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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. Division ( / )
The relation of equality (=) has the property
scalar
inverse operation of Multiplication
commutative law of Exponentiation
2. 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
Quadratic equations
A linear equation
nullary operation
Elimination method
3. Logarithm (Log)
A integral equation
inverse operation of Exponentiation
Equations
Rotations
4. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The simplest equations to solve
The relation of equality (=)
Equations
The operation of exponentiation
5. Operations can have fewer or more than
logarithmic equation
Identities
two inputs
The purpose of using variables
6. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
A solution or root of the equation
symmetric
domain
7. Will have two solutions in the complex number system - but need not have any in the real number system.
identity element of Exponentiation
All quadratic equations
has arity one
Conditional equations
8. 0 - which preserves numbers: a + 0 = a
identity element of addition
transitive
identity element of Exponentiation
Rotations
9. In which abstract algebraic methods are used to study combinatorial questions.
Repeated addition
value - result - or output
Algebraic combinatorics
The operation of exponentiation
10. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
inverse operation of Exponentiation
identity element of addition
operation
11. 1 - which preserves numbers: a
two inputs
transitive
Conditional equations
Identity element of Multiplication
12. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
identity element of Exponentiation
The simplest equations to solve
Difference of two squares - or the difference of perfect squares
Properties of equality
13. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Properties of equality
All quadratic equations
The purpose of using variables
Solving the Equation
14. 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 relation of equality (=) has the property
The sets Xk
Reflexive relation
15. A unary operation
the set Y
inverse operation of addition
has arity one
The operation of exponentiation
16. If a < b and c < d
Identity
system of linear equations
An operation ?
then a + c < b + d
17. Involve only one value - such as negation and trigonometric functions.
two inputs
Equation Solving
Unary operations
Addition
18. If a < b and b < c
then a < c
system of linear equations
Equations
The central technique to linear equations
19. The values of the variables which make the equation true are the solutions of the equation and can be found through
The real number system
Operations on sets
operands - arguments - or inputs
Equation Solving
20. In which properties common to all algebraic structures are studied
Universal algebra
A linear equation
Variables
range
21. 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.
An operation ?
Universal algebra
Vectors
Change of variables
22. An operation of arity k is called a
k-ary operation
The real number system
identity element of addition
commutative law of Addition
23. 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)
Elementary algebra
two inputs
nullary operation
The operation of addition
24. Is Written as a
commutative law of Multiplication
Reflexive relation
Multiplication
when b > 0
25. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
commutative law of Exponentiation
Exponentiation
Algebraic number theory
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
Elimination method
transitive
Operations on sets
Reunion of broken parts
27. If a < b and c > 0
then ac < bc
operation
Algebraic geometry
Algebra
28. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
nonnegative numbers
Identity element of Multiplication
identity element of Exponentiation
29. 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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30. Can be added and subtracted.
an operation
then a + c < b + d
Vectors
then ac < bc
31. The codomain is the set of real numbers but the range is the
k-ary operation
nonnegative numbers
Algebraic geometry
Unknowns
32. 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'.
nonnegative numbers
Reflexive relation
nullary operation
Solving the Equation
33. Is Written as a + b
The relation of inequality (<) has this property
Addition
The operation of exponentiation
Rotations
34. A
inverse operation of addition
Repeated multiplication
Identities
commutative law of Multiplication
35. 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
domain
when b > 0
Associative law of Exponentiation
Polynomials
36. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The operation of exponentiation
Algebraic geometry
Solution to the system
nullary operation
37. () 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.
The operation of exponentiation
commutative law of Addition
Algebra
A functional equation
38. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
Elementary algebra
radical equation
Difference of two squares - or the difference of perfect squares
39. Is the claim that two expressions have the same value and are equal.
Equations
k-ary operation
logarithmic equation
Knowns
40. Is an equation of the form aX = b for a > 0 - which has solution
A Diophantine equation
exponential equation
Expressions
Elimination method
41. Not commutative a^b?b^a
then ac < bc
commutative law of Exponentiation
The relation of equality (=) has the property
then a < c
42. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Equations
range
the fixed non-negative integer k (the number of arguments)
an operation
43. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
radical equation
Quadratic equations
identity element of Exponentiation
44. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
The method of equating the coefficients
The central technique to linear equations
Abstract algebra
45. 1 - which preserves numbers: a^1 = a
Solution to the system
Change of variables
identity element of Exponentiation
Associative law of Multiplication
46. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
scalar
Expressions
then a < c
Unknowns
47. A + b = b + a
transitive
commutative law of Addition
Identity element of Multiplication
(k+1)-ary relation that is functional on its first k domains
48. Is an equation involving derivatives.
A differential equation
Expressions
Elementary algebra
The operation of exponentiation
49. 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.
Solution to the system
Algebra
Properties of equality
Order of Operations
50. Include composition and convolution
Algebraic equation
A integral equation
range
Operations on functions