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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 binary operation
has arity two
Unary operations
Operations can involve dissimilar objects
an operation
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
Operations can involve dissimilar objects
The method of equating the coefficients
Binary operations
Polynomials
3. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Solution to the system
The simplest equations to solve
Abstract algebra
Reflexive relation
4. 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)
The sets Xk
operation
commutative law of Multiplication
Algebraic number theory
5. Letters from the beginning of the alphabet like a - b - c... often denote
Equations
Reunion of broken parts
Constants
when b > 0
6. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Repeated multiplication
equation
Algebraic number theory
Constants
7. The operation of multiplication means _______________: a
inverse operation of addition
Repeated addition
Real number
exponential equation
8. If it holds for all a and b in X that if a is related to b then b is related to a.
Equations
commutative law of Multiplication
A binary relation R over a set X is symmetric
when b > 0
9. If a < b and c < 0
Reflexive relation
Algebraic geometry
then bc < ac
The sets Xk
10. 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
The relation of equality (=)
Knowns
Quadratic equations can also be solved
11. Is an algebraic 'sentence' containing an unknown quantity.
Operations on functions
nullary operation
Polynomials
when b > 0
12. Is Written as ab or a^b
Exponentiation
The purpose of using variables
the set Y
A functional equation
13. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
logarithmic equation
exponential equation
Associative law of Exponentiation
Equations
14. Is Written as a
identity element of Exponentiation
Multiplication
Elementary algebra
Associative law of Exponentiation
15. In which properties common to all algebraic structures are studied
Repeated multiplication
Abstract algebra
Universal algebra
Change of variables
16. The inner product operation on two vectors produces a
scalar
Universal algebra
A functional equation
Operations can involve dissimilar objects
17. 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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18. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
nonnegative numbers
The purpose of using variables
Repeated addition
19. The value produced is called
the set Y
A solution or root of the equation
substitution
value - result - or output
20. If a = b then b = a
Operations on sets
symmetric
Solution to the system
Reflexive relation
21. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Multiplication
Solution to the system
Real number
The real number system
22. 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.
The real number system
Reflexive relation
substitution
The relation of inequality (<) has this property
23. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Knowns
Properties of equality
commutative law of Multiplication
Expressions
24. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Quadratic equations can also be solved
radical equation
Identity element of Multiplication
Pure mathematics
25. Is an equation in which a polynomial is set equal to another polynomial.
Binary operations
A polynomial equation
logarithmic equation
symmetric
26. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
Identity
inverse operation of addition
Exponentiation
27. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Rotations
an operation
Identities
The operation of exponentiation
28. The squaring operation only produces
nonnegative numbers
operation
transitive
Abstract algebra
29. There are two common types of operations:
The relation of equality (=)'s property
unary and binary
has arity one
Operations
30. Are denoted by letters at the beginning - a - b - c - d - ...
Knowns
A binary relation R over a set X is symmetric
k-ary operation
equation
31. The operation of exponentiation means ________________: a^n = a
Equations
Algebraic combinatorics
Repeated multiplication
An operation ?
32. Is an equation of the form log`a^X = b for a > 0 - which has solution
Exponentiation
logarithmic equation
The operation of exponentiation
finitary operation
33. Include the binary operations union and intersection and the unary operation of complementation.
Algebraic combinatorics
has arity one
The logical values true and false
Operations on sets
34. Operations can have fewer or more than
Quadratic equations
Equations
two inputs
The relation of inequality (<) has this property
35. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
operands - arguments - or inputs
Identity
Properties of equality
36. If a < b and c > 0
Solving the Equation
Reflexive relation
then ac < bc
The real number system
37. If a = b and b = c then a = c
scalar
A functional equation
Identities
transitive
38. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
inverse operation of Exponentiation
Elimination method
symmetric
equation
39. k-ary operation is a
Pure mathematics
(k+1)-ary relation that is functional on its first k domains
A functional equation
Unknowns
40. Can be combined using logic operations - such as and - or - and not.
substitution
The central technique to linear equations
then ac < bc
The logical values true and false
41. (a
Exponentiation
An operation ?
reflexive
Associative law of Multiplication
42. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
scalar
An operation ?
The logical values true and false
43. 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
scalar
Change of variables
substitution
Elimination method
44. A
commutative law of Multiplication
Knowns
substitution
symmetric
45. An operation of arity zero is simply an element of the codomain Y - called a
Real number
The operation of addition
Rotations
nullary operation
46. 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)
domain
inverse operation of Exponentiation
then bc < ac
The operation of addition
47. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
Unary operations
then bc < ac
A linear equation
48. 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
Difference of two squares - or the difference of perfect squares
Repeated addition
finitary operation
Elimination method
49. Referring to the finite number of arguments (the value k)
identity element of addition
radical equation
finitary operation
Operations on sets
50. Is Written as a + b
Real number
Addition
A Diophantine equation
A functional equation