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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. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
Algebraic geometry
operation
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.
2. 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
radical equation
when b > 0
domain
then bc < ac
3. Is an equation involving integrals.
scalar
Algebraic geometry
Quadratic equations can also be solved
A integral equation
4. An operation of arity k is called a
when b > 0
The method of equating the coefficients
Number line or real line
k-ary operation
5. (a + b) + c = a + (b + c)
A integral equation
Repeated addition
Equations
associative law of addition
6. 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'.
reflexive
Conditional equations
Reflexive relation
Categories of Algebra
7. A unary operation
Rotations
A linear equation
The relation of equality (=)'s property
has arity one
8. 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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9. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
when b > 0
A binary relation R over a set X is symmetric
Abstract algebra
Multiplication
10. 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).
operation
Binary operations
The relation of equality (=) has the property
A integral equation
11. Can be defined axiomatically up to an isomorphism
The real number system
The purpose of using variables
Identities
The relation of equality (=) has the property
12. The squaring operation only produces
The logical values true and false
nonnegative numbers
transitive
Reflexive relation
13. 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 Diophantine equation
A functional equation
An operation ?
Properties of equality
14. Include the binary operations union and intersection and the unary operation of complementation.
has arity one
Identity
Operations on sets
Abstract algebra
15. 1 - which preserves numbers: a
Identity element of Multiplication
The sets Xk
Number line or real line
A solution or root of the equation
16. Is an equation involving derivatives.
operation
A differential equation
nullary operation
logarithmic equation
17. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Exponentiation
Operations on functions
commutative law of Addition
The purpose of using variables
18. The values of the variables which make the equation true are the solutions of the equation and can be found through
then ac < bc
commutative law of Multiplication
Operations on functions
Equation Solving
19. Is a function of the form ? : V ? Y - where V ? X1
Binary operations
Rotations
Algebra
An operation ?
20. Is an action or procedure which produces a new value from one or more input values.
an operation
Reflexive relation
All quadratic equations
domain
21. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
The relation of equality (=)'s property
Linear algebra
Identities
Repeated addition
22. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
scalar
Algebra
Solution to the system
Solving the Equation
23. Referring to the finite number of arguments (the value k)
Multiplication
The sets Xk
commutative law of Multiplication
finitary operation
24. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Operations
A solution or root of the equation
inverse operation of Multiplication
25. In which abstract algebraic methods are used to study combinatorial questions.
(k+1)-ary relation that is functional on its first k domains
operation
Algebraic combinatorics
The relation of equality (=)'s property
26. The process of expressing the unknowns in terms of the knowns is called
The method of equating the coefficients
An operation ?
Solving the Equation
Quadratic equations
27. In which the specific properties of vector spaces are studied (including matrices)
Difference of two squares - or the difference of perfect squares
Universal algebra
scalar
Linear algebra
28. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Conditional equations
Solution to the system
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.
Properties of equality
29. Involve only one value - such as negation and trigonometric functions.
Unary operations
A binary relation R over a set X is symmetric
identity element of addition
has arity two
30. 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).
Conditional equations
Quadratic equations
All quadratic equations
Number line or real line
31. Can be added and subtracted.
Rotations
Operations
Vectors
A solution or root of the equation
32. Is Written as ab or a^b
Difference of two squares - or the difference of perfect squares
Exponentiation
then bc < ac
substitution
33. 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
Reflexive relation
Reunion of broken parts
Properties of equality
inverse operation of Multiplication
34. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
Difference of two squares - or the difference of perfect squares
nullary operation
inverse operation of Exponentiation
35. 0 - which preserves numbers: a + 0 = a
commutative law of Multiplication
The logical values true and false
identity element of addition
Unknowns
36. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Elimination method
The relation of equality (=)
Vectors
Unknowns
37. 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)
operation
Algebraic combinatorics
unary and binary
when b > 0
38. Division ( / )
system of linear equations
Unknowns
Universal algebra
inverse operation of Multiplication
39. Operations can have fewer or more than
The simplest equations to solve
Equation Solving
two inputs
nonnegative numbers
40. Will have two solutions in the complex number system - but need not have any in the real number system.
Algebra
All quadratic equations
Difference of two squares - or the difference of perfect squares
associative law of addition
41. Not commutative a^b?b^a
The operation of addition
exponential equation
commutative law of Exponentiation
A polynomial equation
42. () 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.
scalar
Algebra
Solving the Equation
Exponentiation
43. Is an equation of the form X^m/n = a - for m - n integers - which has solution
finitary operation
Quadratic equations can also be solved
radical equation
Difference of two squares - or the difference of perfect squares
44. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Universal algebra
the set Y
inverse operation of addition
45. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Algebraic number theory
Categories of Algebra
Change of variables
unary and binary
46. Subtraction ( - )
commutative law of Multiplication
Conditional equations
inverse operation of addition
domain
47. Is algebraic equation of degree one
when b > 0
substitution
A linear equation
symmetric
48. 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.
An operation ?
The relation of equality (=) has the property
Expressions
The purpose of using variables
49. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
operation
Order of Operations
equation
then ac < bc
50. A vector can be multiplied by a scalar to form another vector
The simplest equations to solve
Operations can involve dissimilar objects
commutative law of Addition
The relation of equality (=) has the property