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






2. Can be combined using logic operations - such as and - or - and not.






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






4. Operations can have fewer or more than






5. If a < b and b < c






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






7. 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






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






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






10. If a < b and c < 0






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






12. Is called the codomain of the operation






13. 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.






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






15. 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)






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






17. 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






18. Is the claim that two expressions have the same value and are equal.






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






20. A unary operation






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






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






23. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction






24. 1 - which preserves numbers: a






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






26. A






27. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.






28. If a = b then b = a






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






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






32. 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).






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






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






35. Is called the type or arity of the operation






36. 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.






37. 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)






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






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






40. Can be added and subtracted.






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






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






43. That 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.






44. Will have two solutions in the complex number system - but need not have any in the real number system.






45. 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






46. (a






47. Logarithm (Log)






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






49. Not associative






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