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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 vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
value - result - or output
identity element of addition
The relation of equality (=)
2. If a = b and b = c then a = c
Solution to the system
A transcendental equation
transitive
Operations on sets
3. The values combined are called
Polynomials
when b > 0
operands - arguments - or inputs
Difference of two squares - or the difference of perfect squares
4. Is called the codomain of the operation
Rotations
the set Y
Operations
Unknowns
5. Is Written as a + b
identity element of Exponentiation
A differential equation
Addition
finitary operation
6. 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
Properties of equality
scalar
has arity one
7. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Real number
Repeated multiplication
Solution to the system
8. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
commutative law of Multiplication
Exponentiation
Repeated multiplication
9. 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
Exponentiation
Number line or real line
Real number
Reunion of broken parts
10. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
commutative law of Multiplication
Categories of Algebra
Unary operations
11. Is algebraic equation of degree one
A linear equation
Repeated addition
Algebraic combinatorics
Linear algebra
12. May not be defined for every possible value.
Operations
The operation of exponentiation
reflexive
Operations on sets
13. 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'.
The method of equating the coefficients
Solution to the system
Reflexive relation
The relation of inequality (<) has this property
14. Can be added and subtracted.
Abstract algebra
The purpose of using variables
Vectors
Solution to the system
15. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
An operation ?
A Diophantine equation
Expressions
The relation of equality (=)'s property
16. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)
Algebraic combinatorics
operation
Reflexive relation
Operations
17. 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)
An operation ?
The operation of addition
A integral equation
A linear equation
18. Is Written as a
Conditional equations
Multiplication
Elementary algebra
Number line or real line
19. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Addition
unary and binary
Repeated multiplication
Unknowns
20. 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
commutative law of Addition
unary and binary
when b > 0
A differential equation
21. Is an algebraic 'sentence' containing an unknown quantity.
Knowns
A binary relation R over a set X is symmetric
The relation of equality (=)
Polynomials
22. Is an equation of the form aX = b for a > 0 - which has solution
operation
exponential equation
Polynomials
A solution or root of the equation
23. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
range
Variables
Unary operations
24. Not commutative a^b?b^a
All quadratic equations
commutative law of Exponentiation
nonnegative numbers
Algebraic geometry
25. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
Algebraic geometry
Constants
operation
26. There are two common types of operations:
Algebraic geometry
A functional equation
unary and binary
value - result - or output
27. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
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.
inverse operation of Multiplication
operation
Equations
28. Letters from the beginning of the alphabet like a - b - c... often denote
inverse operation of addition
substitution
Algebraic geometry
Constants
29. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
Categories of Algebra
A Diophantine equation
A functional equation
30. 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)
Quadratic equations can also be solved
has arity two
The operation of exponentiation
The real number system
31. Transivity: if a < b and b < c then a < c; that if a < b and c < d then a + c < b + d; that if a < b and c > 0 then ac < bc; that if a < b and c < 0 then bc < ac.
Quadratic equations can also be solved
The relation of inequality (<) has this property
Algebraic combinatorics
commutative law of Exponentiation
32. Include the binary operations union and intersection and the unary operation of complementation.
Conditional equations
associative law of addition
Operations on sets
then a + c < b + d
33. 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 Diophantine equation
Linear algebra
Change of variables
exponential equation
34. 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.
Reunion of broken parts
Identity element of Multiplication
Rotations
The relation of equality (=) has the property
35. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
The simplest equations to solve
Rotations
Order of Operations
when b > 0
36. The operation of exponentiation means ________________: a^n = a
Pure mathematics
Repeated multiplication
Identity element of Multiplication
inverse operation of Exponentiation
37. Is an equation of the form log`a^X = b for a > 0 - which has solution
scalar
Elementary algebra
A differential equation
logarithmic equation
38. Subtraction ( - )
the set Y
Change of variables
Categories of Algebra
inverse operation of addition
39. Can be combined using the function composition operation - performing the first rotation and then the second.
an operation
the set Y
A integral equation
Rotations
40. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
operation
substitution
Categories of Algebra
Quadratic equations can also be solved
41. 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
Order of Operations
The method of equating the coefficients
inverse operation of addition
radical equation
42. 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.
operation
The central technique to linear equations
A integral equation
Properties of equality
43. The values for which an operation is defined form a set called its
Categories of Algebra
identity element of Exponentiation
Algebraic geometry
domain
44. 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
Number line or real line
Operations on functions
Reunion of broken parts
The relation of inequality (<) has this property
45. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Addition
Categories of Algebra
The sets Xk
Expressions
46. Is an equation involving derivatives.
A differential equation
The logical values true and false
The sets Xk
The central technique to linear equations
47. Include composition and convolution
scalar
then bc < ac
Operations on functions
finitary operation
48. If a < b and c < d
Binary operations
radical equation
then a + c < b + d
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
Universal algebra
(k+1)-ary relation that is functional on its first k domains
k-ary operation
50. 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
Equations
identity element of addition
Linear algebra
Elimination method