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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. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Pure mathematics
Variables
The method of equating the coefficients
nonnegative numbers
2. Is Written as ab or a^b
Solution to the system
Operations
Exponentiation
A linear equation
3. Letters from the beginning of the alphabet like a - b - c... often denote
two inputs
Constants
The sets Xk
Equation Solving
4. The values for which an operation is defined form a set called its
All quadratic equations
Constants
operands - arguments - or inputs
domain
5. A + b = b + a
Repeated multiplication
Abstract algebra
has arity two
commutative law of Addition
6. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
The real number system
The relation of equality (=)'s property
system of linear equations
Universal algebra
7. Is Written as a
Real number
Multiplication
Binary operations
Algebraic number theory
8. Referring to the finite number of arguments (the value k)
nullary operation
finitary operation
The real number system
then a < c
9. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
reflexive
The method of equating the coefficients
the set Y
10. Is an equation of the form log`a^X = b for a > 0 - which has solution
inverse operation of Multiplication
Unary operations
logarithmic equation
A functional equation
11. k-ary operation is a
Number line or real line
Algebraic geometry
(k+1)-ary relation that is functional on its first k domains
Exponentiation
12. 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
Solution to the system
Real number
finitary operation
Equations
13. 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
The method of equating the coefficients
Conditional equations
A integral equation
(k+1)-ary relation that is functional on its first k domains
14. If it holds for all a and b in X that if a is related to b then b is related to a.
Solving the Equation
Equation Solving
when b > 0
A binary relation R over a set X is symmetric
15. Is an equation involving a transcendental function of one of its variables.
Pure mathematics
A transcendental equation
(k+1)-ary relation that is functional on its first k domains
Binary operations
16. (a
then a + c < b + d
Associative law of Multiplication
(k+1)-ary relation that is functional on its first k domains
operands - arguments - or inputs
17. An operation of arity k is called a
Algebraic combinatorics
k-ary operation
Vectors
Solving the Equation
18. Not associative
Associative law of Exponentiation
Identity
All quadratic equations
associative law of addition
19. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
commutative law of Addition
The sets Xk
Binary operations
Change of variables
20. Is an equation where the unknowns are required to be integers.
Algebra
Identity element of Multiplication
A Diophantine equation
Operations on sets
21. 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)
Equations
transitive
operation
Exponentiation
22. Is an equation involving integrals.
The relation of inequality (<) has this property
Quadratic equations can also be solved
Variables
A integral equation
23. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
system of linear equations
Associative law of Multiplication
Difference of two squares - or the difference of perfect squares
reflexive
24. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Reflexive relation
Number line or real line
Conditional equations
The operation of addition
25. Operations can have fewer or more than
has arity one
A integral equation
A transcendental equation
two inputs
26. Include composition and convolution
operands - arguments - or inputs
Algebraic equation
Operations on functions
The operation of addition
27. In which properties common to all algebraic structures are studied
range
nonnegative numbers
Universal algebra
substitution
28. In which the specific properties of vector spaces are studied (including matrices)
Operations on sets
Linear algebra
A differential equation
Algebraic equation
29. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
The central technique to linear equations
inverse operation of Exponentiation
Expressions
30. If a < b and b < c
Unknowns
Operations on sets
then a < c
substitution
31. Can be combined using the function composition operation - performing the first rotation and then the second.
nonnegative numbers
Reflexive relation
Variables
Rotations
32. Is an equation of the form aX = b for a > 0 - which has solution
commutative law of Exponentiation
Operations on sets
exponential equation
Universal algebra
33. An operation of arity zero is simply an element of the codomain Y - called a
Abstract algebra
A functional equation
nullary operation
identity element of Exponentiation
34. 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
Multiplication
Identity
A binary relation R over a set X is symmetric
35. The values combined are called
operands - arguments - or inputs
Solving the Equation
k-ary operation
finitary operation
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 multiplication
The central technique to linear equations
Algebraic geometry
Vectors
37. 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.
substitution
Properties of equality
Abstract algebra
inverse operation of addition
38. A
Identities
Elementary algebra
commutative law of Multiplication
Operations
39. The codomain is the set of real numbers but the range is the
commutative law of Exponentiation
nonnegative numbers
equation
(k+1)-ary relation that is functional on its first k domains
40. The inner product operation on two vectors produces a
k-ary operation
the set Y
Real number
scalar
41. The process of expressing the unknowns in terms of the knowns is called
Rotations
A functional equation
commutative law of Multiplication
Solving the Equation
42. If a < b and c > 0
logarithmic equation
The relation of equality (=)'s property
k-ary operation
then ac < bc
43. 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
has arity one
operation
A linear equation
44. 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)
associative law of addition
The operation of addition
Conditional equations
commutative law of Addition
45. May not be defined for every possible value.
A integral equation
Operations
The simplest equations to solve
Order of Operations
46. () 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 relation of equality (=) has the property
nonnegative numbers
exponential equation
Algebra
47. Is called the codomain of the operation
then ac < bc
the set Y
The relation of equality (=) has the property
The relation of equality (=)
48. Are true for only some values of the involved variables: x2 - 1 = 4.
inverse operation of Exponentiation
Conditional equations
Solving the Equation
A Diophantine equation
49. Is called the type or arity of the operation
A Diophantine equation
value - result - or output
the fixed non-negative integer k (the number of arguments)
Algebraic geometry
50. In an equation with a single unknown - a value of that unknown for which the equation is true is called
commutative law of Exponentiation
operation
reflexive
A solution or root of the equation
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