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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 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).
Change of variables
operation
The method of equating the coefficients
A polynomial equation
2. The relation of equality (=) is...reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
An operation ?
Difference of two squares - or the difference of perfect squares
The relation of equality (=)
Properties of equality
3. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
substitution
domain
Operations on functions
4. Is an equation involving derivatives.
Identity
A differential equation
A polynomial equation
nonnegative numbers
5. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
finitary operation
when b > 0
Equations
6. The squaring operation only produces
Operations can involve dissimilar objects
Rotations
Solving the Equation
nonnegative numbers
7. The value produced is called
nonnegative numbers
Equations
The real number system
value - result - or output
8. Include the binary operations union and intersection and the unary operation of complementation.
Quadratic equations can also be solved
range
Constants
Operations on sets
9. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
identity element of addition
associative law of addition
A binary relation R over a set X is symmetric
10. If a = b then b = a
Multiplication
symmetric
nullary operation
range
11. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
The relation of equality (=)'s property
Solution to the system
All quadratic equations
Algebraic equation
12. Is an equation involving a transcendental function of one of its variables.
Reflexive relation
A transcendental equation
Quadratic equations can also be solved
The method of equating the coefficients
13. (a + b) + c = a + (b + c)
A solution or root of the equation
associative law of addition
logarithmic equation
A linear equation
14. Include composition and convolution
Operations on functions
Constants
Algebraic combinatorics
A functional equation
15. Not associative
Knowns
Abstract algebra
domain
Associative law of Exponentiation
16. Operations can have fewer or more than
Algebraic geometry
Quadratic equations can also be solved
Conditional equations
two inputs
17. k-ary operation is a
operation
Solving the Equation
(k+1)-ary relation that is functional on its first k domains
Rotations
18. Is an equation involving integrals.
Operations
A integral equation
identity element of addition
Algebraic equation
19. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
operation
Unknowns
the fixed non-negative integer k (the number of arguments)
an operation
20. Can be defined axiomatically up to an isomorphism
The purpose of using variables
The real number system
Unary operations
The method of equating the coefficients
21. Is an equation of the form aX = b for a > 0 - which has solution
Knowns
exponential equation
the set Y
Conditional equations
22. Is an action or procedure which produces a new value from one or more input values.
Abstract algebra
an operation
Change of variables
The sets Xk
23. If a = b and b = c then a = c
associative law of addition
transitive
An operation ?
Operations can involve dissimilar objects
24. 0 - which preserves numbers: a + 0 = a
Multiplication
identity element of addition
Algebraic combinatorics
nullary operation
25. 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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26. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The relation of equality (=)
The relation of equality (=) has the property
Solution to the system
Number line or real line
27. Involve only one value - such as negation and trigonometric functions.
A transcendental equation
k-ary operation
Algebraic geometry
Unary operations
28. 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.
Operations
transitive
the set Y
Change of variables
29. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Repeated addition
Abstract algebra
the set Y
All quadratic equations
30. In an equation with a single unknown - a value of that unknown for which the equation is true is called
Abstract algebra
A solution or root of the equation
Expressions
Associative law of Exponentiation
31. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
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.
The central technique to linear equations
Vectors
32. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
identity element of addition
Repeated multiplication
Quadratic equations can also be solved
The relation of equality (=)
33. Is an equation of the form log`a^X = b for a > 0 - which has solution
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.
logarithmic equation
Quadratic equations
Identity element of Multiplication
34. Is an equation in which a polynomial is set equal to another polynomial.
Order of Operations
Repeated multiplication
Expressions
A polynomial equation
35. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Reflexive relation
Binary operations
Rotations
inverse operation of Exponentiation
36. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
A solution or root of the equation
Operations can involve dissimilar objects
The simplest equations to solve
37. Referring to the finite number of arguments (the value k)
Quadratic equations
finitary operation
Change of variables
then ac < bc
38. There are two common types of operations:
Universal algebra
Multiplication
unary and binary
Solution to the system
39. 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.
value - result - or output
The relation of inequality (<) has this property
k-ary operation
A integral equation
40. Is an algebraic 'sentence' containing an unknown quantity.
Identities
nonnegative numbers
Polynomials
Quadratic equations
41. Can be added and subtracted.
Categories of Algebra
Vectors
The simplest equations to solve
Abstract algebra
42. May not be defined for every possible value.
Constants
Equations
has arity two
Operations
43. 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)
Properties of equality
A linear equation
operation
An operation ?
44. 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).
Quadratic equations
The operation of exponentiation
Identities
Difference of two squares - or the difference of perfect squares
45. Is Written as a + b
Equation Solving
value - result - or output
Addition
Repeated addition
46. 1 - which preserves numbers: a^1 = a
Equations
identity element of Exponentiation
operation
associative law of addition
47. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Change of variables
range
A linear equation
Abstract algebra
48. Can be combined using the function composition operation - performing the first rotation and then the second.
identity element of Exponentiation
Rotations
Algebraic geometry
symmetric
49. A binary operation
has arity two
scalar
Change of variables
Algebraic combinatorics
50. If it holds for all a and b in X that if a is related to b then b is related to a.
A binary relation R over a set X is symmetric
The sets Xk
Linear algebra
Identity