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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. Are denoted by letters at the beginning - a - b - c - d - ...
Equations
Elementary algebra
operation
Knowns
2. 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
commutative law of Exponentiation
The relation of inequality (<) has this property
Addition
3. If a < b and b < c
Change of variables
Universal algebra
then a < c
Vectors
4. Is Written as ab or a^b
Exponentiation
The logical values true and false
substitution
transitive
5. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Universal algebra
two inputs
Solution to the system
A solution or root of the equation
6. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Number line or real line
Equations
unary and binary
Addition
7. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
associative law of addition
Constants
Abstract algebra
identity element of Exponentiation
8. An operation of arity zero is simply an element of the codomain Y - called a
range
The operation of addition
nullary operation
an operation
9. () 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
reflexive
Conditional equations
Addition
10. Is an action or procedure which produces a new value from one or more input values.
an operation
unary and binary
The relation of inequality (<) has this property
then a + c < b + d
11. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
the set Y
Equations
Binary operations
operands - arguments - or inputs
12. 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
The method of equating the coefficients
Variables
value - result - or output
Repeated addition
13. 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.
The real number system
Operations on functions
The central technique to linear equations
Algebraic equation
14. A binary operation
value - result - or output
has arity two
Conditional equations
operation
15. Can be defined axiomatically up to an isomorphism
Repeated multiplication
Change of variables
Real number
The real number system
16. If a < b and c > 0
then ac < bc
Repeated addition
Reflexive relation
Operations on sets
17. 0 - which preserves numbers: a + 0 = a
commutative law of Addition
Unknowns
Expressions
identity element of addition
18. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
an operation
The method of equating the coefficients
Identities
radical equation
19. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Identities
Order of Operations
Algebraic number theory
Equations
20. 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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21. If it holds for all a and b in X that if a is related to b then b is related to a.
Algebraic geometry
A binary relation R over a set X is symmetric
A polynomial equation
The relation of equality (=)
22. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
The sets Xk
Linear algebra
Identity
Elimination method
23. Symbols that denote numbers - is to allow the making of generalizations in mathematics
All quadratic equations
The purpose of using variables
Change of variables
Equations
24. Not commutative a^b?b^a
commutative law of Exponentiation
A linear equation
Universal algebra
Variables
25. 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).
A solution or root of the equation
operation
The method of equating the coefficients
Vectors
26. Is Written as a + b
Equations
Addition
Operations on functions
reflexive
27. Is the claim that two expressions have the same value and are equal.
range
identity element of Exponentiation
Equations
Associative law of Multiplication
28. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
The method of equating the coefficients
nullary operation
Expressions
system of linear equations
29. If a < b and c < d
A differential equation
Quadratic equations
then a + c < b + d
Solution to the system
30. 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
Operations on sets
Elementary algebra
Operations
Repeated addition
31. Referring to the finite number of arguments (the value k)
A functional equation
inverse operation of Multiplication
two inputs
finitary operation
32. The values combined are called
Algebraic equation
An operation ?
Algebraic combinatorics
operands - arguments - or inputs
33. 1 - which preserves numbers: a^1 = a
Categories of Algebra
then a < c
identity element of Exponentiation
associative law of addition
34. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
The relation of equality (=)
A functional equation
Elimination method
Quadratic equations can also be solved
35. (a + b) + c = a + (b + c)
system of linear equations
the set Y
Elimination method
associative law of addition
36. 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
Associative law of Multiplication
Elimination method
The real number system
Equations
37. 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).
The logical values true and false
Properties of equality
then a < c
Quadratic equations
38. 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.
Repeated addition
Change of variables
All quadratic equations
Conditional equations
39. 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 relation of equality (=)'s property
The sets Xk
Change of variables
The operation of addition
40. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Vectors
Operations can involve dissimilar objects
identity element of addition
41. The codomain is the set of real numbers but the range is the
Real number
nonnegative numbers
Change of variables
The relation of inequality (<) has this property
42. 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 set Y
Exponentiation
reflexive
operation
43. May not be defined for every possible value.
Operations can involve dissimilar objects
The relation of equality (=)
Operations
Constants
44. Is called the codomain of the operation
the fixed non-negative integer k (the number of arguments)
Repeated addition
the set Y
Difference of two squares - or the difference of perfect squares
45. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
k-ary operation
when b > 0
Vectors
46. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
the set Y
Operations can involve dissimilar objects
Solving the 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.
47. The values for which an operation is defined form a set called its
domain
The method of equating the coefficients
Conditional equations
Repeated addition
48. Are called the domains of the operation
The operation of addition
A integral equation
Properties of equality
The sets Xk
49. Logarithm (Log)
inverse operation of Exponentiation
Linear algebra
Properties of equality
Operations
50. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
the fixed non-negative integer k (the number of arguments)
The relation of inequality (<) has this property
The relation of equality (=)
has arity one