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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. Is an algebraic 'sentence' containing an unknown quantity.
Operations on sets
All quadratic equations
unary and binary
Polynomials
2. Logarithm (Log)
Equation Solving
The method of equating the coefficients
inverse operation of Exponentiation
Conditional equations
3. In an equation with a single unknown - a value of that unknown for which the equation is true is called
The relation of equality (=) has the property
Operations can involve dissimilar objects
A solution or root of the equation
The purpose of using variables
4. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
equation
radical equation
Elimination method
5. Subtraction ( - )
The logical values true and false
Pure mathematics
Associative law of Multiplication
inverse operation of addition
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).
The method of equating the coefficients
Universal algebra
The central technique to linear equations
Quadratic equations
7. If a < b and b < c
A integral equation
Order of Operations
The purpose of using variables
then a < c
8. An operation of arity k is called a
then a + c < b + d
k-ary operation
Elementary algebra
A polynomial equation
9. The values combined are called
Conditional equations
operands - arguments - or inputs
Associative law of Multiplication
Associative law of Exponentiation
10. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
the set Y
A integral equation
The sets Xk
11. Include composition and convolution
A polynomial equation
Operations on functions
The central technique to linear equations
Variables
12. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Number line or real line
Quadratic equations can also be solved
Identity
transitive
13. A vector can be multiplied by a scalar to form another vector
equation
Operations on sets
reflexive
Operations can involve dissimilar objects
14. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
then bc < ac
operands - arguments - or inputs
Algebraic geometry
15. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
The relation of equality (=)'s property
Knowns
Variables
Difference of two squares - or the difference of perfect squares
16. If a < b and c < 0
then a < c
then bc < ac
Operations on sets
Equation Solving
17. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
the fixed non-negative integer k (the number of arguments)
transitive
nonnegative numbers
18. Is an equation involving a transcendental function of one of its variables.
Equation Solving
operands - arguments - or inputs
A transcendental equation
Equations
19. Is an equation of the form aX = b for a > 0 - which has solution
A transcendental equation
(k+1)-ary relation that is functional on its first k domains
unary and binary
exponential equation
20. 0 - which preserves numbers: a + 0 = a
Quadratic equations
identity element of addition
Associative law of Exponentiation
The operation of addition
21. Are denoted by letters at the beginning - a - b - c - d - ...
commutative law of Addition
Operations on sets
operation
Knowns
22. The squaring operation only produces
inverse operation of Exponentiation
Universal algebra
nonnegative numbers
operation
23. 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.
Knowns
A integral equation
The relation of inequality (<) has this property
substitution
24. Division ( / )
Identity
transitive
Equations
inverse operation of Multiplication
25. In which properties common to all algebraic structures are studied
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 relation of inequality (<) has this property
Universal algebra
Difference of two squares - or the difference of perfect squares
26. If a = b then b = a
unary and binary
range
symmetric
has arity two
27. 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
Quadratic equations can also be solved
Polynomials
then a < c
28. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
domain
A differential equation
A binary relation R over a set X is symmetric
Solution to the system
29. () 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.
an operation
Algebra
reflexive
Algebraic combinatorics
30. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Reunion of broken parts
transitive
Categories of Algebra
Linear algebra
31. 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
when b > 0
Order of Operations
A transcendental equation
Reflexive relation
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
nonnegative numbers
Number line or real line
substitution
inverse operation of Exponentiation
33. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Exponentiation
The relation of equality (=)
Polynomials
Difference of two squares - or the difference of perfect squares
34. The process of expressing the unknowns in terms of the knowns is called
The relation of inequality (<) has this property
Change of variables
inverse operation of Exponentiation
Solving the Equation
35. The value produced is called
unary and binary
Binary operations
Operations can involve dissimilar objects
value - result - or output
36. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Algebraic number theory
inverse operation of Multiplication
radical equation
The sets Xk
37. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
Algebra
The purpose of using variables
Conditional equations
38. k-ary operation is a
Equation Solving
exponential equation
Order of Operations
(k+1)-ary relation that is functional on its first k domains
39. Involve only one value - such as negation and trigonometric functions.
Properties of equality
Solution to the system
Unary operations
then ac < bc
40. Operations can have fewer or more than
Equations
two inputs
Reflexive relation
radical equation
41. 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)
Expressions
The operation of addition
A polynomial equation
range
42. There are two common types of operations:
Equations
unary and binary
A solution or root of the equation
An operation ?
43. A binary operation
then ac < bc
has arity two
A solution or root of the equation
The simplest equations to solve
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)
Universal algebra
operation
Operations can involve dissimilar objects
unary and binary
45. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
then bc < ac
The operation of exponentiation
The method of equating the coefficients
46. If it holds for all a and b in X that if a is related to b then b is related to a.
Constants
Repeated addition
(k+1)-ary relation that is functional on its first k domains
A binary relation R over a set X is symmetric
47. 1 - which preserves numbers: a
Universal algebra
has arity one
system of linear equations
Identity element of Multiplication
48. 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'.
Reflexive relation
Change of variables
scalar
unary and binary
49. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic number theory
Abstract algebra
Operations can involve dissimilar objects
operation
50. A unary operation
domain
has arity one
Algebra
nullary operation