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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. In which the specific properties of vector spaces are studied (including matrices)






2. Is Written as ab or a^b






3. Is called the codomain of the operation






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






5. There are two common types of operations:






6. Not commutative a^b?b^a






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






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






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






10. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of






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






12. May not be defined for every possible value.






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






14. 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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15. 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.






16. () 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.






17. Can be defined axiomatically up to an isomorphism






18. 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).






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






20. 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






21. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the






22. Not associative






23. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that






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






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






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






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






28. 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






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






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






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






32. Is Written as a






33. 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






34. A unary operation






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






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






37. A + b = b + a






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






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






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






41. If a = b then b = a






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






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






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






45. 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).






46. Is an equation involving integrals.






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






48. Include composition and convolution






49. 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.






50. Are called the domains of the operation