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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. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
Solution to the system
Algebraic geometry
The logical values true and false
2. In which abstract algebraic methods are used to study combinatorial questions.
The simplest equations to solve
A transcendental equation
Algebraic combinatorics
Solution to the system
3. If a = b then b = a
unary and binary
exponential equation
symmetric
nullary operation
4. The squaring operation only produces
nonnegative numbers
then bc < ac
has arity two
identity element of addition
5. () 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.
then a + c < b + d
Algebra
The method of equating the coefficients
has arity two
6. 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.
substitution
Change of variables
A binary relation R over a set X is symmetric
The simplest equations to solve
7. Is Written as a + b
scalar
The relation of equality (=) has the property
the fixed non-negative integer k (the number of arguments)
Addition
8. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Exponentiation
k-ary operation
Quadratic equations can also be solved
Equations
9. If a < b and c > 0
Identity element of Multiplication
Algebra
then ac < bc
A linear equation
10. Symbols that denote numbers - is to allow the making of generalizations in mathematics
associative law of addition
Change of variables
The purpose of using variables
Addition
11. 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)
nonnegative numbers
finitary operation
The operation of addition
substitution
12. 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
Properties of equality
substitution
A differential equation
finitary operation
13. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
The logical values true and false
Identities
Knowns
two inputs
14. The operation of multiplication means _______________: a
The real number system
Associative law of Exponentiation
Unknowns
Repeated addition
15. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
inverse operation of Exponentiation
Abstract algebra
two inputs
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.
16. Is an algebraic 'sentence' containing an unknown quantity.
The relation of equality (=) has the property
Exponentiation
Operations on functions
Polynomials
17. If a < b and c < 0
then bc < ac
An operation ?
reflexive
Operations can involve dissimilar objects
18. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Equation Solving
associative law of addition
Solution to the system
Rotations
19. A unary operation
Identities
A polynomial equation
The relation of equality (=) has the property
has arity one
20. 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
the fixed non-negative integer k (the number of arguments)
domain
Algebraic number theory
21. Subtraction ( - )
The operation of addition
The relation of equality (=)
Algebraic number theory
inverse operation of addition
22. The process of expressing the unknowns in terms of the knowns is called
A linear equation
Solving the Equation
Polynomials
The relation of equality (=) has the property
23. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.
Repeated multiplication
operation
has arity one
The relation of inequality (<) has this property
24. (a
Addition
Associative law of Multiplication
Conditional equations
The operation of exponentiation
25. b = b
unary and binary
the set Y
reflexive
Change of variables
26. 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
Pure mathematics
operation
Change of variables
Elementary algebra
27. Is an equation involving integrals.
A integral equation
Order of Operations
Quadratic equations can also be solved
The relation of equality (=) has the property
28. Is an action or procedure which produces a new value from one or more input values.
exponential equation
Quadratic equations can also be solved
an operation
Equations
29. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
Equation Solving
Associative law of Multiplication
The operation of addition
30. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
nonnegative numbers
Number line or real line
scalar
Order of Operations
31. 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
Categories of Algebra
Reunion of broken parts
32. 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.
commutative law of Exponentiation
identity element of Exponentiation
A transcendental equation
The central technique to linear equations
33. May not be defined for every possible value.
A polynomial equation
k-ary operation
Operations
Variables
34. Is an equation of the form X^m/n = a - for m - n integers - which has solution
The logical values true and false
radical equation
Algebraic geometry
A Diophantine equation
35. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
then ac < bc
domain
Quadratic equations can also be solved
Operations on functions
36. 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.
The operation of exponentiation
Properties of equality
A transcendental equation
has arity one
37. Not commutative a^b?b^a
Algebraic combinatorics
commutative law of Exponentiation
Associative law of Multiplication
All quadratic equations
38. The values of the variables which make the equation true are the solutions of the equation and can be found through
Knowns
domain
Exponentiation
Equation Solving
39. Applies abstract algebra to the problems of geometry
The purpose of using variables
exponential equation
Algebraic geometry
Reunion of broken parts
40. 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.
transitive
The relation of equality (=)
The relation of equality (=) has the property
the set Y
41. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
The sets Xk
Conditional equations
Unknowns
42. Is an equation of the form log`a^X = b for a > 0 - which has solution
Properties of equality
All quadratic equations
Solving the Equation
logarithmic equation
43. 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)
The operation of exponentiation
value - result - or output
then ac < bc
The relation of inequality (<) has this property
44. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
value - result - or output
has arity two
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.
45. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
substitution
Algebraic combinatorics
Binary operations
Properties of equality
46. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Solving the Equation
Repeated multiplication
value - result - or output
Categories of Algebra
47. k-ary operation is a
Abstract algebra
(k+1)-ary relation that is functional on its first k domains
identity element of addition
then bc < ac
48. The operation of exponentiation means ________________: a^n = 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.
Associative law of Multiplication
Repeated multiplication
identity element of addition
49. Is Written as ab or a^b
k-ary operation
Rotations
Exponentiation
Constants
50. Not associative
Associative law of Exponentiation
exponential equation
A linear equation
A transcendental equation