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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. 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
Properties of equality
Exponentiation
The real number system
substitution
2. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
An operation ?
The relation of equality (=)'s property
Algebraic number theory
The operation of exponentiation
3. An operation of arity zero is simply an element of the codomain Y - called a
Multiplication
Exponentiation
Solution to the system
nullary operation
4. Not associative
Algebraic geometry
scalar
A Diophantine equation
Associative law of Exponentiation
5. 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.
Reflexive relation
The relation of inequality (<) has this property
Elementary algebra
identity element of addition
6. The process of expressing the unknowns in terms of the knowns is called
k-ary operation
Solving the Equation
A polynomial equation
Algebraic combinatorics
7. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
symmetric
Number line or real line
Algebraic number theory
8. Is an equation in which a polynomial is set equal to another polynomial.
Associative law of Multiplication
Expressions
A polynomial equation
Multiplication
9. 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 real number system
Real number
unary and binary
has arity one
10. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
commutative law of Exponentiation
Algebra
Associative law of Exponentiation
11. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
commutative law of Multiplication
Linear algebra
Algebraic geometry
12. Will have two solutions in the complex number system - but need not have any in the real number system.
Difference of two squares - or the difference of perfect squares
scalar
commutative law of Addition
All quadratic equations
13. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
unary and binary
The relation of inequality (<) has this property
then a + c < b + d
The simplest equations to solve
14. Can be combined using logic operations - such as and - or - and not.
Quadratic equations
Variables
The logical values true and false
A solution or root of the equation
15. Is an equation involving derivatives.
Real number
A differential equation
has arity two
Variables
16. 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
A transcendental equation
Knowns
Abstract algebra
The method of equating the coefficients
17. A unary operation
has arity one
logarithmic equation
Expressions
Unary operations
18. Is Written as a + b
Addition
Order of Operations
then ac < bc
The sets Xk
19. Is an equation involving integrals.
The logical values true and false
A differential equation
A integral equation
Quadratic equations
20. If a = b then b = a
symmetric
The operation of exponentiation
transitive
The relation of equality (=)'s property
21. b = b
nonnegative numbers
The relation of equality (=)'s property
A functional equation
reflexive
22. Are called the domains of the operation
reflexive
The sets Xk
The simplest equations to solve
Solution to the system
23. 1 - which preserves numbers: a
domain
the set Y
Addition
Identity element of Multiplication
24. 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.
Knowns
The central technique to linear equations
Solving the Equation
Repeated addition
25. In which the specific properties of vector spaces are studied (including matrices)
Multiplication
Linear algebra
Expressions
A polynomial equation
26. Is algebraic equation of degree one
Conditional equations
A linear equation
equation
Repeated addition
27. Is the claim that two expressions have the same value and are equal.
Number line or real line
Equations
Binary operations
Categories of Algebra
28. The value produced is called
value - result - or output
A transcendental equation
system of linear equations
The relation of equality (=)
29. 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
has arity two
An operation ?
Algebraic equation
Reunion of broken parts
30. Are denoted by letters at the beginning - a - b - c - d - ...
value - result - or output
Algebraic combinatorics
Knowns
k-ary operation
31. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
The relation of equality (=)
Expressions
substitution
equation
32. 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.
Properties of equality
The real number system
Algebraic geometry
operation
33. Include composition and convolution
A integral equation
Operations on functions
A binary relation R over a set X is symmetric
Algebraic equation
34. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
Abstract algebra
commutative law of Exponentiation
radical equation
35. Is Written as a
an operation
Order of Operations
when b > 0
Multiplication
36. The operation of multiplication means _______________: a
Repeated addition
Reflexive relation
Repeated multiplication
Solution to the system
37. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
Expressions
The relation of equality (=)
operation
finitary operation
38. If a = b and b = c then a = c
finitary operation
the fixed non-negative integer k (the number of arguments)
transitive
Properties of equality
39. If a < b and b < c
nullary operation
then a < c
The logical values true and false
(k+1)-ary relation that is functional on its first k domains
40. () 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.
A linear equation
Polynomials
Algebra
Associative law of Multiplication
41. If a < b and c < d
associative law of addition
the set Y
then a + c < b + d
Associative law of Multiplication
42. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
then a + c < b + d
exponential equation
substitution
43. If it holds for all a and b in X that if a is related to b then b is related to a.
Properties of equality
Solving the Equation
A binary relation R over a set X is symmetric
Knowns
44. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
Rotations
Constants
Reflexive relation
45. (a
Multiplication
Associative law of Multiplication
Number line or real line
The central technique to linear equations
46. Is an equation where the unknowns are required to be integers.
commutative law of Multiplication
transitive
A Diophantine equation
Operations can involve dissimilar objects
47. 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).
system of linear equations
inverse operation of Multiplication
operation
nonnegative numbers
48. Is called the type or arity of the operation
finitary operation
Pure mathematics
the fixed non-negative integer k (the number of arguments)
reflexive
49. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
A linear equation
Number line or real line
A functional equation
an operation
50. Is an equation of the form log`a^X = b for a > 0 - which has solution
Algebraic geometry
Equation Solving
Identity
logarithmic equation