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






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






3. A + b = b + a






4. Is Written as ab or a^b






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






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






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






8. 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).






9. 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.






10. 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.






11. Applies abstract algebra to the problems of geometry






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






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






14. The values combined are called






15. Not commutative a^b?b^a






16. Is called the type or arity of the operation






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






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






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






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






21. Is called the codomain of the operation






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






23. The operation of multiplication means _______________: a






24. A unary operation






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






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






27. Can be defined axiomatically up to an isomorphism






28. k-ary operation is a






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






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






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






32. Include the binary operations union and intersection and the unary operation of complementation.






33. Division ( / )






34. 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






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






36. An operation of arity k is called a






37. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym






38. Is an equation involving derivatives.






39. The squaring operation only produces






40. 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






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






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






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






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






45. If a < b and c < 0






46. Operations can have fewer or more than






47. Letters from the beginning of the alphabet like a - b - c... often denote






48. Is an equation involving integrals.






49. 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'.






50. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).