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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
symmetric
The relation of equality (=)'s property
Identity
The operation of exponentiation
2. Is an equation of the form X^m/n = a - for m - n integers - which has solution
commutative law of Exponentiation
Repeated multiplication
radical equation
transitive
3. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
commutative law of Exponentiation
Constants
Abstract algebra
4. 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
All quadratic equations
Real number
The relation of inequality (<) has this property
Properties of equality
5. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
A differential equation
two inputs
Operations
6. Are called the domains of the operation
then bc < ac
Real number
two inputs
The sets Xk
7. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Real number
Elimination method
Quadratic equations can also be solved
Reflexive relation
8. Applies abstract algebra to the problems of geometry
the fixed non-negative integer k (the number of arguments)
Algebraic geometry
Algebraic combinatorics
Knowns
9. Is Written as a
Knowns
Operations on functions
substitution
Multiplication
10. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
Reunion of broken parts
A binary relation R over a set X is symmetric
Exponentiation
11. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
operands - arguments - or inputs
identity element of addition
associative law of addition
12. If a < b and c < d
scalar
then a + c < b + d
Knowns
Unary operations
13. The values of the variables which make the equation true are the solutions of the equation and can be found through
Expressions
the fixed non-negative integer k (the number of arguments)
Equation Solving
has arity two
14. Involve only one value - such as negation and trigonometric functions.
Unary operations
Identity element of Multiplication
Repeated addition
All quadratic equations
15. b = b
domain
Difference of two squares - or the difference of perfect squares
reflexive
Solution to the system
16. Is Written as ab or a^b
A Diophantine equation
Exponentiation
Linear algebra
The relation of equality (=)
17. 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
The relation of equality (=) has the property
then a + c < b + d
Number line or real line
18. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)
Abstract algebra
Algebraic equation
A differential equation
The operation of exponentiation
19. Is Written as a + b
Solution to the system
Addition
symmetric
Operations on functions
20. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Difference of two squares - or the difference of perfect squares
Number line or real line
exponential equation
Solution to the system
21. 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).
The simplest equations to solve
Quadratic equations
Quadratic equations can also be solved
Properties of equality
22. 0 - which preserves numbers: a + 0 = a
identity element of addition
(k+1)-ary relation that is functional on its first k domains
then a < c
Algebraic combinatorics
23. Is an equation involving integrals.
associative law of addition
A integral equation
Equations
The central technique to linear equations
24. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Abstract algebra
The relation of equality (=)
symmetric
Variables
25. Referring to the finite number of arguments (the value k)
Algebraic combinatorics
finitary operation
Repeated multiplication
inverse operation of Multiplication
26. A binary operation
then bc < ac
has arity two
nonnegative numbers
A integral equation
27. Is an equation in which a polynomial is set equal to another polynomial.
Multiplication
nonnegative numbers
The relation of equality (=)'s property
A polynomial equation
28. The values for which an operation is defined form a set called its
Reunion of broken parts
identity element of addition
commutative law of Exponentiation
domain
29. 1 - which preserves numbers: a
A polynomial equation
Operations
then bc < ac
Identity element of Multiplication
30. Not commutative a^b?b^a
commutative law of Exponentiation
operands - arguments - or inputs
then ac < bc
Variables
31. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
Repeated multiplication
A integral equation
Repeated addition
32. 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
operation
substitution
operation
identity element of addition
33. There are two common types of operations:
Reflexive relation
unary and binary
Operations on sets
Operations
34. A + b = b + a
domain
Addition
identity element of Exponentiation
commutative law of Addition
35. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
A polynomial equation
substitution
Unknowns
Properties of equality
36. 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 operation of exponentiation
inverse operation of Exponentiation
Properties of equality
The method of equating the coefficients
37. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
Conditional equations
when b > 0
The central technique to linear equations
38. A unary operation
Reflexive relation
nonnegative numbers
has arity one
The sets Xk
39. A
logarithmic equation
Addition
The real number system
commutative law of Multiplication
40. The values combined are called
operands - arguments - or inputs
value - result - or output
when b > 0
Variables
41. 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
A polynomial equation
Associative law of Multiplication
A Diophantine equation
42. Is an equation involving derivatives.
A differential equation
Elimination method
The relation of equality (=)
nullary operation
43. The value produced is called
Properties of equality
the set Y
value - result - or output
range
44. The codomain is the set of real numbers but the range is the
Expressions
The relation of equality (=) has the property
Algebraic geometry
nonnegative numbers
45. Is an action or procedure which produces a new value from one or more input values.
an operation
Elimination method
Unknowns
Equations
46. In which properties common to all algebraic structures are studied
A solution or root of the equation
Universal algebra
Algebraic combinatorics
has arity two
47. 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
scalar
Constants
when b > 0
Linear algebra
48. Can be added and subtracted.
k-ary operation
then bc < ac
Change of variables
Vectors
49. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Rotations
Algebra
The operation of addition
50. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Reflexive relation
(k+1)-ary relation that is functional on its first k domains
Expressions
Reunion of broken parts