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






2. 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.






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






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






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






7. Is an equation involving derivatives.






8. 1 - which preserves numbers: a






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






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






11. If a < b and c < 0






12. 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.






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






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






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






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






17. An operation of arity k is called a






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






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






20. Applies abstract algebra to the problems of geometry






21. 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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22. Is Written as a






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






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






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






26. There are two common types of operations:






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






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






29. A






30. 1 - which preserves numbers: a^1 = a






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 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'.






33. Can be added and subtracted.






34. 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






35. Not commutative a^b?b^a






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






37. If a < b and b < c






38. The inner product operation on two vectors produces a






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






40. 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)






41. A binary operation






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






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






44. The value produced is called






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






46. The operation of multiplication means _______________: a






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






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






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






50. Is algebraic equation of degree one