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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. Is an equation involving integrals.
Constants
A integral equation
A transcendental equation
then a + c < b + d
2. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Polynomials
A solution or root of the equation
Repeated multiplication
Operations on functions
3. Is an equation involving derivatives.
A differential equation
A transcendental equation
finitary operation
The central technique to linear equations
4. Is an equation in which the unknowns are functions rather than simple quantities.
Associative law of Multiplication
Operations on sets
The simplest equations to solve
A functional equation
5. Can be defined axiomatically up to an isomorphism
Equations
Quadratic equations can also be solved
commutative law of Multiplication
The real number system
6. Can be expressed in the form ax^2 + bx + c = 0 - where a is not zero (if it were zero - then the equation would not be quadratic but linear).
scalar
Quadratic equations
substitution
The simplest equations to solve
7. 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
Multiplication
has arity two
substitution
8. The squaring operation only produces
nonnegative numbers
equation
Rotations
two inputs
9. 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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10. If a < b and c < d
then a + c < b + d
The operation of exponentiation
The relation of equality (=) has the property
equation
11. 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
Identity element of Multiplication
Elimination method
A polynomial equation
Properties of equality
12. Can be combined using logic operations - such as and - or - and not.
The logical values true and false
Constants
transitive
Linear algebra
13. 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)
Identities
operation
inverse operation of Exponentiation
Linear algebra
14. If a < b and c < 0
has arity one
operation
identity element of Exponentiation
then bc < ac
15. A + b = b + a
inverse operation of Multiplication
The operation of exponentiation
logarithmic equation
commutative law of Addition
16. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
Algebraic geometry
Associative law of Multiplication
Variables
17. Referring to the finite number of arguments (the value k)
when b > 0
commutative law of Exponentiation
finitary operation
domain
18. Not commutative a^b?b^a
Expressions
commutative law of Exponentiation
range
Reflexive relation
19. 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'.
Properties of equality
Operations on sets
The relation of equality (=)
Reflexive relation
20. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
inverse operation of Exponentiation
value - result - or output
The real number system
The relation of equality (=)
21. In which abstract algebraic methods are used to study combinatorial questions.
Elimination method
Algebraic combinatorics
Linear algebra
Solving the Equation
22. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
The purpose of using variables
k-ary operation
value - result - or output
23. Is Written as a
then ac < bc
equation
Algebraic geometry
Multiplication
24. Operations can have fewer or more than
The logical values true and false
has arity one
two inputs
A integral equation
25. A binary operation
exponential equation
Knowns
finitary operation
has arity two
26. 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)
Linear algebra
The operation of addition
scalar
identity element of Exponentiation
27. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
The method of equating the coefficients
Difference of two squares - or the difference of perfect squares
Universal algebra
reflexive
28. If it holds for all a and b in X that if a is related to b then b is related to a.
Linear algebra
A binary relation R over a set X is symmetric
then bc < ac
range
29. 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.
the set Y
Conditional equations
An operation ?
Change of variables
30. Will have two solutions in the complex number system - but need not have any in the real number system.
Equations
Algebraic number theory
Algebraic equation
All quadratic equations
31. The codomain is the set of real numbers but the range is the
nonnegative numbers
Constants
The operation of addition
unary and binary
32. Division ( / )
unary and binary
The relation of equality (=)
inverse operation of Multiplication
Operations on functions
33. Is called the type or arity of the operation
nonnegative numbers
the fixed non-negative integer k (the number of arguments)
associative law of addition
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.
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.
A functional equation
The relation of equality (=) has the property
The relation of equality (=)
exponential equation
35. The inner product operation on two vectors produces a
Reunion of broken parts
an operation
Operations can involve dissimilar objects
scalar
36. An operation of arity zero is simply an element of the codomain Y - called a
domain
nonnegative numbers
Unknowns
nullary operation
37. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Conditional equations
The central technique to linear equations
Number line or real line
when b > 0
38. 1 - which preserves numbers: a^1 = a
identity element of Exponentiation
Operations on functions
the set Y
Abstract algebra
39. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
operation
inverse operation of Exponentiation
Conditional equations
40. Is an equation of the form aX = b for a > 0 - which has solution
domain
Algebraic equation
exponential equation
the fixed non-negative integer k (the number of arguments)
41. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Binary operations
Solution to the system
Unknowns
Polynomials
42. (a
Knowns
Associative law of Multiplication
The simplest equations to solve
exponential equation
43. 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 relation of inequality (<) has this property
Number line or real line
Multiplication
Operations on sets
44. Not associative
Associative law of Exponentiation
Expressions
operands - arguments - or inputs
radical equation
45. 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 method of equating the coefficients
Equations
The logical values true and false
Quadratic equations can also be solved
46. 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
commutative law of Exponentiation
unary and binary
Difference of two squares - or the difference of perfect squares
Reunion of broken parts
47. There are two common types of operations:
Solution to the system
Operations
unary and binary
nullary operation
48. Can be added and subtracted.
A linear equation
The simplest equations to solve
Vectors
Reflexive relation
49. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
domain
Algebraic equation
Repeated addition
exponential equation
50. The values for which an operation is defined form a set called its
Equation Solving
reflexive
Number line or real line
domain