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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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Study First
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. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
Quadratic equations can also be solved
The operation of addition
A Diophantine equation
2. The squaring operation only produces
nonnegative numbers
operation
then a < c
the set Y
3. An operation of arity k is called a
operands - arguments - or inputs
A differential equation
logarithmic equation
k-ary operation
4. If a < b and c < d
A Diophantine equation
then a + c < b + d
Expressions
inverse operation of Exponentiation
5. A unary operation
has arity one
inverse operation of addition
commutative law of Addition
Difference of two squares - or the difference of perfect squares
6. Is an equation in which a polynomial is set equal to another polynomial.
range
Reunion of broken parts
A polynomial equation
nullary operation
7. Operations can have fewer or more than
range
two inputs
The simplest equations to solve
Equation Solving
8. 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.
A polynomial equation
inverse operation of addition
Properties of equality
The central technique to linear equations
9. In which properties common to all algebraic structures are studied
radical equation
Categories of Algebra
The relation of equality (=)'s property
Universal algebra
10. Logarithm (Log)
inverse operation of Exponentiation
Operations
Reunion of broken parts
A functional equation
11. 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)
Pure mathematics
Associative law of Exponentiation
operation
The logical values true and false
12. May not be defined for every possible value.
Algebraic number theory
A Diophantine equation
The method of equating the coefficients
Operations
13. The process of expressing the unknowns in terms of the knowns is called
Pure mathematics
Operations on sets
Solving the Equation
an operation
14. If a < b and c > 0
Algebra
then ac < bc
The real number system
Operations on functions
15. Is an equation involving derivatives.
Addition
Operations can involve dissimilar objects
A differential equation
Elementary algebra
16. 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'.
Quadratic equations can also be solved
Reflexive relation
Rotations
Difference of two squares - or the difference of perfect squares
17. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
Repeated multiplication
radical equation
an operation
18. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Equation Solving
The method of equating the coefficients
Difference of two squares - or the difference of perfect squares
k-ary operation
19. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
Reflexive relation
when b > 0
The sets Xk
20. Can be combined using logic operations - such as and - or - and not.
system of linear equations
domain
A transcendental equation
The logical values true and false
21. 1 - which preserves numbers: a
Algebraic combinatorics
Solving the Equation
Identity element of Multiplication
Constants
22. () 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.
Algebra
Repeated multiplication
Categories of Algebra
Operations on sets
23. Is an equation in which the unknowns are functions rather than simple quantities.
associative law of addition
an operation
A functional equation
Polynomials
24. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Operations on sets
Expressions
Categories of Algebra
Unknowns
25. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
radical equation
A transcendental equation
Identity
26. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Abstract algebra
Reflexive relation
Change of variables
Identity
27. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
The operation of addition
A functional equation
Pure mathematics
28. The values combined are called
Vectors
The operation of addition
Real number
operands - arguments - or inputs
29. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Addition
reflexive
Order of Operations
30. 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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31. 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)
Abstract algebra
The operation of exponentiation
Variables
has arity one
32. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Vectors
radical equation
Identities
Unary operations
33. 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.
A Diophantine equation
The central technique to linear equations
Solution to the system
has arity two
34. Is a basic technique used to simplify problems in which the original variables are replaced with new ones; the new and old variables being related in some specified way.
Properties of equality
Algebraic geometry
Unary operations
Change of variables
35. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
Equation Solving
Real number
Identity
36. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
finitary operation
nonnegative numbers
The method of equating the coefficients
Algebraic equation
37. 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
system of linear equations
when b > 0
An operation ?
Operations
38. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
value - result - or output
commutative law of Multiplication
Algebraic equation
39. Include the binary operations union and intersection and the unary operation of complementation.
Order of Operations
Linear algebra
Associative law of Exponentiation
Operations on sets
40. Are denoted by letters at the beginning - a - b - c - d - ...
Knowns
The relation of inequality (<) has this property
Conditional equations
an operation
41. Referring to the finite number of arguments (the value k)
finitary operation
Categories of Algebra
commutative law of Exponentiation
Algebraic geometry
42. Can be added and subtracted.
Vectors
Categories of Algebra
All quadratic equations
Quadratic equations can also be solved
43. Can be defined axiomatically up to an isomorphism
Quadratic equations can also be solved
The real number system
has arity one
Exponentiation
44. b = b
exponential equation
reflexive
The simplest equations to solve
Number line or real line
45. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Identity element of Multiplication
then a + c < b + d
Algebraic number theory
system of linear equations
46. 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
substitution
Operations on sets
range
nonnegative numbers
47. Involve only one value - such as negation and trigonometric functions.
Unary operations
Multiplication
Operations can involve dissimilar objects
Solving the Equation
48. 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)
Exponentiation
An operation ?
The operation of addition
The relation of equality (=) has the property
49. If it holds for all a and b in X that if a is related to b then b is related to a.
range
A binary relation R over a set X is symmetric
Solving the Equation
An operation ?
50. 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.
Exponentiation
The relation of inequality (<) has this property
an operation
inverse operation of Multiplication