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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. 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






2. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.






3. Is called the type or arity of the operation






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






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






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






7. The value produced is called






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






9. If a < b and c > 0






10. 1 - which preserves numbers: a






11. 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.






12. 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)






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






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






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






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






17. 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.






18. 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






19. If a < b and c < d






20. Applies abstract algebra to the problems of geometry






21. 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.






22. Is Written as ab or a^b






23. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.






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






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






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






27. A binary operation






28. 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)






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






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






31. 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






32. Is an equation involving integrals.






33. 0 - which preserves numbers: a + 0 = a






34. (a






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






36. In an equation with a single unknown - a value of that unknown for which the equation is true is called






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






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






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






40. An operation of arity k is called a






41. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.






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






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






44. Logarithm (Log)






45. Is an equation involving derivatives.






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






47. 1 - which preserves numbers: a^1 = a






48. Is algebraic equation of degree one






49. If a = b and b = c then a = c






50. Not commutative a^b?b^a