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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. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
A linear equation
Binary operations
Difference of two squares - or the difference of perfect squares
2. 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.
Real number
Solving the Equation
The relation of inequality (<) has this property
nonnegative numbers
3. Is an equation of the form X^m/n = a - for m - n integers - which has solution
(k+1)-ary relation that is functional on its first k domains
inverse operation of Multiplication
radical equation
scalar
4. Are true for only some values of the involved variables: x2 - 1 = 4.
A functional equation
The operation of addition
Identities
Conditional equations
5. Logarithm (Log)
inverse operation of Exponentiation
Change of variables
Algebraic combinatorics
Elimination method
6. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
A functional equation
Solving the Equation
then a < c
7. An operation of arity zero is simply an element of the codomain Y - called a
substitution
Categories of Algebra
nullary operation
A polynomial equation
8. Is called the codomain of the operation
reflexive
identity element of Exponentiation
Variables
the set Y
9. Involve only one value - such as negation and trigonometric functions.
logarithmic equation
(k+1)-ary relation that is functional on its first k domains
Unary operations
Rotations
10. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The simplest equations to solve
logarithmic equation
then a < c
commutative law of Addition
11. Is Written as a + b
Addition
A integral equation
inverse operation of Exponentiation
Unknowns
12. 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.
Properties of equality
Solution to the system
Equation Solving
Operations on sets
13. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Operations can involve dissimilar objects
Equations
The purpose of using variables
then ac < bc
14. 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).
Variables
Equations
Algebraic combinatorics
Quadratic equations
15. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
identity element of addition
Variables
Addition
The simplest equations to solve
16. Symbols that denote numbers - is to allow the making of generalizations in mathematics
then a + c < b + d
domain
range
The purpose of using variables
17. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
The central technique to linear equations
Universal algebra
when b > 0
Binary operations
18. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Algebraic geometry
Algebraic equation
Unknowns
logarithmic equation
19. Is an equation involving derivatives.
Order of Operations
unary and binary
A differential equation
The relation of inequality (<) has this property
20. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
finitary operation
(k+1)-ary relation that is functional on its first k domains
Unary operations
21. Referring to the finite number of arguments (the value k)
Vectors
An operation ?
Algebra
finitary operation
22. 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
Unknowns
The relation of equality (=)'s property
then a + c < b + d
23. The inner product operation on two vectors produces a
inverse operation of Exponentiation
Properties of equality
Rotations
scalar
24. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
Reunion of broken parts
Reflexive relation
Change of variables
25. Are called the domains of the operation
Associative law of Exponentiation
transitive
The sets Xk
Reunion of broken parts
26. A
Reunion of broken parts
system of linear equations
an operation
commutative law of Multiplication
27. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Expressions
Number line or real line
identity element of Exponentiation
Solving the Equation
28. The values of the variables which make the equation true are the solutions of the equation and can be found through
Reflexive relation
associative law of addition
Equation Solving
The method of equating the coefficients
29. Is an equation involving integrals.
A solution or root of the equation
A integral equation
nullary operation
substitution
30. Operations can have fewer or more than
system of linear equations
finitary operation
Repeated multiplication
two inputs
31. Division ( / )
inverse operation of Multiplication
Properties of equality
Rotations
Addition
32. (a + b) + c = a + (b + c)
associative law of addition
has arity two
Vectors
The relation of equality (=)
33. If a = b then b = a
equation
Operations on functions
A solution or root of the equation
symmetric
34. If a = b and b = c then a = c
associative law of addition
Quadratic equations can also be solved
then a < c
transitive
35. Is an equation in which a polynomial is set equal to another polynomial.
identity element of Exponentiation
inverse operation of Exponentiation
The real number system
A polynomial equation
36. 1 - which preserves numbers: a
Identity element of Multiplication
scalar
an operation
then bc < ac
37. 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)
reflexive
Polynomials
Linear algebra
operation
38. A + b = b + a
Knowns
commutative law of Addition
has arity one
symmetric
39. The process of expressing the unknowns in terms of the knowns is called
reflexive
equation
Addition
Solving the Equation
40. If a < b and b < c
A polynomial equation
inverse operation of Multiplication
then a < c
transitive
41. A binary operation
Number line or real line
Quadratic equations can also be solved
symmetric
has arity two
42. Can be combined using the function composition operation - performing the first rotation and then the second.
Solving the Equation
Multiplication
radical equation
Rotations
43. The operation of exponentiation means ________________: a^n = a
reflexive
Repeated multiplication
radical equation
Reunion of broken parts
44. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Vectors
Exponentiation
Order of Operations
Unary operations
45. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
A Diophantine equation
A solution or root of the equation
The logical values true and false
46. 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)
logarithmic equation
Repeated addition
The operation of addition
commutative law of Addition
47. b = b
A functional equation
reflexive
commutative law of Addition
(k+1)-ary relation that is functional on its first k domains
48. A vector can be multiplied by a scalar to form another vector
then bc < ac
Operations can involve dissimilar objects
The operation of exponentiation
Variables
49. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Elimination method
then a < c
transitive
Solution to the system
50. (a
Associative law of Multiplication
identity element of addition
reflexive
The simplest equations to solve