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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. 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
Binary operations
Algebraic combinatorics
Elementary algebra
Number line or real line
2. An operation of arity k is called a
k-ary operation
system of linear equations
Equations
inverse operation of addition
3. The values for which an operation is defined form a set called its
domain
substitution
Algebraic number theory
The sets Xk
4. In which abstract algebraic methods are used to study combinatorial questions.
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.
k-ary operation
Operations on sets
Algebraic combinatorics
5. Subtraction ( - )
Polynomials
inverse operation of addition
system of linear equations
All quadratic equations
6. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
A differential equation
A integral equation
A functional equation
7. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
The relation of equality (=)
k-ary operation
Variables
then bc < ac
8. Is an equation of the form log`a^X = b for a > 0 - which has solution
Identity element of Multiplication
radical equation
logarithmic equation
The purpose of using variables
9. 1 - which preserves numbers: a
Identity element of Multiplication
Order of Operations
Vectors
Equations
10. The values of the variables which make the equation true are the solutions of the equation and can be found through
Identity
Unary operations
Equation Solving
A polynomial equation
11. 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.
All quadratic equations
Linear algebra
Order of Operations
12. () 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.
Repeated addition
Linear algebra
Operations
Algebra
13. The operation of multiplication means _______________: a
the fixed non-negative integer k (the number of arguments)
Knowns
Repeated addition
Categories of Algebra
14. A unary operation
The relation of equality (=)'s property
Operations on functions
has arity one
Rotations
15. Is algebraic equation of degree one
Abstract algebra
radical equation
A linear equation
A polynomial equation
16. 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
unary and binary
Algebraic number theory
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.
17. If a < b and c > 0
Identities
then ac < bc
Conditional equations
Pure mathematics
18. 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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19. b = b
Algebra
reflexive
The relation of inequality (<) has this property
Vectors
20. 0 - which preserves numbers: a + 0 = a
The real number system
A Diophantine equation
identity element of addition
Solving the Equation
21. Is an action or procedure which produces a new value from one or more input values.
Reflexive relation
The sets Xk
an operation
then a < c
22. 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
Real number
then a < c
radical equation
equation
23. 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.
The relation of equality (=) has the property
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.
Difference of two squares - or the difference of perfect squares
Algebraic combinatorics
24. The squaring operation only produces
Repeated addition
(k+1)-ary relation that is functional on its first k domains
nonnegative numbers
Vectors
25. There are two common types of operations:
operation
unary and binary
symmetric
Reflexive relation
26. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
nullary operation
A integral equation
Algebraic equation
Identities
27. 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)
The operation of addition
Categories of Algebra
Real number
reflexive
28. Is the claim that two expressions have the same value and are equal.
The relation of inequality (<) has this property
The relation of equality (=)'s property
Equations
Elimination method
29. 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
inverse operation of addition
A Diophantine equation
when b > 0
30. Referring to the finite number of arguments (the value k)
Categories of Algebra
finitary operation
scalar
has arity one
31. k-ary operation is a
nullary operation
then bc < ac
(k+1)-ary relation that is functional on its first k domains
A linear equation
32. Operations can have fewer or more than
Multiplication
two inputs
value - result - or output
A linear equation
33. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Solution to the system
then a < c
then a + c < b + d
Exponentiation
34. Not commutative a^b?b^a
Rotations
Pure mathematics
commutative law of Exponentiation
The operation of addition
35. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
Algebraic equation
Operations on functions
A polynomial equation
36. The value produced is called
value - result - or output
Algebraic equation
Elementary algebra
Identity
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
scalar
when b > 0
Identities
Properties of equality
38. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Identities
Order of Operations
Linear algebra
k-ary operation
39. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
when b > 0
Algebraic equation
Associative law of Multiplication
Vectors
40. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
operation
A polynomial equation
range
The relation of equality (=)
41. A
then a < c
commutative law of Multiplication
An operation ?
identity element of Exponentiation
42. Are true for only some values of the involved variables: x2 - 1 = 4.
Elimination method
Conditional equations
A solution or root of the equation
Algebraic geometry
43. Is an equation involving a transcendental function of one of its variables.
Vectors
A transcendental equation
Real number
nullary operation
44. Are called the domains of the operation
inverse operation of Multiplication
The sets Xk
Algebra
Categories of Algebra
45. If a < b and c < d
A differential equation
then a + c < b + d
value - result - or output
Quadratic equations can also be solved
46. Symbols that denote numbers - is to allow the making of generalizations in mathematics
reflexive
Quadratic equations
operands - arguments - or inputs
The purpose of using variables
47. Are denoted by letters at the beginning - a - b - c - d - ...
reflexive
Knowns
(k+1)-ary relation that is functional on its first k domains
the fixed non-negative integer k (the number of arguments)
48. In which the specific properties of vector spaces are studied (including matrices)
Multiplication
Binary operations
Algebra
Linear algebra
49. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
Operations
substitution
Real number
50. The codomain is the set of real numbers but the range is the
Knowns
The real number system
The relation of equality (=)'s property
nonnegative numbers