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






2. () 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.






3. If a < b and b < c






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






5. 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






6. 1 - which preserves numbers: a






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






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






9. The value produced is called






10. Are called the domains of the operation






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






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






13. If a < b and c < d






14. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)






15. 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.






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






17. Is called the type or arity of the operation






18. b = b






19. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.






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






21. Is algebraic equation of degree one






22. 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






23. A unary operation






24. Is Written as ab or a^b






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






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






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






28. 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)






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






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






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






32. An operation of arity k is called a






33. 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)






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






35. Not commutative a^b?b^a






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






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






38. Subtraction ( - )






39. A + b = b + a






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






41. k-ary operation is a






42. There are two common types of operations:






43. If a < b and c > 0






44. Operations can have fewer or more than






45. 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).






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






47. 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






48. Can be defined axiomatically up to an isomorphism






49. May not be defined for every possible value.






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