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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. The values combined are called
range
The simplest equations to solve
operands - arguments - or inputs
Vectors
2. 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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3. A
operation
commutative law of Multiplication
Linear algebra
the fixed non-negative integer k (the number of arguments)
4. 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
Difference of two squares - or the difference of perfect squares
Real number
identity element of addition
Equations
5. 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
Repeated multiplication
Elimination method
The relation of inequality (<) has this property
A functional equation
6. There are two common types of operations:
unary and binary
Equations
domain
identity element of Exponentiation
7. 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
Reunion of broken parts
when b > 0
symmetric
Abstract algebra
8. The inner product operation on two vectors produces a
nonnegative numbers
scalar
the fixed non-negative integer k (the number of arguments)
Constants
9. 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.
Change of variables
Elementary algebra
The simplest equations to solve
Equations
10. A + b = b + a
Real number
The relation of equality (=) has the property
Elementary algebra
commutative law of Addition
11. Is an equation where the unknowns are required to be integers.
Algebraic number theory
A binary relation R over a set X is symmetric
A Diophantine equation
Multiplication
12. Logarithm (Log)
inverse operation of Exponentiation
The relation of equality (=)'s property
Addition
substitution
13. If a = b then b = a
unary and binary
symmetric
has arity two
A functional equation
14. Is called the type or arity of the operation
The relation of equality (=)
value - result - or output
the fixed non-negative integer k (the number of arguments)
Vectors
15. 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
Unknowns
The simplest equations to solve
Conditional equations
16. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity element of Multiplication
Identity
Multiplication
Quadratic equations can also be solved
17. Can be combined using logic operations - such as and - or - and not.
Variables
The logical values true and false
Multiplication
exponential equation
18. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
system of linear equations
Unknowns
Universal algebra
Constants
19. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
equation
operands - arguments - or inputs
Operations can involve dissimilar objects
20. The process of expressing the unknowns in terms of the knowns is called
Multiplication
Real number
Solving the Equation
A differential equation
21. Is an action or procedure which produces a new value from one or more input values.
system of linear equations
transitive
an operation
Algebraic geometry
22. Is an equation involving a transcendental function of one of its variables.
Variables
when b > 0
Elementary algebra
A transcendental equation
23. Is Written as ab or a^b
then bc < ac
Exponentiation
Number line or real line
Repeated addition
24. Can be defined axiomatically up to an isomorphism
Associative law of Exponentiation
commutative law of Addition
The real number system
exponential equation
25. Applies abstract algebra to the problems of geometry
Variables
A integral equation
two inputs
Algebraic geometry
26. Referring to the finite number of arguments (the value k)
finitary operation
A transcendental equation
Operations on sets
Abstract algebra
27. Is an equation in which a polynomial is set equal to another polynomial.
Operations on sets
has arity one
A polynomial equation
Algebra
28. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
Repeated multiplication
A differential equation
A solution or root of the equation
29. 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.
A functional equation
The relation of inequality (<) has this property
Order of Operations
Constants
30. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Algebra
operands - arguments - or inputs
Variables
Real number
31. 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
Vectors
substitution
The real number system
All quadratic equations
32. 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)
Categories of Algebra
Associative law of Multiplication
Algebraic equation
The operation of exponentiation
33. Include composition and convolution
Reflexive relation
reflexive
operation
Operations on functions
34. In which abstract algebraic methods are used to study combinatorial questions.
The relation of equality (=)'s property
Operations on sets
Algebraic combinatorics
symmetric
35. 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)
Change of variables
The purpose of using variables
The operation of addition
Repeated multiplication
36. Operations can have fewer or more than
when b > 0
The purpose of using variables
nonnegative numbers
two inputs
37. b = b
nonnegative numbers
The relation of equality (=) has the property
reflexive
operation
38. Is algebraic equation of degree one
A linear equation
(k+1)-ary relation that is functional on its first k domains
Exponentiation
The sets Xk
39. Not associative
Properties of equality
A polynomial equation
Associative law of Exponentiation
unary and binary
40. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Operations can involve dissimilar objects
system of linear equations
operands - arguments - or inputs
Algebraic equation
41. Are denoted by letters at the beginning - a - b - c - d - ...
Operations can involve dissimilar objects
The operation of addition
Knowns
Vectors
42. 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
nonnegative numbers
Exponentiation
The method of equating the coefficients
Solution to the system
43. Are true for only some values of the involved variables: x2 - 1 = 4.
identity element of Exponentiation
commutative law of Multiplication
Conditional equations
Polynomials
44. 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)
Multiplication
A solution or root of the equation
operation
All quadratic equations
45. Is called the codomain of the operation
Difference of two squares - or the difference of perfect squares
Elimination method
inverse operation of addition
the set Y
46. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
Unary operations
Real number
The simplest equations to solve
Number line or real line
47. Is an equation involving integrals.
A integral equation
Algebra
The relation of equality (=)'s property
Elementary algebra
48. Subtraction ( - )
Universal algebra
inverse operation of addition
Operations can involve dissimilar objects
Algebraic combinatorics
49. If a < b and c < 0
then bc < ac
k-ary operation
nonnegative numbers
Equation Solving
50. Is Written as a
Algebraic equation
Multiplication
Operations on sets
logarithmic equation