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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.
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. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
inverse operation of Exponentiation
system of linear equations
The relation of equality (=)
Identity
2. Can be added and subtracted.
Vectors
Operations on sets
All quadratic equations
The relation of equality (=)'s property
3. 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
finitary operation
exponential equation
associative law of addition
substitution
4. Is called the type or arity of the operation
The relation of equality (=)'s property
the fixed non-negative integer k (the number of arguments)
finitary operation
Identity element of Multiplication
5. Is an equation involving derivatives.
A differential equation
Reunion of broken parts
A Diophantine equation
Expressions
6. k-ary operation is a
identity element of addition
The sets Xk
Associative law of Exponentiation
(k+1)-ary relation that is functional on its first k domains
7. 0 - which preserves numbers: a + 0 = a
The operation of addition
Properties of equality
Number line or real line
identity element of addition
8. An operation of arity zero is simply an element of the codomain Y - called a
The real number system
Binary operations
Pure mathematics
nullary operation
9. 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
Solving the Equation
Equation Solving
The sets Xk
10. If a < b and c > 0
then ac < bc
substitution
inverse operation of Exponentiation
equation
11. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
Number line or real line
A differential equation
The central technique to linear equations
12. The operation of exponentiation means ________________: a^n = a
An operation ?
Repeated multiplication
Identities
Operations on sets
13. Is an equation of the form aX = b for a > 0 - which has solution
Linear algebra
commutative law of Exponentiation
commutative law of Addition
exponential equation
14. In which properties common to all algebraic structures are studied
unary and binary
commutative law of Multiplication
Categories of Algebra
Universal algebra
15. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
Order of Operations
A solution or root of the equation
scalar
16. b = b
reflexive
Quadratic equations can also be solved
Multiplication
domain
17. Subtraction ( - )
The logical values true and false
inverse operation of addition
(k+1)-ary relation that is functional on its first k domains
Quadratic equations can also be solved
18. Involve only one value - such as negation and trigonometric functions.
Unary operations
then bc < ac
symmetric
Rotations
19. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
Conditional equations
Constants
symmetric
20. 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
equation
Elimination method
Repeated multiplication
Repeated addition
21. If a < b and c < 0
two inputs
then bc < ac
system of linear equations
The relation of inequality (<) has this property
22. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
Properties of equality
then bc < ac
then ac < bc
23. Are denoted by letters at the beginning - a - b - c - d - ...
then a < c
Algebra
Knowns
The relation of equality (=) has the property
24. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Identity element of Multiplication
radical equation
The method of equating the coefficients
Operations
25. The operation of multiplication means _______________: a
Repeated addition
then a + c < b + d
scalar
exponential equation
26. There are two common types of operations:
A polynomial equation
identity element of Exponentiation
inverse operation of addition
unary and binary
27. 1 - which preserves numbers: a
Equation Solving
commutative law of Exponentiation
unary and binary
Identity element of Multiplication
28. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The relation of equality (=)'s property
The relation of equality (=)
unary and binary
Solution to the system
29. Is Written as ab or a^b
Exponentiation
The simplest equations to solve
commutative law of Exponentiation
Identities
30. In which the specific properties of vector spaces are studied (including matrices)
Operations
Linear algebra
Difference of two squares - or the difference of perfect squares
Identities
31. Can be combined using logic operations - such as and - or - and not.
then a < c
The logical values true and false
Vectors
Linear algebra
32. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
nonnegative numbers
unary and binary
Order of Operations
Elimination method
33. A binary operation
has arity two
Algebra
Linear algebra
Real number
34. () 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.
symmetric
system of linear equations
Algebra
Operations can involve dissimilar objects
35. 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)
value - result - or output
Identities
The operation of addition
Equations
36. The values for which an operation is defined form a set called its
Number line or real line
Categories of Algebra
A differential equation
domain
37. The inner product operation on two vectors produces a
reflexive
substitution
unary and binary
scalar
38. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Exponentiation
Operations can involve dissimilar objects
the fixed non-negative integer k (the number of arguments)
39. Is an equation of the form log`a^X = b for a > 0 - which has solution
An operation ?
logarithmic equation
Solution to the system
operation
40. 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
Exponentiation
Algebraic number theory
Solution to the system
41. If it holds for all a and b in X that if a is related to b then b is related to a.
inverse operation of addition
has arity two
equation
A binary relation R over a set X is symmetric
42. Is an equation involving integrals.
A solution or root of the equation
Universal algebra
A integral equation
Unknowns
43. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Unary operations
associative law of addition
an operation
44. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
Constants
Knowns
Algebraic equation
45. 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
operation
A polynomial equation
Linear algebra
The method of equating the coefficients
46. 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.
has arity two
exponential equation
Change of variables
an operation
47. If a < b and c < d
then a + c < b + d
Solving the Equation
All quadratic equations
reflexive
48. An operation of arity k is called a
k-ary operation
Variables
Binary operations
commutative law of Multiplication
49. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
The real number system
Number line or real line
Equation Solving
has arity one
50. A unary operation
Operations
A Diophantine equation
has arity one
Expressions