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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 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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2. Is an equation of the form log`a^X = b for a > 0 - which has solution
Variables
Algebraic geometry
inverse operation of addition
logarithmic equation
3. Are called the domains of the operation
associative law of addition
The operation of addition
Equations
The sets Xk
4. 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
substitution
Pure mathematics
Reunion of broken parts
5. Is called the type or arity of the operation
associative law of addition
Algebra
nonnegative numbers
the fixed non-negative integer k (the number of arguments)
6. (a
A polynomial equation
Associative law of Multiplication
Algebra
system of linear equations
7. k-ary operation is a
Addition
(k+1)-ary relation that is functional on its first k domains
symmetric
commutative law of Exponentiation
8. Can be defined axiomatically up to an isomorphism
nonnegative numbers
The real number system
operands - arguments - or inputs
Multiplication
9. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
A polynomial equation
Expressions
A binary relation R over a set X is symmetric
10. Is an equation involving a transcendental function of one of its variables.
A differential equation
Solution to the system
A transcendental equation
Binary operations
11. The codomain is the set of real numbers but the range is the
nonnegative numbers
The relation of equality (=)
Operations on functions
an operation
12. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
identity element of addition
then a < c
commutative law of Multiplication
13. Is to add - subtract - multiply - or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated - the other side of the equation is the value of the variable.
The central technique to linear equations
radical equation
commutative law of Exponentiation
Algebra
14. Applies abstract algebra to the problems of geometry
exponential equation
inverse operation of addition
Algebraic geometry
reflexive
15. Is an equation in which the unknowns are functions rather than simple quantities.
A binary relation R over a set X is symmetric
A functional equation
A Diophantine equation
The method of equating the coefficients
16. 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.
inverse operation of addition
Universal algebra
The relation of inequality (<) has this property
Order of Operations
17. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
domain
The central technique to linear equations
Rotations
Unknowns
18. Is an equation involving integrals.
A integral equation
inverse operation of Multiplication
A differential equation
Binary operations
19. 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
Identity element of Multiplication
Unary operations
Real number
range
20. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
operation
Repeated addition
Algebraic combinatorics
21. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Repeated multiplication
Identity
Difference of two squares - or the difference of perfect squares
substitution
22. Division ( / )
inverse operation of Multiplication
Change of variables
two inputs
Equations
23. 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
All quadratic equations
then bc < ac
An operation ?
24. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
A differential equation
Operations
equation
Operations on sets
25. (a + b) + c = a + (b + c)
commutative law of Addition
Real number
Reunion of broken parts
associative law of addition
26. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Number line or real line
Multiplication
(k+1)-ary relation that is functional on its first k domains
The purpose of using variables
27. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Properties of equality
Change of variables
Solution to the system
Algebra
28. The operation of multiplication means _______________: a
Unknowns
Repeated addition
Unary operations
unary and binary
29. If a < b and c < d
exponential equation
then a + c < b + d
nullary operation
reflexive
30. Is called the codomain of the operation
A binary relation R over a set X is symmetric
the set Y
then ac < bc
The method of equating the coefficients
31. Is Written as ab or a^b
Multiplication
Elementary algebra
equation
Exponentiation
32. 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
nullary operation
substitution
Real number
identity element of Exponentiation
33. If a < b and c > 0
associative law of addition
The operation of addition
then ac < bc
inverse operation of Multiplication
34. Are denoted by letters at the beginning - a - b - c - d - ...
The sets Xk
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.
associative law of addition
Knowns
35. 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).
Solution to the system
operation
Quadratic equations can also be solved
Equations
36. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
Quadratic equations
Unary operations
The logical values true and false
37. 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.
Multiplication
Expressions
Properties of equality
Identities
38. In which the specific properties of vector spaces are studied (including matrices)
Equations
Vectors
logarithmic equation
Linear algebra
39. Is an equation involving derivatives.
A differential equation
Abstract algebra
two inputs
The relation of equality (=) has the property
40. Logarithm (Log)
The simplest equations to solve
inverse operation of Exponentiation
commutative law of Exponentiation
Identity
41. Is Written as a + b
unary and binary
Knowns
Abstract algebra
Addition
42. Is an algebraic 'sentence' containing an unknown quantity.
The sets Xk
Equations
A solution or root of the equation
Polynomials
43. An operation of arity k is called a
The simplest equations to solve
All quadratic equations
A Diophantine equation
k-ary operation
44. In an equation with a single unknown - a value of that unknown for which the equation is true is called
nullary operation
Vectors
A solution or root of the equation
exponential equation
45. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
k-ary operation
The relation of equality (=)'s property
The relation of equality (=)
Categories of Algebra
46. In which properties common to all algebraic structures are studied
Binary operations
Reflexive relation
Algebraic equation
Universal algebra
47. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.
value - result - or output
Algebra
A differential equation
commutative law of Multiplication
48. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
A integral equation
exponential equation
Categories of Algebra
All quadratic equations
49. Referring to the finite number of arguments (the value k)
finitary operation
nonnegative numbers
symmetric
A functional equation
50. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Quadratic equations can also be solved
range
Reflexive relation
reflexive