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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 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
inverse operation of Exponentiation
Real number
transitive
Properties of equality
2. Not commutative a^b?b^a
Operations
equation
commutative law of Exponentiation
Polynomials
3. A
associative law of addition
Change of variables
Identity
commutative law of Multiplication
4. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The central technique to linear equations
Equation Solving
Solution to the system
inverse operation of Exponentiation
5. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
operands - arguments - or inputs
Number line or real line
commutative law of Exponentiation
(k+1)-ary relation that is functional on its first k domains
6. () 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.
The purpose of using variables
Algebra
Constants
Addition
7. Is an equation of the form log`a^X = b for a > 0 - which has solution
Equations
logarithmic equation
symmetric
Binary operations
8. There are two common types of operations:
inverse operation of Multiplication
Number line or real line
has arity one
unary and binary
9. An operation of arity k is called a
commutative law of Addition
k-ary operation
Quadratic equations
inverse operation of addition
10. 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)
The relation of equality (=) has the property
Difference of two squares - or the difference of perfect squares
Algebra
The operation of exponentiation
11. The value produced is called
The relation of equality (=) has the property
Linear algebra
value - result - or output
A transcendental equation
12. The values for which an operation is defined form a set called its
Algebraic number theory
operands - arguments - or inputs
domain
then ac < bc
13. Is an equation of the form aX = b for a > 0 - which has solution
then a + c < b + d
the set Y
exponential equation
Operations on functions
14. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
Unknowns
Solving the Equation
An operation ?
15. Is an action or procedure which produces a new value from one or more input values.
Categories of Algebra
an operation
identity element of Exponentiation
Pure mathematics
16. Are denoted by letters at the beginning - a - b - c - d - ...
A transcendental equation
Solution to the system
then bc < ac
Knowns
17. 0 - which preserves numbers: a + 0 = a
nonnegative numbers
Reunion of broken parts
identity element of addition
A solution or root of the equation
18. The values combined are called
logarithmic equation
operands - arguments - or inputs
when b > 0
Properties of equality
19. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
A functional equation
Repeated multiplication
Solving the Equation
20. 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 central technique to linear equations
domain
The relation of equality (=)'s property
substitution
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 sets Xk
has arity two
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.
Quadratic equations
22. If a < b and c < 0
The purpose of using variables
The central technique to linear equations
Unary operations
then bc < ac
23. Can be defined axiomatically up to an isomorphism
The real number system
The central technique to linear equations
Operations
Unary operations
24. Are called the domains of the operation
The sets Xk
The operation of exponentiation
Operations on functions
inverse operation of Exponentiation
25. In an equation with a single unknown - a value of that unknown for which the equation is true is called
nullary operation
Pure mathematics
A solution or root of the equation
two inputs
26. 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.
commutative law of Exponentiation
Polynomials
symmetric
Properties of equality
27. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Conditional equations
has arity two
Categories of Algebra
reflexive
28. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Knowns
Exponentiation
Variables
Rotations
29. A unary operation
then ac < bc
Operations on functions
unary and binary
has arity one
30. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
Vectors
identity element of addition
Order of Operations
31. An operation of arity zero is simply an element of the codomain Y - called a
associative law of addition
nullary operation
radical equation
A Diophantine equation
32. If a = b and b = c then a = c
transitive
A binary relation R over a set X is symmetric
A transcendental equation
identity element of addition
33. Is an equation involving integrals.
A integral equation
symmetric
domain
Solution to the system
34. The inner product operation on two vectors produces a
All quadratic equations
Real number
Identity element of Multiplication
scalar
35. 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
Algebra
The method of equating the coefficients
Associative law of Exponentiation
inverse operation of Exponentiation
36. 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
Identities
The relation of equality (=)
identity element of Exponentiation
Reunion of broken parts
37. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Unknowns
Universal algebra
The operation of exponentiation
the set Y
38. Include composition and convolution
reflexive
Operations on functions
commutative law of Exponentiation
The relation of inequality (<) has this property
39. 1 - which preserves numbers: a
Constants
Identity element of Multiplication
Addition
system of linear equations
40. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
commutative law of Exponentiation
an operation
Solution to the system
41. Not associative
Associative law of Exponentiation
Difference of two squares - or the difference of perfect squares
Properties of equality
A transcendental equation
42. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
the fixed non-negative integer k (the number of arguments)
Quadratic equations can also be solved
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.
Addition
43. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
commutative law of Addition
identity element of addition
symmetric
44. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
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.
identity element of addition
Identity
Order of Operations
45. Can be added and subtracted.
Vectors
A polynomial equation
operation
inverse operation of Multiplication
46. May not be defined for every possible value.
Universal algebra
then bc < ac
Number line or real line
Operations
47. In which abstract algebraic methods are used to study combinatorial questions.
unary and binary
then ac < bc
Algebraic combinatorics
Vectors
48. Subtraction ( - )
inverse operation of addition
the fixed non-negative integer k (the number of arguments)
Real number
then bc < ac
49. The squaring operation only produces
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.
Binary operations
A linear equation
nonnegative numbers
50. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
Multiplication
Expressions
nonnegative numbers