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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. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Identity element of Multiplication
Algebraic combinatorics
Reunion of broken parts
Order of Operations
2. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
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.
A polynomial equation
Solving the Equation
Variables
3. An operation of arity k is called a
identity element of addition
radical equation
Linear algebra
k-ary operation
4. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Solution to the system
exponential equation
Number line or real line
Addition
5. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
The relation of equality (=) has the property
two inputs
(k+1)-ary relation that is functional on its first k domains
6. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po
logarithmic equation
Identities
All quadratic equations
Elimination method
7. The operation of multiplication means _______________: a
Operations can involve dissimilar objects
Repeated addition
then a < c
Conditional equations
8. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
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.
Unknowns
has arity one
Change of variables
9. 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.
Solution to the system
Solving the Equation
Change of variables
Variables
10. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym
Reunion of broken parts
Knowns
A linear equation
inverse operation of Multiplication
11. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Binary operations
The relation of equality (=)'s property
Reunion of broken parts
Pure mathematics
12. Is Written as ab or a^b
Exponentiation
(k+1)-ary relation that is functional on its first k domains
transitive
reflexive
13. Operations can have fewer or more than
two inputs
Operations on functions
Change of variables
A differential equation
14. Referring to the finite number of arguments (the value k)
inverse operation of Multiplication
finitary operation
Difference of two squares - or the difference of perfect squares
inverse operation of Exponentiation
15. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
Linear algebra
A solution or root of the equation
the fixed non-negative integer k (the number of arguments)
16. If a = b and b = c then a = c
when b > 0
transitive
Conditional equations
nullary operation
17. May not be defined for every possible value.
reflexive
Equations
Exponentiation
Operations
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)
Identity element of Multiplication
The operation of exponentiation
Quadratic equations can also be solved
Associative law of Exponentiation
19. If a < b and c < d
logarithmic equation
Binary operations
then a + c < b + d
Equations
20. Is called the codomain of the operation
the set Y
then ac < bc
Conditional equations
Knowns
21. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Elimination method
operation
Categories of Algebra
Real number
22. In an equation with a single unknown - a value of that unknown for which the equation is true is called
has arity one
equation
Difference of two squares - or the difference of perfect squares
A solution or root of the equation
23. () 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
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.
Elimination method
equation
24. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
The relation of equality (=) has the property
Operations on functions
Equation Solving
Equations
25. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
Elementary algebra
Operations
inverse operation of Multiplication
26. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
The purpose of using variables
Reunion of broken parts
logarithmic equation
27. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
the fixed non-negative integer k (the number of arguments)
Rotations
Identities
Binary operations
28. Not commutative a^b?b^a
Expressions
Pure mathematics
Addition
commutative law of Exponentiation
29. If a < b and c < 0
then ac < bc
Operations on functions
then bc < ac
The logical values true and false
30. Is an action or procedure which produces a new value from one or more input values.
an operation
Equation Solving
transitive
Operations on sets
31. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
Variables
Associative law of Exponentiation
Operations on functions
32. Are called the domains of the operation
The sets Xk
Conditional equations
Unary operations
All quadratic equations
33. The operation of exponentiation means ________________: a^n = a
The sets Xk
commutative law of Addition
Repeated multiplication
The relation of inequality (<) has this property
34. Include the binary operations union and intersection and the unary operation of complementation.
commutative law of Addition
inverse operation of Multiplication
Operations on sets
Addition
35. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
The relation of equality (=)'s property
unary and binary
A Diophantine equation
36. 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 polynomial equation
The central technique to linear equations
range
nonnegative numbers
37. 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
A transcendental equation
Quadratic equations can also be solved
The method of equating the coefficients
Reflexive relation
38. 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).
reflexive
Quadratic equations can also be solved
commutative law of Addition
Quadratic equations
39. The value produced is called
associative law of addition
inverse operation of addition
value - result - or output
Unknowns
40. Is Written as a
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.
Operations on sets
Multiplication
nonnegative numbers
41. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Identities
Elimination method
Polynomials
equation
42. Can be combined using the function composition operation - performing the first rotation and then the second.
identity element of addition
Rotations
when b > 0
Properties of equality
43. A
system of linear equations
A functional equation
commutative law of Multiplication
Difference of two squares - or the difference of perfect squares
44. Is algebraic equation of degree one
commutative law of Addition
A linear equation
inverse operation of Multiplication
A Diophantine equation
45. Is an equation where the unknowns are required to be integers.
A Diophantine equation
equation
Algebraic geometry
Reflexive relation
46. Is an equation involving integrals.
Identity element of Multiplication
A integral equation
A differential equation
Equation Solving
47. 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)
The relation of equality (=) has the property
when b > 0
operation
Rotations
48. Applies abstract algebra to the problems of geometry
Algebraic geometry
substitution
Operations on sets
A functional equation
49. Include composition and convolution
Vectors
Difference of two squares - or the difference of perfect squares
The relation of equality (=) has the property
Operations on functions
50. 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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