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






3. Is Written as a






4. If a < b and c < d






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






6. In which properties common to all algebraic structures are studied






7. Are called the domains of the operation






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






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






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. The inner product operation on two vectors produces a






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






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






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






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






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






18. Operations can have fewer or more than






19. 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)






20. The operation of multiplication means _______________: a






21. 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






22. Is called the codomain of the operation






23. A binary operation






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






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






26. 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'.






27. (a + b) + c = a + (b + c)






28. k-ary operation is a






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






30. Is Written as a + b






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






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






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






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






35. Subtraction ( - )






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






37. 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.






38. Is algebraic equation of degree one






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






40. An operation of arity k is called a






41. Is an equation involving derivatives.






42. Include composition and convolution






43. Can be defined axiomatically up to an isomorphism






44. 1 - which preserves numbers: a






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






46. A






47. If a < b and c < 0






48. 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).






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






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