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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 involving integrals.






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






3. Is an equation involving derivatives.






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






5. Can be defined axiomatically up to an isomorphism






6. 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).






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






8. The squaring operation only produces






9. 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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10. If a < b and c < d






11. 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






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






13. 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)






14. If a < b and c < 0






15. A + b = b + a






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






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






18. Not commutative a^b?b^a






19. 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'.






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






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






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






23. Is Written as a






24. Operations can have fewer or more than






25. A binary operation






26. 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)






27. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity






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






29. 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.






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






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






32. Division ( / )






33. Is called the type or arity of the operation






34. 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.






35. The inner product operation on two vectors produces a






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






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






38. 1 - which preserves numbers: a^1 = a






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






40. Is an equation of the form aX = b for a > 0 - which has solution






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






42. (a






43. 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.






44. Not associative






45. 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






46. 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






47. There are two common types of operations:






48. Can be added and subtracted.






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






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