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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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 b < c
Binary operations
Operations on sets
then a < c
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.
2. 1 - which preserves numbers: a^1 = a
associative law of addition
Binary operations
identity element of Exponentiation
Unknowns
3. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
commutative law of Addition
domain
system of linear equations
4. If a = b and b = c then a = c
Change of variables
transitive
has arity one
Operations can involve dissimilar objects
5. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Algebraic combinatorics
The method of equating the coefficients
The simplest equations to solve
logarithmic equation
6. (a + b) + c = a + (b + c)
scalar
associative law of addition
Elementary algebra
A binary relation R over a set X is symmetric
7. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
The operation of exponentiation
Algebraic number theory
Properties of equality
Identity element of Multiplication
8. 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)
Polynomials
operation
Equation Solving
an operation
9. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Elimination method
identity element of Exponentiation
Repeated addition
Abstract algebra
10. If a < b and c < 0
inverse operation of addition
Real number
A differential equation
then bc < ac
11. The values of the variables which make the equation true are the solutions of the equation and can be found through
A solution or root of the equation
Equation Solving
symmetric
substitution
12. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Properties of equality
value - result - or output
The operation of exponentiation
Unknowns
13. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
the set Y
nonnegative numbers
Algebraic combinatorics
Order of Operations
14. The value produced is called
Operations
Algebraic geometry
Binary operations
value - result - or output
15. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Addition
A solution or root of the equation
Categories of Algebra
Abstract algebra
16. The codomain is the set of real numbers but the range is the
A transcendental equation
symmetric
then a + c < b + d
nonnegative numbers
17. If a < b and c > 0
then ac < bc
Change of variables
nonnegative numbers
then a + c < b + d
18. 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
Properties of equality
Exponentiation
when b > 0
Real number
19. Is Written as a
an operation
logarithmic equation
Multiplication
A polynomial equation
20. Logarithm (Log)
unary and binary
inverse operation of Exponentiation
Quadratic equations
Pure mathematics
21. Not commutative a^b?b^a
commutative law of Exponentiation
operation
nullary operation
All quadratic equations
22. The values for which an operation is defined form a set called its
Reflexive relation
domain
Variables
Operations on sets
23. Is Written as ab or a^b
then ac < bc
Properties of equality
Exponentiation
Solution to the system
24. If a = b then b = a
symmetric
A binary relation R over a set X is symmetric
k-ary 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.
25. 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
Reunion of broken parts
The real number system
The operation of addition
Equation Solving
26. 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)
Order of Operations
Linear algebra
Exponentiation
The operation of exponentiation
27. 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
Linear algebra
then ac < bc
Real number
The logical values true and false
28. 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
Elimination method
Knowns
Change of variables
Associative law of Exponentiation
29. A vector can be multiplied by a scalar to form another vector
Linear algebra
A polynomial equation
Operations on functions
Operations can involve dissimilar objects
30. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
the set Y
an operation
Vectors
31. Is Written as a + b
Rotations
Addition
Associative law of Exponentiation
domain
32. The operation of multiplication means _______________: a
Repeated addition
then ac < bc
Repeated multiplication
Associative law of Multiplication
33. Is an equation in which a polynomial is set equal to another polynomial.
operation
Algebraic number theory
Operations on functions
A polynomial equation
34. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
scalar
Rotations
Expressions
35. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Elimination method
system of linear equations
Abstract algebra
k-ary operation
36. k-ary operation is a
A functional equation
Variables
Repeated multiplication
(k+1)-ary relation that is functional on its first k domains
37. Is an equation of the form log`a^X = b for a > 0 - which has solution
Algebraic combinatorics
logarithmic equation
Variables
Associative law of Multiplication
38. The values combined are called
operands - arguments - or inputs
Real number
Equation Solving
Solving the Equation
39. Is an equation where the unknowns are required to be integers.
inverse operation of addition
Variables
Expressions
A Diophantine equation
40. Can be combined using logic operations - such as and - or - and not.
logarithmic equation
Constants
The logical values true and false
Number line or real line
41. Not associative
inverse operation of Multiplication
Number line or real line
Associative law of Exponentiation
The operation of addition
42. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Solving the Equation
k-ary operation
Linear algebra
Categories of Algebra
43. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
Expressions
Associative law of Multiplication
radical equation
44. 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
Unknowns
Universal algebra
substitution
nullary operation
45. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
A binary relation R over a set X is symmetric
unary and binary
Identity element of Multiplication
46. Is called the type or arity of the operation
Unary operations
Operations
A differential equation
the fixed non-negative integer k (the number of arguments)
47. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
(k+1)-ary relation that is functional on its first k domains
the fixed non-negative integer k (the number of arguments)
Pure mathematics
an operation
48. 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.
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49. In which the specific properties of vector spaces are studied (including matrices)
the fixed non-negative integer k (the number of arguments)
operation
The logical values true and false
Linear algebra
50. A
Universal algebra
Reunion of broken parts
Properties of equality
commutative law of Multiplication