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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. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Real number
Associative law of Multiplication
Quadratic equations can also be solved
Difference of two squares - or the difference of perfect squares
2. Applies abstract algebra to the problems of geometry
Algebraic geometry
range
commutative law of Addition
An operation ?
3. Not commutative a^b?b^a
The operation of exponentiation
commutative law of Exponentiation
nonnegative numbers
Associative law of Exponentiation
4. The operation of multiplication means _______________: a
Expressions
Number line or real line
A solution or root of the equation
Repeated addition
5. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
A integral equation
Pure mathematics
Reflexive relation
A differential equation
6. Can be added and subtracted.
Unary operations
Repeated addition
nonnegative numbers
Vectors
7. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Quadratic equations
The relation of equality (=)
Repeated addition
An operation ?
8. Is an equation in which a polynomial is set equal to another polynomial.
A integral equation
Linear algebra
associative law of addition
A polynomial equation
9. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Algebra
unary and binary
The purpose of using variables
Binary operations
10. A + b = b + a
Unary operations
Associative law of Exponentiation
commutative law of Addition
Rotations
11. The values of the variables which make the equation true are the solutions of the equation and can be found through
Reunion of broken parts
Reflexive relation
Number line or real line
Equation Solving
12. May not be defined for every possible value.
Identity element of Multiplication
Operations
The logical values true and false
Elimination method
13. Will have two solutions in the complex number system - but need not have any in the real number system.
Equation Solving
Algebraic equation
All quadratic equations
Operations on functions
14. The inner product operation on two vectors produces a
Vectors
commutative law of Exponentiation
A differential equation
scalar
15. Symbols that denote numbers - is to allow the making of generalizations in mathematics
operands - arguments - or inputs
operation
The purpose of using variables
The logical values true and false
16. Are called the domains of the operation
transitive
Constants
The sets Xk
A transcendental equation
17. In an equation with a single unknown - a value of that unknown for which the equation is true is called
associative law of addition
A solution or root of the equation
The operation of exponentiation
A polynomial equation
18. 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.
The relation of equality (=)
range
A differential equation
19. A unary operation
Algebraic combinatorics
has arity one
The operation of exponentiation
The relation of inequality (<) has this property
20. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Constants
Variables
Difference of two squares - or the difference of perfect squares
finitary operation
21. 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
Difference of two squares - or the difference of perfect squares
Rotations
A transcendental equation
Reunion of broken parts
22. 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.
Operations on sets
Properties of equality
A transcendental equation
Categories of Algebra
23. Is an action or procedure which produces a new value from one or more input values.
unary and binary
The relation of equality (=) has the property
Order of Operations
an operation
24. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
identity element of Exponentiation
identity element of addition
The simplest equations to solve
domain
25. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Change of variables
The sets Xk
Operations on sets
Algebraic equation
26. Is Written as ab or a^b
A transcendental equation
identity element of addition
Exponentiation
The real number system
27. 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
Reflexive relation
Solution to the system
Knowns
28. A
commutative law of Multiplication
operation
Associative law of Exponentiation
Algebraic combinatorics
29. 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
Difference of two squares - or the difference of perfect squares
Binary operations
The method of equating the coefficients
Reflexive relation
30. 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).
inverse operation of Exponentiation
Solution to the system
operation
A Diophantine equation
31. Involve only one value - such as negation and trigonometric functions.
Unary operations
Polynomials
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.
Knowns
32. 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.
Change of variables
radical equation
Vectors
The relation of inequality (<) has this property
33. Is an algebraic 'sentence' containing an unknown quantity.
Repeated addition
radical equation
Polynomials
Order of Operations
34. Include the binary operations union and intersection and the unary operation of complementation.
Conditional equations
Operations on sets
Unknowns
Solving the Equation
35. Can be combined using the function composition operation - performing the first rotation and then the second.
Order of Operations
The real number system
associative law of addition
Rotations
36. 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.
Repeated addition
Operations on functions
The central technique to linear equations
reflexive
37. The values for which an operation is defined form a set called its
domain
nonnegative numbers
then bc < ac
commutative law of Multiplication
38. 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 central technique to linear equations
A differential equation
A integral equation
The operation of exponentiation
39. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Identity
Identity element of Multiplication
range
then bc < ac
40. Is an equation in which the unknowns are functions rather than simple quantities.
operation
an operation
The logical values true and false
A functional equation
41. There are two common types of operations:
unary and binary
Algebraic number theory
Universal algebra
Reflexive relation
42. Referring to the finite number of arguments (the value k)
A binary relation R over a set X is symmetric
finitary operation
radical equation
Reunion of broken parts
43. Include composition and convolution
Solving the Equation
Operations on functions
Quadratic equations can also be solved
commutative law of Addition
44. Is a function of the form ? : V ? Y - where V ? X1
Change of variables
Universal algebra
An 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.
45. If a < b and c > 0
Order of Operations
The purpose of using variables
Quadratic equations
then ac < bc
46. The codomain is the set of real numbers but the range is the
value - result - or output
Identities
Operations on sets
nonnegative numbers
47. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Polynomials
symmetric
Number line or real line
The relation of inequality (<) has this property
48. Is an equation of the form log`a^X = b for a > 0 - which has solution
The sets Xk
operation
logarithmic equation
radical equation
49. Is an equation of the form aX = b for a > 0 - which has solution
equation
exponential equation
Solving the Equation
Difference of two squares - or the difference of perfect squares
50. 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)
Knowns
A transcendental equation
The operation of addition
commutative law of Multiplication