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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. Is an equation where the unknowns are required to be integers.
A Diophantine equation
The purpose of using variables
A integral equation
associative law of addition
2. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Equation Solving
Linear algebra
Algebra
3. If a < b and c < d
Change of variables
exponential equation
A solution or root of the equation
then a + c < b + d
4. Referring to the finite number of arguments (the value k)
finitary operation
The central technique to linear equations
commutative law of Exponentiation
Universal algebra
5. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
Quadratic equations can also be solved
then bc < ac
The sets Xk
6. Operations can have fewer or more than
A differential equation
The logical values true and false
Conditional equations
two inputs
7. Can be added and subtracted.
commutative law of Exponentiation
Difference of two squares - or the difference of perfect squares
Vectors
Universal algebra
8. Include composition and convolution
Quadratic equations can also be solved
inverse operation of addition
Associative law of Exponentiation
Operations on functions
9. An operation of arity k is called a
Number line or real line
k-ary operation
Universal algebra
Algebraic equation
10. Is an equation involving integrals.
Equations
A integral equation
then bc < ac
finitary operation
11. 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 one
Elimination method
A linear equation
The relation of inequality (<) has this property
12. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Algebraic number theory
operation
Unknowns
A linear equation
13. Is called the type or arity of the operation
Universal algebra
A transcendental equation
Difference of two squares - or the difference of perfect squares
the fixed non-negative integer k (the number of arguments)
14. Is an equation involving derivatives.
A differential equation
k-ary operation
identity element of Exponentiation
Real number
15. The codomain is the set of real numbers but the range is the
Solution to the system
Identity element of Multiplication
nonnegative numbers
The sets Xk
16. Not associative
A functional equation
Identities
The relation of inequality (<) has this property
Associative law of Exponentiation
17. A vector can be multiplied by a scalar to form another vector
Repeated multiplication
Operations can involve dissimilar objects
(k+1)-ary relation that is functional on its first k domains
Unknowns
18. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
substitution
associative law of addition
Algebraic number theory
Expressions
19. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Repeated addition
All quadratic equations
The simplest equations to solve
The relation of inequality (<) has this property
20. Are denoted by letters at the beginning - a - b - c - d - ...
Properties of equality
Variables
A binary relation R over a set X is symmetric
Knowns
21. 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.
The purpose of using variables
Algebraic equation
Properties of equality
Algebraic geometry
22. If a = b and b = c then a = c
transitive
Operations on sets
Vectors
The method of equating the coefficients
23. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
The operation of addition
A Diophantine equation
Reflexive relation
24. 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 simplest equations to solve
then a < c
The central technique to linear equations
scalar
25. Is Written as a + b
The relation of equality (=)'s property
Algebra
Addition
the fixed non-negative integer k (the number of arguments)
26. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Vectors
Associative law of Exponentiation
Linear algebra
Quadratic equations can also be solved
27. Letters from the beginning of the alphabet like a - b - c... often denote
Properties of equality
Equation Solving
Constants
value - result - or output
28. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
domain
Associative law of Multiplication
Real number
29. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Difference of two squares - or the difference of perfect squares
radical equation
Polynomials
commutative law of Multiplication
30. k-ary operation is a
The relation of equality (=) has the property
(k+1)-ary relation that is functional on its first k domains
exponential equation
The central technique to linear equations
31. 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)
Repeated addition
Variables
The operation of addition
Associative law of Multiplication
32. (a + b) + c = a + (b + c)
value - result - or output
associative law of addition
domain
Linear algebra
33. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Vectors
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.
Solution to the system
range
34. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
the set Y
exponential equation
an operation
35. 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.
Properties of equality
The relation of equality (=) has the property
Algebraic geometry
operation
36. Is called the codomain of the operation
Elementary algebra
the set Y
nullary operation
Change of variables
37. Subtraction ( - )
inverse operation of addition
All quadratic equations
Solution to the system
operation
38. The operation of exponentiation means ________________: a^n = a
A functional equation
reflexive
Addition
Repeated multiplication
39. Applies abstract algebra to the problems of geometry
system of linear equations
operation
Associative law of Exponentiation
Algebraic geometry
40. 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)
Quadratic equations can also be solved
operation
Reunion of broken parts
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.
41. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Equation Solving
system of linear equations
Properties of equality
two inputs
42. Not commutative a^b?b^a
Reflexive relation
The relation of inequality (<) has this property
The central technique to linear equations
commutative law of Exponentiation
43. May not be defined for every possible value.
Operations
Expressions
radical equation
unary and binary
44. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
Expressions
equation
finitary operation
45. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
associative law of addition
Number line or real line
Equations
Change of variables
46. 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
Operations can involve dissimilar objects
finitary operation
Repeated multiplication
47. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Operations on functions
Properties of equality
A solution or root of the equation
has arity one
48. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
Identity
Associative law of Multiplication
transitive
49. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
A differential equation
value - result - or output
Order of Operations
50. The inner product operation on two vectors produces a
A polynomial equation
identity element of Exponentiation
Elimination method
scalar
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