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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
Start Test
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 then b = a
symmetric
then bc < ac
Equations
Operations can involve dissimilar objects
2. Not commutative a^b?b^a
Change of variables
commutative law of Exponentiation
A Diophantine equation
Universal algebra
3. Are called the domains of the operation
The sets Xk
A linear equation
The central technique to linear equations
Algebraic geometry
4. 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.
the set Y
Equations
Properties of equality
The relation of equality (=)
5. 0 - which preserves numbers: a + 0 = a
operation
Quadratic equations can also be solved
identity element of addition
two inputs
6. Is Written as a
Algebraic geometry
Multiplication
Conditional equations
nullary operation
7. 1 - which preserves numbers: a
equation
has arity one
Identity element of Multiplication
Addition
8. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
commutative law of Exponentiation
Operations on functions
the fixed non-negative integer k (the number of arguments)
9. The operation of multiplication means _______________: a
Knowns
nullary operation
Universal algebra
Repeated addition
10. Operations can have fewer or more than
Identity element of Multiplication
domain
two inputs
A Diophantine equation
11. Can be defined axiomatically up to an isomorphism
system of linear equations
The real number system
the fixed non-negative integer k (the number of arguments)
commutative law of Exponentiation
12. Can be written in terms of n-th roots: a^m/n = (nva)^m and thus even roots of negative numbers do not exist in the real number system - has the property: a^ba^c = a^b+c - has the property: (a^b)^c = a^bc - In general a^b ? b^a and (a^b)^c ? a^(b^c)
reflexive
The operation of exponentiation
inverse operation of addition
unary and binary
13. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Quadratic equations can also be solved
Operations on functions
Variables
logarithmic equation
14. 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.
Elimination method
The central technique to linear equations
A polynomial equation
Solving the Equation
15. A vector can be multiplied by a scalar to form another vector
A differential equation
has arity two
Operations can involve dissimilar objects
the set Y
16. In which abstract algebraic methods are used to study combinatorial questions.
Universal algebra
A solution or root of the equation
Algebraic combinatorics
Change of variables
17. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Abstract algebra
Properties of equality
Algebraic combinatorics
system of linear equations
18. Is an equation of the form X^m/n = a - for m - n integers - which has solution
has arity one
radical equation
then a < c
The operation of addition
19. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
commutative law of Multiplication
Difference of two squares - or the difference of perfect squares
Unary operations
20. Is an equation involving derivatives.
then a + c < b + d
A differential equation
Vectors
Algebraic number theory
21. Is called the codomain of the operation
the set Y
Binary operations
Repeated multiplication
Operations
22. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
commutative law of Addition
then ac < bc
Reflexive relation
23. An example of solving a system of linear equations is by using the elimination method: Multiplying the terms in the second equation by 2: Adding the two equations together to get: which simplifies to Since the fact that x = 2 is known - it is then po
Elimination method
Algebraic number theory
operation
Identities
24. A unary operation
has arity one
Operations
A transcendental equation
then bc < ac
25. 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 real number system
equation
Change of variables
(k+1)-ary relation that is functional on its first k domains
26. If a < b and c > 0
then ac < bc
Conditional equations
Categories of Algebra
The purpose of using variables
27. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Equations
when b > 0
Order of Operations
system of linear equations
28. Is an equation involving integrals.
A integral equation
Algebraic geometry
has arity one
Identity
29. Division ( / )
Knowns
inverse operation of Multiplication
when b > 0
operands - arguments - or inputs
30. There are two common types of operations:
The relation of equality (=)
unary and binary
commutative law of Multiplication
The relation of inequality (<) has this property
31. If it holds for all a and b in X that if a is related to b then b is related to a.
The sets Xk
Polynomials
commutative law of Exponentiation
A binary relation R over a set X is symmetric
32. In which properties common to all algebraic structures are studied
Universal algebra
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.
Equation Solving
Quadratic equations can also be solved
33. Are denoted by letters at the beginning - a - b - c - d - ...
has arity one
reflexive
Knowns
radical equation
34. 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 transcendental equation
Quadratic equations
Number line or real line
The relation of equality (=) has the property
35. 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
Addition
commutative law of Multiplication
Pure mathematics
36. An operation of arity k is called a
identity element of Exponentiation
k-ary operation
unary and binary
Vectors
37. The values combined are called
operands - arguments - or inputs
Elimination method
Reflexive relation
A functional equation
38. A + b = b + a
Operations
value - result - or output
commutative law of Addition
Abstract algebra
39. Letters from the beginning of the alphabet like a - b - c... often denote
Universal algebra
Constants
reflexive
inverse operation of Multiplication
40. Can be added and subtracted.
Unknowns
Vectors
Unary operations
Repeated multiplication
41. Applies abstract algebra to the problems of geometry
The relation of equality (=)'s property
Operations on sets
A binary relation R over a set X is symmetric
Algebraic geometry
42. Not associative
Associative law of Exponentiation
A polynomial equation
Abstract algebra
symmetric
43. Include composition and convolution
operands - arguments - or inputs
nonnegative numbers
exponential equation
Operations on functions
44. An operation of arity zero is simply an element of the codomain Y - called a
The logical values true and false
nullary operation
Constants
A transcendental equation
45. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
Polynomials
Equations
Multiplication
46. k-ary operation is a
Rotations
(k+1)-ary relation that is functional on its first k domains
Reflexive relation
range
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.
Algebra
A Diophantine equation
Operations
Algebraic equation
48. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
Repeated multiplication
Pure mathematics
operands - arguments - or inputs
49. (a
Identities
All quadratic equations
Identity
Associative law of Multiplication
50. 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.