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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
Start Test
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. That 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.
Variables
The relation of equality (=) has the property
The real number system
A functional equation
2. If it holds for all a and b in X that if a is related to b then b is related to a.
scalar
operation
All quadratic equations
A binary relation R over a set X is symmetric
3. 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)
The operation of exponentiation
identity element of Exponentiation
then a < c
Difference of two squares - or the difference of perfect squares
4. 0 - which preserves numbers: a + 0 = a
identity element of addition
Operations on functions
the set Y
A linear equation
5. 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'.
operation
The relation of equality (=)
Unary operations
Reflexive relation
6. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Repeated addition
Identity element of Multiplication
Any real number can be added to both sides. Any real number can be subtracted from both sides. Any real number can be multiplied to both sides. Any non-zero real number can divide both sides. Some functions can be applied to both sides.
Vectors
7. Are true for only some values of the involved variables: x2 - 1 = 4.
The simplest equations to solve
logarithmic equation
exponential equation
Conditional equations
8. Logarithm (Log)
commutative law of Exponentiation
has arity two
inverse operation of Exponentiation
Algebraic geometry
9. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Linear algebra
then a < c
Identity
Solving the Equation
10. Is an equation involving integrals.
Algebra
Elementary algebra
A integral equation
commutative law of Exponentiation
11. 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.
The relation of equality (=)
Properties of equality
finitary operation
Knowns
12. Referring to the finite number of arguments (the value k)
finitary operation
Repeated addition
substitution
Operations can involve dissimilar objects
13. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
The simplest equations to solve
then a < c
Properties of equality
Expressions
14. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Quadratic equations
A polynomial equation
range
The real number system
15. Division ( / )
Unknowns
value - result - or output
Identity element of Multiplication
inverse operation of Multiplication
16. 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.
radical equation
A polynomial equation
The relation of inequality (<) has this property
range
17. Not associative
Associative law of Exponentiation
Addition
Equations
the fixed non-negative integer k (the number of arguments)
18. Include composition and convolution
The relation of equality (=) has the property
The logical values true and false
substitution
Operations on functions
19. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
two inputs
range
Binary operations
Quadratic equations can also be solved
20. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Quadratic equations
Equations
The purpose of using variables
Number line or real line
21. k-ary operation is a
two inputs
(k+1)-ary relation that is functional on its first k domains
then ac < bc
substitution
22. 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.
Binary operations
The central technique to linear equations
The relation of equality (=)'s property
Operations on functions
23. (a + b) + c = a + (b + c)
A polynomial equation
finitary operation
associative law of addition
Variables
24. 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
Quadratic equations
The method of equating the coefficients
inverse operation of Exponentiation
Algebraic combinatorics
25. () 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.
Identity
Algebra
Algebraic equation
exponential equation
26. Is an equation of the form aX = b for a > 0 - which has solution
equation
exponential equation
Order of Operations
Universal algebra
27. The operation of multiplication means _______________: a
Repeated addition
(k+1)-ary relation that is functional on its first k domains
The simplest equations to solve
Algebraic number theory
28. In which properties common to all algebraic structures are studied
exponential equation
Universal algebra
then bc < ac
the set Y
29. 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).
Algebraic equation
Equation Solving
Order of Operations
operation
30. If a = b and b = c then a = c
then bc < ac
system of linear equations
transitive
The relation of inequality (<) has this property
31. Will have two solutions in the complex number system - but need not have any in the real number system.
Categories of Algebra
Algebraic equation
All quadratic equations
The central technique to linear equations
32. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Associative law of Multiplication
Properties of equality
exponential equation
33. In which abstract algebraic methods are used to study combinatorial questions.
Constants
two inputs
The sets Xk
Algebraic combinatorics
34. Subtraction ( - )
unary and binary
inverse operation of addition
operation
All quadratic equations
35. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi
inverse operation of Multiplication
nonnegative numbers
Associative law of Multiplication
Elementary algebra
36. The squaring operation only produces
A functional equation
nonnegative numbers
the fixed non-negative integer k (the number of arguments)
Addition
37. An operation of arity zero is simply an element of the codomain Y - called a
Multiplication
Reunion of broken parts
Constants
nullary operation
38. Is an equation of the form log`a^X = b for a > 0 - which has solution
finitary operation
logarithmic equation
reflexive
The method of equating the coefficients
39. The codomain is the set of real numbers but the range is the
range
Addition
The sets Xk
nonnegative numbers
40. The process of expressing the unknowns in terms of the knowns is called
Change of variables
The method of equating the coefficients
Solving the Equation
A binary relation R over a set X is symmetric
41. Is Written as ab or a^b
Exponentiation
Difference of two squares - or the difference of perfect squares
Identity
nonnegative numbers
42. The operation of exponentiation means ________________: a^n = a
Equations
commutative law of Multiplication
equation
Repeated multiplication
43. Is an equation involving a transcendental function of one of its variables.
Unary operations
nullary operation
A transcendental equation
Repeated addition
44. A unary operation
Reunion of broken parts
has arity one
inverse operation of Multiplication
inverse operation of Exponentiation
45. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
A binary relation R over a set X is symmetric
identity element of addition
identity element of Exponentiation
46. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
exponential equation
Equations
The relation of equality (=) has the property
Categories of Algebra
47. Is called the type or arity of the operation
Constants
Multiplication
the fixed non-negative integer k (the number of arguments)
Abstract algebra
48. The values for which an operation is defined form a set called its
domain
Repeated multiplication
Identity element of Multiplication
Equations
49. A + b = b + a
inverse operation of addition
Solving the Equation
commutative law of Addition
k-ary operation
50. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Operations
Order of Operations
Pure mathematics
All quadratic equations