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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. If a < b and c < 0
The method of equating the coefficients
Difference of two squares - or the difference of perfect squares
then bc < ac
A Diophantine equation
2. 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.
Multiplication
Properties of equality
unary and binary
Conditional equations
3. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Conditional equations
Linear algebra
two inputs
Algebraic equation
4. A vector can be multiplied by a scalar to form another vector
Polynomials
domain
Operations can involve dissimilar objects
Expressions
5. 1 - which preserves numbers: a^1 = a
Operations can involve dissimilar objects
identity element of Exponentiation
nonnegative numbers
The relation of inequality (<) has this property
6. Is a function of the form ? : V ? Y - where V ? X1
An operation ?
The relation of equality (=)'s property
nonnegative numbers
Identity
7. Is an equation involving a transcendental function of one of its variables.
The logical values true and false
Operations can involve dissimilar objects
Reflexive relation
A transcendental equation
8. Referring to the finite number of arguments (the value k)
operands - arguments - or inputs
symmetric
the fixed non-negative integer k (the number of arguments)
finitary operation
9. Operations can have fewer or more than
Operations on sets
Binary operations
two inputs
Vectors
10. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A solution or root of the equation
Equation Solving
commutative law of Exponentiation
The relation of equality (=)'s property
11. An operation of arity k is called a
The operation of addition
k-ary operation
Operations on functions
A binary relation R over a set X is symmetric
12. 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
inverse operation of addition
Change of variables
Constants
13. The value produced is called
value - result - or output
Algebraic combinatorics
Universal algebra
Real number
14. Logarithm (Log)
inverse operation of Exponentiation
Pure mathematics
k-ary operation
The logical values true and false
15. The operation of multiplication means _______________: a
Binary operations
Reflexive relation
Repeated addition
operation
16. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Exponentiation
Operations on functions
when b > 0
Unknowns
17. 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
Unknowns
The relation of inequality (<) has this property
Associative law of Multiplication
18. The operation of exponentiation means ________________: a^n = a
A Diophantine equation
All quadratic equations
The logical values true and false
Repeated multiplication
19. Is called the type or arity of the operation
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.
the fixed non-negative integer k (the number of arguments)
Linear algebra
Rotations
20. 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.
identity element of Exponentiation
The relation of equality (=) has the property
commutative law of Addition
Associative law of Multiplication
21. 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.
A integral equation
Pure mathematics
A binary relation R over a set X is symmetric
Change of variables
22. 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).
Rotations
Quadratic equations
Associative law of Exponentiation
then a + c < b + d
23. 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.
24. The values combined are called
logarithmic equation
scalar
operands - arguments - or inputs
Operations on functions
25. 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
system of linear equations
Identity element of Multiplication
Elimination method
then a < c
26. 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
when b > 0
domain
has arity two
unary and binary
27. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
A differential equation
Operations
system of linear equations
Algebraic equation
28. 0 - which preserves numbers: a + 0 = a
the fixed non-negative integer k (the number of arguments)
The relation of equality (=)
nullary operation
identity element of addition
29. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Unary operations
Expressions
domain
Pure mathematics
30. 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
Categories of Algebra
Change of variables
The method of equating the coefficients
inverse operation of Multiplication
31. A
then a < c
commutative law of Multiplication
Operations on sets
Equations
32. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
then a < c
associative law of addition
A linear equation
33. If a = b then b = a
operands - arguments - or inputs
symmetric
Order of Operations
reflexive
34. The inner product operation on two vectors produces a
domain
The operation of addition
scalar
Order of Operations
35. A unary operation
The central technique to linear equations
has arity one
A Diophantine equation
exponential equation
36. (a
Exponentiation
Associative law of Multiplication
The method of equating the coefficients
Algebraic geometry
37. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
value - result - or output
range
the set Y
38. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
A differential equation
A functional equation
the set Y
39. Can be added and subtracted.
Vectors
(k+1)-ary relation that is functional on its first k domains
Reunion of broken parts
Difference of two squares - or the difference of perfect squares
40. 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
has arity one
Properties of equality
The operation of exponentiation
41. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Reflexive relation
then ac < bc
Order of Operations
unary and binary
42. 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
Algebraic combinatorics
The simplest equations to solve
has arity two
substitution
43. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
reflexive
The sets Xk
Solution to the system
Associative law of Exponentiation
44. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The sets Xk
The purpose of using variables
inverse operation of addition
scalar
45. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Constants
range
Elementary algebra
Associative law of Multiplication
46. Can be defined axiomatically up to an isomorphism
The real number system
k-ary operation
Linear algebra
A binary relation R over a set X is symmetric
47. 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)
has arity two
commutative law of Addition
operation
The operation of exponentiation
48. Not associative
when b > 0
Associative law of Exponentiation
commutative law of Exponentiation
Identities
49. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
symmetric
Identities
Polynomials
The relation of inequality (<) has this property
50. Algebra comes from Arabic al-jebr meaning '______________'. Studies the effects of adding and multiplying numbers - variables - and polynomials - along with their factorization and determining their roots. Works directly with numbers. Also covers sym
A binary relation R over a set X is symmetric
An operation ?
Reunion of broken parts
Operations on functions