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






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






3. If a = b then b = a






4. The squaring operation only produces






5. () 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.






6. 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.






7. Is Written as a + b






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






9. If a < b and c > 0






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






11. 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)






12. 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






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






14. The operation of multiplication means _______________: a






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






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






17. If a < b and c < 0






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






19. A unary operation






20. 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






21. Subtraction ( - )






22. The process of expressing the unknowns in terms of the knowns is 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. (a






25. b = b






26. 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






27. Is an equation involving integrals.






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






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






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






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






32. 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.






33. May not be defined for every possible value.






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






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






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. Not commutative a^b?b^a






38. The values of the variables which make the equation true are the solutions of the equation and can be found through






39. Applies abstract algebra to the problems of geometry






40. 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.






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






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






43. 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)






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






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






47. k-ary operation is a






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






49. Is Written as ab or a^b






50. Not associative