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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. 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
Elementary algebra
All quadratic equations
Operations
has arity one
2. 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)
substitution
The operation of exponentiation
Elementary algebra
The operation of addition
3. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Algebraic equation
Number line or real line
(k+1)-ary relation that is functional on its first k domains
The method of equating the coefficients
4. Include composition and convolution
range
Operations on functions
Universal algebra
Equations
5. Is called the codomain of the operation
commutative law of Exponentiation
Repeated multiplication
Polynomials
the set Y
6. Can be defined axiomatically up to an isomorphism
Reunion of broken parts
Equations
then ac < bc
The real number system
7. Is an equation where the unknowns are required to be integers.
A functional equation
A Diophantine equation
Algebraic geometry
the set Y
8. 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
Vectors
A Diophantine equation
The method of equating the coefficients
operation
9. Division ( / )
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.
An operation ?
The operation of exponentiation
inverse operation of Multiplication
10. 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.
Categories of Algebra
The real number system
The central technique to linear equations
Properties of equality
11. 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
Operations on functions
finitary operation
Identity element of Multiplication
12. Are called the domains of the operation
nullary operation
The operation of addition
The sets Xk
associative law of addition
13. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
Quadratic equations
Variables
Operations on sets
14. The operation of multiplication means _______________: a
substitution
Repeated addition
Solving the Equation
symmetric
15. If a < b and c < 0
Universal algebra
Pure mathematics
Constants
then bc < ac
16. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
has arity one
two inputs
Repeated multiplication
17. (a + b) + c = a + (b + c)
has arity one
associative law of addition
unary and binary
Universal algebra
18. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
The operation of exponentiation
Algebraic number theory
The relation of equality (=)
Categories of Algebra
19. An operation of arity zero is simply an element of the codomain Y - called a
Repeated addition
nullary operation
inverse operation of Multiplication
when b > 0
20. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
an operation
A differential equation
the fixed non-negative integer k (the number of arguments)
21. There are two common types of operations:
Repeated addition
value - result - or output
unary and binary
Categories of Algebra
22. If a < b and c < d
A functional equation
then a + c < b + d
Abstract algebra
The real number system
23. Include the binary operations union and intersection and the unary operation of complementation.
A functional equation
range
Unknowns
Operations on sets
24. Is Written as ab or a^b
Exponentiation
reflexive
A linear equation
substitution
25. Is an equation in which the unknowns are functions rather than simple quantities.
An operation ?
A functional equation
Change of variables
nullary operation
26. 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.
Addition
Quadratic equations can also be solved
A Diophantine equation
Change of variables
27. Is an algebraic 'sentence' containing an unknown quantity.
Real number
Algebraic combinatorics
A linear equation
Polynomials
28. 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
radical equation
nonnegative numbers
Equations
Reunion of broken parts
29. Can be added and subtracted.
Conditional equations
then a + c < b + d
Vectors
Quadratic equations can also be solved
30. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The method of equating the coefficients
The relation of equality (=)
A functional equation
Universal algebra
31. The process of expressing the unknowns in terms of the knowns is called
when b > 0
Binary operations
Solving the Equation
The real number system
32. The codomain is the set of real numbers but the range is the
An operation ?
Difference of two squares - or the difference of perfect squares
nonnegative numbers
Multiplication
33. Operations can have fewer or more than
transitive
Real number
Categories of Algebra
two inputs
34. 1 - which preserves numbers: a
Polynomials
Elementary algebra
k-ary operation
Identity element of Multiplication
35. In which properties common to all algebraic structures are studied
The operation of addition
Universal algebra
the set Y
Operations on functions
36. Is Written as a
Multiplication
Operations on functions
Algebra
finitary operation
37. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
Difference of two squares - or the difference of perfect squares
Elimination method
operation
38. 0 - which preserves numbers: a + 0 = a
Algebraic geometry
identity element of addition
A linear equation
Equations
39. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
Quadratic equations
The operation of addition
Rotations
40. 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.
reflexive
The relation of inequality (<) has this property
Properties of equality
Operations on sets
41. A
commutative law of Multiplication
identity element of addition
The operation of addition
Solving the Equation
42. An operation of arity k is called a
inverse operation of Exponentiation
logarithmic equation
Polynomials
k-ary operation
43. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s
substitution
Equation Solving
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.
commutative law of Multiplication
44. Is an equation of the form log`a^X = b for a > 0 - which has solution
Pure mathematics
logarithmic equation
Expressions
reflexive
45. A unary operation
operation
has arity one
A binary relation R over a set X is symmetric
The logical values true and false
46. The inner product operation on two vectors produces a
Elimination method
commutative law of Multiplication
identity element of Exponentiation
scalar
47. Is an equation involving derivatives.
operation
system of linear equations
A differential equation
Operations can involve dissimilar objects
48. 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
A integral equation
when b > 0
The relation of equality (=) has the property
The purpose of using variables
49. Involve only one value - such as negation and trigonometric functions.
nullary operation
Repeated addition
Unary operations
Operations
50. 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)
nonnegative numbers
Multiplication
operation
identity element of addition
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