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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Expressions
The purpose of using variables
inverse operation of Exponentiation
symmetric
2. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
then ac < bc
Unary operations
A linear equation
Algebraic equation
3. A vector can be multiplied by a scalar to form another vector
The relation of equality (=) has the property
unary and binary
Equation Solving
Operations can involve dissimilar objects
4. The value produced is called
Expressions
Order of Operations
Unknowns
value - result - or output
5. Is a function of the form ? : V ? Y - where V ? X1
k-ary operation
An operation ?
Reunion of broken parts
the fixed non-negative integer k (the number of arguments)
6. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
substitution
radical equation
A solution or root of the equation
7. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
the set Y
Unknowns
The relation of equality (=) has the property
The logical values true and false
8. Is an equation of the form aX = b for a > 0 - which has solution
Reunion of broken parts
exponential equation
Solution to the system
commutative law of Multiplication
9. (a + b) + c = a + (b + c)
Elementary algebra
A Diophantine equation
associative law of addition
The relation of equality (=) has the property
10. Is Written as a + b
then a + c < b + d
Binary operations
system of linear equations
Addition
11. Is an equation involving integrals.
Quadratic equations
Reunion of broken parts
A integral 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.
12. 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
logarithmic equation
(k+1)-ary relation that is functional on its first k domains
Equations
13. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
Knowns
Properties of equality
Order of Operations
14. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Variables
Quadratic equations can also be solved
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.
Polynomials
15. Is an action or procedure which produces a new value from one or more input values.
an operation
range
Universal algebra
The method of equating the coefficients
16. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Constants
Identity element of Multiplication
The simplest equations to solve
identity element of Exponentiation
17. If a = b and b = c then a = c
commutative law of Exponentiation
transitive
Knowns
nonnegative numbers
18. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Knowns
then a < c
Identities
when b > 0
19. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Quadratic equations
identity element of Exponentiation
The relation of equality (=)
The logical values true and false
20. k-ary operation is a
Operations
(k+1)-ary relation that is functional on its first k domains
Difference of two squares - or the difference of perfect squares
then ac < bc
21. 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
Equation Solving
nullary operation
The method of equating the coefficients
22. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Repeated multiplication
inverse operation of addition
Unknowns
Pure mathematics
23. Not associative
identity element of Exponentiation
domain
Associative law of Exponentiation
symmetric
24. Involve only one value - such as negation and trigonometric functions.
A binary relation R over a set X is symmetric
Solving the Equation
Variables
Unary operations
25. Operations can have fewer or more than
The relation of equality (=)'s property
two inputs
A solution or root of the equation
A integral equation
26. Will have two solutions in the complex number system - but need not have any in the real number system.
system of linear equations
Quadratic equations can also be solved
then ac < bc
All quadratic equations
27. Include composition and convolution
nonnegative numbers
Operations on functions
Identities
Binary operations
28. Is called the codomain of the operation
A solution or root of the equation
The relation of equality (=) has the property
the set Y
Linear algebra
29. If it holds for all a and b in X that if a is related to b then b is related to a.
The operation of addition
Operations can involve dissimilar objects
A binary relation R over a set X is symmetric
The operation of exponentiation
30. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
inverse operation of Exponentiation
Knowns
Categories of Algebra
Solution to the system
31. A unary operation
has arity one
Change of variables
two inputs
Order of Operations
32. Can be defined axiomatically up to an isomorphism
nullary operation
The relation of equality (=)'s property
The real number system
then ac < bc
33. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
inverse operation of Exponentiation
operation
An operation ?
equation
34. 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.
inverse operation of addition
commutative law of Exponentiation
Properties of equality
identity element of Exponentiation
35. 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
A transcendental equation
Real number
inverse operation of addition
Equations
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.
Difference of two squares - or the difference of perfect squares
Reflexive relation
The central technique to linear equations
Algebraic combinatorics
37. If a < b and c > 0
Associative law of Multiplication
then a < c
then ac < bc
Quadratic equations can also be solved
38. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
then ac < bc
Conditional equations
Associative law of Multiplication
39. 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
Elimination method
Elementary algebra
The simplest equations to solve
Polynomials
40. Not commutative a^b?b^a
The method of equating the coefficients
Properties of equality
when b > 0
commutative law of Exponentiation
41. 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)
Polynomials
The purpose of using variables
The operation of addition
Addition
42. 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'.
Repeated addition
A transcendental equation
Universal algebra
Reflexive relation
43. Is an equation involving a transcendental function of one of its variables.
A differential equation
k-ary operation
substitution
A transcendental equation
44. Applies abstract algebra to the problems of geometry
Algebraic geometry
system of linear equations
Identity element of Multiplication
an operation
45. 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
scalar
substitution
logarithmic equation
Expressions
46. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
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.
nonnegative numbers
Abstract algebra
The simplest equations to solve
47. An operation of arity k is called a
k-ary operation
domain
commutative law of Addition
Expressions
48. In which abstract algebraic methods are used to study combinatorial questions.
an operation
Algebraic combinatorics
The purpose of using variables
Algebra
49. Is an algebraic 'sentence' containing an unknown quantity.
range
Polynomials
radical equation
scalar
50. Is Written as ab or a^b
transitive
Addition
nonnegative numbers
Exponentiation