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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. The value produced is called
An operation ?
two inputs
Properties of equality
value - result - or output
2. 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
Algebraic equation
two inputs
Quadratic equations can also be solved
Elementary algebra
3. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
Algebraic equation
k-ary operation
Number line or real line
4. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
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.
operation
commutative law of Exponentiation
Quadratic equations can also be solved
5. 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
Repeated multiplication
The method of equating the coefficients
Repeated addition
A differential equation
6. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
A functional equation
identity element of addition
The relation of equality (=)'s property
7. 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
A solution or root of the equation
commutative law of Multiplication
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.
8. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Change of variables
The simplest equations to solve
Pure mathematics
The relation of equality (=)
9. Not commutative a^b?b^a
commutative law of Exponentiation
An operation ?
Number line or real line
The purpose of using variables
10. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
operation
Operations on functions
Operations on sets
11. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
commutative law of Multiplication
(k+1)-ary relation that is functional on its first k domains
The relation of equality (=)
then bc < ac
12. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
symmetric
radical equation
Elementary algebra
13. Can be defined axiomatically up to an isomorphism
nonnegative numbers
Identity
Categories of Algebra
The real number system
14. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
The simplest equations to solve
k-ary operation
An operation ?
15. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
The purpose of using variables
logarithmic equation
associative law of addition
16. If a < b and b < c
Solving the Equation
Repeated multiplication
logarithmic equation
then a < c
17. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
Elimination method
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 linear equation
18. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Abstract algebra
Quadratic equations
Algebraic combinatorics
Unknowns
19. 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 transcendental equation
nonnegative numbers
operation
Operations on sets
20. The values combined are called
Operations on functions
operands - arguments - or inputs
Algebra
Pure mathematics
21. 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
Categories of Algebra
The real number system
Expressions
22. In which abstract algebraic methods are used to study combinatorial questions.
has arity two
Algebraic combinatorics
identity element of Exponentiation
The relation of equality (=)'s property
23. Is Written as a
Unknowns
commutative law of Multiplication
Associative law of Multiplication
Multiplication
24. In which properties common to all algebraic structures are studied
Unknowns
Expressions
Solving the Equation
Universal algebra
25. 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
identity element of Exponentiation
operands - arguments - or inputs
finitary operation
Real number
26. 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
Equations
Elimination method
A transcendental equation
Reunion of broken parts
27. If a = b then b = a
identity element of Exponentiation
Solution to the system
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.
symmetric
28. Applies abstract algebra to the problems of geometry
Algebraic geometry
identity element of Exponentiation
A polynomial equation
operation
29. If a < b and c > 0
when b > 0
then ac < bc
Algebraic number theory
Variables
30. 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.
An operation ?
The real number system
A polynomial equation
The relation of inequality (<) has this property
31. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Universal algebra
The relation of equality (=)
Binary operations
A integral equation
32. The values for which an operation is defined form a set called its
domain
inverse operation of Exponentiation
Addition
Unary operations
33. 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
operation
Equations
scalar
34. 1 - which preserves numbers: a^1 = a
Change of variables
Equations
identity element of Exponentiation
system of linear equations
35. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
operation
Elimination method
Vectors
36. The inner product operation on two vectors produces a
scalar
Repeated addition
Multiplication
Identity
37. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.
Reflexive relation
nonnegative numbers
Repeated multiplication
The sets Xk
38. 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
Binary operations
Abstract algebra
radical equation
39. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Constants
Multiplication
Addition
The purpose of using variables
40. Is Written as a + b
Elimination method
Addition
A solution or root of the equation
logarithmic equation
41. Is the claim that two expressions have the same value and are equal.
Algebraic geometry
then ac < bc
Identity element of Multiplication
Equations
42. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A solution or root of the equation
nonnegative numbers
The operation of addition
the set Y
43. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
the set Y
Algebraic equation
commutative law of Addition
exponential equation
44. Is an equation involving a transcendental function of one of its variables.
Operations on sets
A transcendental equation
Associative law of Exponentiation
radical equation
45. Can be combined using logic operations - such as and - or - and not.
The relation of inequality (<) has this property
has arity two
Elimination method
The logical values true and false
46. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
The central technique to linear equations
range
then ac < bc
Operations
47. Can be combined using the function composition operation - performing the first rotation and then the second.
inverse operation of addition
Rotations
the set Y
The relation of equality (=)
48. If a < b and c < 0
Properties of equality
Reflexive relation
Identities
then bc < ac
49. Referring to the finite number of arguments (the value k)
Repeated multiplication
Solution to the system
The central technique to linear equations
finitary operation
50. 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
when b > 0
Universal algebra
Equations
equation