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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.
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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. Include composition and convolution
Operations on functions
The relation of equality (=)
Solution to the system
The logical values true and false
2. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Addition
identity element of addition
Order of Operations
Change of variables
3. 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.
range
Properties of equality
Repeated addition
The method of equating the coefficients
4. Can be added and subtracted.
An operation ?
Vectors
substitution
Algebraic equation
5. Is Written as ab or a^b
Exponentiation
operation
Difference of two squares - or the difference of perfect squares
Unknowns
6. Include the binary operations union and intersection and the unary operation of complementation.
The operation of exponentiation
operation
Operations on sets
unary and binary
7. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)
substitution
operation
commutative law of Multiplication
Identity
8. 1 - which preserves numbers: a
Binary operations
operation
Identity element of Multiplication
The purpose of using variables
9. Are denoted by letters at the beginning - a - b - c - d - ...
Knowns
commutative law of Exponentiation
commutative law of Addition
symmetric
10. The squaring operation only produces
nonnegative numbers
system of linear equations
range
An operation ?
11. 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.
nullary operation
The central technique to linear 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.
reflexive
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
has arity two
Unknowns
Unary operations
Elimination method
13. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Operations on functions
The simplest equations to solve
Algebraic equation
The purpose of using variables
14. Are called the domains of the operation
Exponentiation
then bc < ac
Change of variables
The sets Xk
15. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
inverse operation of Multiplication
A differential equation
Algebraic number theory
Variables
16. A vector can be multiplied by a scalar to form another vector
Real number
operands - arguments - or inputs
nonnegative numbers
Operations can involve dissimilar objects
17. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Multiplication
Difference of two squares - or the difference of perfect squares
Pure mathematics
Identities
18. Involve only one value - such as negation and trigonometric functions.
Unary operations
commutative law of Addition
Identity
Order of Operations
19. Is an equation involving derivatives.
A differential equation
unary and binary
The logical values true and false
Rotations
20. Will have two solutions in the complex number system - but need not have any in the real number system.
(k+1)-ary relation that is functional on its first k domains
value - result - or output
two inputs
All quadratic equations
21. The values for which an operation is defined form a set called its
Quadratic equations can also be solved
domain
logarithmic equation
has arity two
22. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
The logical values true and false
The real number system
operation
23. (a
The sets Xk
Associative law of Multiplication
Reflexive relation
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.
24. The inner product operation on two vectors produces a
Repeated multiplication
Unary operations
scalar
logarithmic equation
25. A + b = b + a
associative law of addition
operands - arguments - or inputs
commutative law of Addition
operation
26. Is an equation involving a transcendental function of one of its variables.
Equations
A transcendental equation
Difference of two squares - or the difference of perfect squares
Conditional equations
27. 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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28. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
then a < c
Expressions
logarithmic equation
equation
29. () 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.
Repeated multiplication
substitution
Algebra
operation
30. If a < b and b < c
Operations can involve dissimilar objects
Binary operations
then a < c
A functional equation
31. 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
Repeated multiplication
identity element of Exponentiation
when b > 0
Universal algebra
32. Not commutative a^b?b^a
commutative law of Exponentiation
The relation of equality (=) has the property
nonnegative numbers
exponential equation
33. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
Algebraic geometry
Universal algebra
Algebraic number theory
34. 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
The relation of equality (=)'s property
Reunion of broken parts
then ac < bc
Multiplication
35. Is a function of the form ? : V ? Y - where V ? X1
Algebraic geometry
Quadratic equations
domain
An operation ?
36. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
then a + c < b + d
The simplest equations to solve
then a < c
nonnegative numbers
37. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
Repeated multiplication
identity element of Exponentiation
Operations on functions
38. Referring to the finite number of arguments (the value k)
Difference of two squares - or the difference of perfect squares
Exponentiation
finitary operation
Real number
39. 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).
The relation of inequality (<) has this property
Expressions
Categories of Algebra
operation
40. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
A Diophantine equation
Identities
Associative law of Exponentiation
system of linear equations
41. 0 - which preserves numbers: a + 0 = a
Elementary algebra
finitary operation
identity element of addition
The simplest equations to solve
42. In which properties common to all algebraic structures are studied
inverse operation of Exponentiation
Algebra
Universal algebra
symmetric
43. 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)
an operation
The operation of addition
Reflexive relation
identity element of addition
44. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of inequality (<) has this property
Algebraic equation
The relation of equality (=)
inverse operation of addition
45. Not associative
Unknowns
finitary operation
(k+1)-ary relation that is functional on its first k domains
Associative law of Exponentiation
46. If a = b and b = c then a = c
Equation Solving
Operations on functions
transitive
A differential equation
47. Is called the type or arity of the operation
then a + c < b + d
Identity
Expressions
the fixed non-negative integer k (the number of arguments)
48. (a + b) + c = a + (b + c)
then a + c < b + d
Reunion of broken parts
associative law of addition
Algebraic combinatorics
49. Is an equation where the unknowns are required to be integers.
A Diophantine equation
A transcendental equation
Knowns
Operations on sets
50. Can be combined using the function composition operation - performing the first rotation and then the second.
Categories of Algebra
an operation
Identity
Rotations
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