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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. The inner product operation on two vectors produces a
Solution to the system
scalar
commutative law of Exponentiation
Associative law of Exponentiation
2. 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 addition
The method of equating the coefficients
Associative law of Exponentiation
Vectors
3. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).
operation
A binary relation R over a set X is symmetric
The relation of equality (=)'s property
Expressions
4. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
radical equation
then a < c
then bc < ac
Quadratic equations can also be solved
5. 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
Operations
Reunion of broken parts
Repeated multiplication
two inputs
6. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Algebraic number theory
Pure mathematics
operands - arguments - or inputs
Operations on functions
7. If a = b then b = a
identity element of addition
substitution
commutative law of Addition
symmetric
8. Is the claim that two expressions have the same value and are equal.
identity element of Exponentiation
Operations can involve dissimilar objects
Identity element of Multiplication
Equations
9. The values of the variables which make the equation true are the solutions of the equation and can be found through
inverse operation of addition
then ac < bc
Equation Solving
The logical values true and false
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)
Elimination method
The operation of exponentiation
Constants
then a < c
11. 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
Identity
Repeated multiplication
Algebraic combinatorics
12. 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
Change of variables
radical equation
Elementary algebra
identity element of addition
13. Division ( / )
inverse operation of Multiplication
two inputs
Associative law of Exponentiation
The relation of inequality (<) has this property
14. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Number line or real line
The relation of equality (=)
Operations
Repeated addition
15. A + b = b + a
Associative law of Multiplication
Unknowns
Properties of equality
commutative law of Addition
16. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Unary operations
Solution to the system
equation
A linear equation
17. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
An operation ?
Difference of two squares - or the difference of perfect squares
Quadratic equations can also be solved
the fixed non-negative integer k (the number of arguments)
18. Are called the domains of the operation
Solution to the system
Identities
inverse operation of Multiplication
The sets Xk
19. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Associative law of Multiplication
Rotations
Binary operations
Reflexive relation
20. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
unary and binary
A integral equation
Knowns
21. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Equations
Elementary algebra
A differential equation
22. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Algebraic number theory
Binary operations
Unknowns
Vectors
23. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
A differential equation
inverse operation of addition
value - result - or output
24. Is an equation where the unknowns are required to be integers.
A Diophantine equation
then a + c < b + d
finitary operation
the fixed non-negative integer k (the number of arguments)
25. Is Written as ab or a^b
Reunion of broken parts
Exponentiation
Repeated multiplication
Solving the Equation
26. Involve only one value - such as negation and trigonometric functions.
Repeated addition
substitution
Unary operations
The relation of equality (=)
27. Is an equation of the form aX = b for a > 0 - which has solution
value - result - or output
The purpose of using variables
Universal algebra
exponential equation
28. Are true for only some values of the involved variables: x2 - 1 = 4.
Reunion of broken parts
inverse operation of addition
Conditional equations
Elimination method
29. A vector can be multiplied by a scalar to form another vector
system of linear equations
Operations can involve dissimilar objects
A functional equation
Expressions
30. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Real number
an operation
Identity
31. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Pure mathematics
Identity
Repeated multiplication
range
32. If a = b and b = c then a = c
The method of equating the coefficients
then a + c < b + d
when b > 0
transitive
33. 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)
Equations
Categories of Algebra
A transcendental equation
The operation of addition
34. Subtraction ( - )
inverse operation of addition
The relation of equality (=)
an operation
range
35. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
operands - arguments - or inputs
Constants
The logical values true and false
36. 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
unary and binary
range
37. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
inverse operation of Exponentiation
the fixed non-negative integer k (the number of arguments)
Algebraic geometry
Solution to the system
38. The values combined are called
A functional equation
operands - arguments - or inputs
radical equation
Algebraic equation
39. b = b
inverse operation of Exponentiation
reflexive
Quadratic equations can also be solved
Reunion of broken parts
40. 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.
Real number
The relation of equality (=) has the property
the fixed non-negative integer k (the number of arguments)
Identities
41. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
Algebra
A binary relation R over a set X is symmetric
Identities
42. A
identity element of Exponentiation
commutative law of Multiplication
Solution to the system
Difference of two squares - or the difference of perfect squares
43. Can be combined using the function composition operation - performing the first rotation and then the second.
Algebraic geometry
The central technique to linear equations
has arity one
Rotations
44. Referring to the finite number of arguments (the value k)
finitary operation
transitive
inverse operation of Exponentiation
Number line or real line
45. The operation of multiplication means _______________: a
Repeated addition
A polynomial equation
A differential equation
range
46. 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
Real number
Categories of Algebra
Equations
Number line or real line
47. If a < b and c > 0
then ac < bc
Algebraic combinatorics
The method of equating the coefficients
Polynomials
48. Is called the codomain of the operation
the set Y
Quadratic equations
A differential equation
value - result - or output
49. () 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.
Difference of two squares - or the difference of perfect squares
Number line or real line
Algebra
substitution
50. Is called the type or arity of the operation
Pure mathematics
A transcendental equation
Operations on sets
the fixed non-negative integer k (the number of arguments)