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






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






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






4. 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






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






6. Are called the domains of the operation






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






8. Applies abstract algebra to the problems of geometry






9. Is Written as a






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






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






12. If a < b and c < d






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






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






15. b = b






16. Is Written as ab or a^b






17. 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'.






18. 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)






19. Is Written as a + b






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






21. 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).






22. 0 - which preserves numbers: a + 0 = a






23. Is an equation involving integrals.






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






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






26. A binary operation






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






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






29. 1 - which preserves numbers: a






30. Not commutative a^b?b^a






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






32. 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






33. There are two common types of operations:






34. A + b = b + a






35. Are denoted by letters at the end of the alphabet - x - y - z - w - ...






36. 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






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






38. A unary operation






39. A






40. The values combined are called






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






42. Is an equation involving derivatives.






43. The value produced is called






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






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






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






47. Elementary algebraic techniques are used to rewrite a given equation in the above way before arriving at the solution. then - by subtracting 1 from both sides of the equation - and then dividing both sides by 3 we obtain






48. Can be added and subtracted.






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






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