3. Is an equation involving derivatives.






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






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






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






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






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






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






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. 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






12. 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.






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






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






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






16. 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






17. 1 - which preserves numbers: a^1 = a






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






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






20. 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






21. An operation of arity k is called a






22. Is Written as a + b






23. Is Written as a






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






25. Division ( / )






26. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






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






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






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






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






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






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






34. In which properties common to all algebraic structures are studied






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






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






37. 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)






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






39. 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)






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






41. 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.






42. 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






43. 0 - which preserves numbers: a + 0 = a






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






45. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics






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






47. Include composition and convolution






48. 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.






49. 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).






50. Is algebraic equation of degree one