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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 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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2. Can be added and subtracted.






3. A + b = b + a






4. A unary operation






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






6. 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






7. 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






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






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






10. 0 - which preserves numbers: a + 0 = a






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






12. Is Written as a + b






13. 1 - which preserves numbers: a^1 = a






14. Subtraction ( - )






15. Are called the domains of the operation






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






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






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






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






20. Division ( / )






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






22. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics






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






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






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






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






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






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






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






30. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).






31. Is an equation involving a transcendental function of one of its variables.






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. Operations can have fewer or more than






34. Is an equation involving integrals.






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






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






37. The operation of multiplication means _______________: a






38. Include composition and convolution






39. If a < b and c < 0






40. 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)






41. Is Written as a






42. Not commutative a^b?b^a






43. A






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






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






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






47. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.






48. Is Written as ab or a^b






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






50. If a < b and b < c