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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. 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 central technique to linear equations
The real number system
Multiplication
The operation of exponentiation
2. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
the fixed non-negative integer k (the number of arguments)
Algebraic number theory
substitution
Quadratic equations can also be solved
3. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
The operation of addition
inverse operation of Multiplication
The relation of inequality (<) has this property
Categories of Algebra
4. If a < b and c < 0
commutative law of Exponentiation
then bc < ac
Number line or real line
identity element of addition
5. (a + b) + c = a + (b + c)
associative law of addition
The relation of equality (=)
Abstract algebra
The real number system
6. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
Algebraic equation
Equations
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.
unary and binary
7. The inner product operation on two vectors produces a
Constants
The real number system
The central technique to linear equations
scalar
8. The squaring operation only produces
Quadratic equations
then a < c
Algebraic number theory
nonnegative numbers
9. Will have two solutions in the complex number system - but need not have any in the real number system.
Identities
an operation
All quadratic equations
The relation of inequality (<) has this property
10. If a < b and c < d
then a + c < b + d
exponential equation
Elementary algebra
The relation of equality (=) has the property
11. A binary operation
Algebraic geometry
The operation of exponentiation
commutative law of Addition
has arity two
12. 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
the fixed non-negative integer k (the number of arguments)
Elimination method
commutative law of Multiplication
when b > 0
13. The operation of multiplication means _______________: a
A solution or root of the equation
Reflexive relation
Repeated addition
A binary relation R over a set X is symmetric
14. Not associative
Associative law of Exponentiation
A polynomial equation
Unary operations
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.
15. 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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16. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Addition
A solution or root of the equation
Solving the Equation
Identity
17. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
Algebra
The operation of addition
Polynomials
18. 1 - which preserves numbers: a^1 = a
A functional equation
then a < c
operation
identity element of Exponentiation
19. Not commutative a^b?b^a
commutative law of Exponentiation
nonnegative numbers
All quadratic equations
A Diophantine equation
20. A + b = b + a
two inputs
inverse operation of addition
A functional equation
commutative law of Addition
21. Can be combined using logic operations - such as and - or - and not.
Algebra
A integral equation
The logical values true and false
Change of variables
22. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
The purpose of using variables
Number line or real line
Algebraic combinatorics
The relation of equality (=) has the property
23. Can be added and subtracted.
Vectors
logarithmic equation
The relation of equality (=)'s property
An operation ?
24. In an equation with a single unknown - a value of that unknown for which the equation is true is called
system of linear equations
has arity two
A solution or root of the equation
Operations on functions
25. 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).
Quadratic equations
The relation of equality (=)'s property
Universal algebra
Identities
26. Is an equation involving integrals.
A integral equation
Solution to the system
Abstract algebra
Solving the Equation
27. The codomain is the set of real numbers but the range is the
range
Identities
nonnegative numbers
the set Y
28. 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)
Operations can involve dissimilar objects
Rotations
The operation of addition
Algebraic equation
29. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Change of variables
A Diophantine equation
Difference of two squares - or the difference of perfect squares
then ac < bc
30. Are true for only some values of the involved variables: x2 - 1 = 4.
scalar
Conditional equations
then bc < ac
The relation of equality (=) has the property
31. There are two common types of operations:
A functional equation
The relation of equality (=) has the property
unary and binary
Reflexive relation
32. Is called the codomain of the operation
finitary operation
the set Y
Algebraic combinatorics
Algebra
33. 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.
Algebraic equation
The relation of equality (=) has the property
Categories of Algebra
domain
34. 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.
Pure mathematics
Rotations
Change of variables
Elimination method
35. If a = b and b = c then a = c
transitive
the set Y
commutative law of Multiplication
Polynomials
36. (a
Vectors
The central technique to linear equations
A binary relation R over a set X is symmetric
Associative law of Multiplication
37. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Universal algebra
radical equation
Identity element of Multiplication
A transcendental equation
38. Logarithm (Log)
Equations
Universal algebra
logarithmic equation
inverse operation of Exponentiation
39. 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
Unknowns
Identity element of Multiplication
The relation of inequality (<) has this property
40. Referring to the finite number of arguments (the value k)
equation
finitary operation
when b > 0
The purpose of using variables
41. 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
k-ary operation
the set Y
Reunion of broken parts
A polynomial equation
42. Can be defined axiomatically up to an isomorphism
system of linear equations
then ac < bc
The real number system
The relation of equality (=) has the property
43. 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 relation of inequality (<) has this property
The central technique to linear equations
Pure mathematics
44. Include the binary operations union and intersection and the unary operation of complementation.
Algebraic number theory
The simplest equations to solve
Operations on sets
A functional equation
45. May not be defined for every possible value.
finitary operation
exponential equation
Operations
Equations
46. Applies abstract algebra to the problems of geometry
Algebraic geometry
A transcendental equation
The central technique to linear equations
Number line or real line
47. Can be combined using the function composition operation - performing the first rotation and then the second.
The relation of inequality (<) has this property
nonnegative numbers
Rotations
Reunion of broken parts
48. The values combined are called
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.
operands - arguments - or inputs
Associative law of Exponentiation
Identity element of Multiplication
49. () 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
transitive
Constants
An operation ?
50. If it holds for all a and b in X that if a is related to b then b is related to a.
Constants
nonnegative numbers
Solution to the system
A binary relation R over a set X is symmetric