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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. If a < b and c < 0
Repeated addition
nullary operation
Identity
then bc < ac
2. The value produced is called
value - result - or output
Identity element of Multiplication
Algebra
then ac < bc
3. 0 - which preserves numbers: a + 0 = a
Quadratic equations can also be solved
identity element of addition
substitution
commutative law of Exponentiation
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
Expressions
The relation of inequality (<) has this property
Rotations
5. 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).
then a + c < b + d
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.
operation
The relation of inequality (<) has this property
6. Are denoted by letters at the beginning - a - b - c - d - ...
inverse operation of Exponentiation
The purpose of using variables
Knowns
Identity element of Multiplication
7. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
A Diophantine equation
inverse operation of Exponentiation
(k+1)-ary relation that is functional on its first k domains
Difference of two squares - or the difference of perfect squares
8. Is Written as a + b
then a < c
Addition
A transcendental equation
associative law of addition
9. The process of expressing the unknowns in terms of the knowns is called
Vectors
Real number
Elementary algebra
Solving the Equation
10. A binary operation
has arity two
Abstract algebra
Identities
nullary operation
11. (a
Operations can involve dissimilar objects
A differential equation
Number line or real line
Associative law of Multiplication
12. Is an equation involving a transcendental function of one of its variables.
The purpose of using variables
A transcendental equation
Solving the Equation
two inputs
13. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
nullary operation
Equations
equation
A functional equation
14. 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.
logarithmic equation
Properties of equality
Equation Solving
Equations
15. Are true for only some values of the involved variables: x2 - 1 = 4.
inverse operation of Multiplication
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.
Operations on functions
Conditional equations
16. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Variables
The relation of inequality (<) has this property
two inputs
Identities
17. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Rotations
Operations on functions
The relation of inequality (<) has this property
Variables
18. If it holds for all a and b in X that if a is related to b then b is related to a.
Vectors
Properties of equality
A binary relation R over a set X is symmetric
unary and binary
19. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
The sets Xk
nonnegative numbers
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.
operation
20. Applies abstract algebra to the problems of geometry
Associative law of Multiplication
Identities
Linear algebra
Algebraic geometry
21. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
An operation ?
unary and binary
(k+1)-ary relation that is functional on its first k domains
22. Is the claim that two expressions have the same value and are equal.
k-ary operation
exponential equation
Elementary algebra
Equations
23. 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
Identity element of Multiplication
equation
k-ary operation
substitution
24. k-ary operation is a
nullary operation
radical equation
(k+1)-ary relation that is functional on its first k domains
The relation of inequality (<) has this property
25. 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 relation of equality (=) has the property
scalar
identity element of addition
The method of equating the coefficients
26. Division ( / )
Unary operations
inverse operation of Multiplication
Rotations
Equations
27. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
the fixed non-negative integer k (the number of arguments)
Real number
Variables
28. Is Written as a
finitary operation
Multiplication
k-ary operation
Elementary algebra
29. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi
Operations on sets
Linear algebra
Elementary algebra
Change of variables
30. b = b
Variables
Algebra
finitary operation
reflexive
31. If a = b then b = a
Expressions
substitution
symmetric
Equations
32. Can be added and subtracted.
Vectors
Repeated addition
Exponentiation
Algebraic equation
33. The values of the variables which make the equation true are the solutions of the equation and can be found through
Addition
Equation Solving
value - result - or output
The relation of inequality (<) has this property
34. Is a function of the form ? : V ? Y - where V ? X1
The sets Xk
The operation of exponentiation
An operation ?
logarithmic equation
35. May not be defined for every possible value.
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.
Algebraic geometry
Operations can involve dissimilar objects
Operations
36. Is algebraic equation of degree one
A transcendental equation
The operation of addition
A integral equation
A linear equation
37. Can be combined using the function composition operation - performing the first rotation and then the second.
Rotations
Reunion of broken parts
Equations
Operations on functions
38. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Equation Solving
Number line or real line
A functional equation
Operations can involve dissimilar objects
39. In an equation with a single unknown - a value of that unknown for which the equation is true is called
when b > 0
The relation of equality (=)
identity element of Exponentiation
A solution or root of the equation
40. 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)
operation
operands - arguments - or inputs
(k+1)-ary relation that is functional on its first k domains
Number line or real line
41. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Quadratic equations
Order of Operations
Reflexive relation
The operation of addition
42. Are called the domains of the operation
The relation of equality (=)
The sets Xk
The operation of addition
Multiplication
43. Is an algebraic 'sentence' containing an unknown quantity.
then ac < bc
equation
Polynomials
An operation ?
44. 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
The relation of inequality (<) has this property
nonnegative numbers
Elimination method
Real number
45. A unary operation
Algebraic number theory
A linear equation
domain
has arity one
46. The inner product operation on two vectors produces a
scalar
operation
The operation of exponentiation
two inputs
47. Can be combined using logic operations - such as and - or - and not.
operands - arguments - or inputs
Exponentiation
The logical values true and false
Binary operations
48. A vector can be multiplied by a scalar to form another vector
A binary relation R over a set X is symmetric
The simplest equations to solve
Operations can involve dissimilar objects
substitution
49. Is an equation involving integrals.
unary and binary
logarithmic equation
finitary operation
A integral equation
50. 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 on functions
Change of variables
radical equation
Linear algebra