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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. A + b = b + a
Categories of Algebra
nonnegative numbers
Algebraic equation
commutative law of Addition
2. Letters from the beginning of the alphabet like a - b - c... often denote
Identity element of Multiplication
two inputs
Constants
Operations on sets
3. Are true for only some values of the involved variables: x2 - 1 = 4.
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.
value - result - or output
Conditional equations
4. 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)
Number line or real line
Order of Operations
operation
A functional equation
5. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
value - result - or output
associative law of addition
system of linear equations
6. (a
The method of equating the coefficients
Variables
Associative law of Multiplication
inverse operation of Exponentiation
7. Subtraction ( - )
Equations
operation
A integral equation
inverse operation of addition
8. If a < b and c < d
the set Y
Order of Operations
then a + c < b + d
Operations on functions
9. 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
unary and binary
Expressions
the fixed non-negative integer k (the number of arguments)
when b > 0
10. An operation of arity k is called a
operation
inverse operation of Exponentiation
Knowns
k-ary operation
11. 1 - which preserves numbers: a
two inputs
Vectors
Identity element of Multiplication
A integral equation
12. 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.
Categories of Algebra
symmetric
Change of variables
has arity one
13. A vector can be multiplied by a scalar to form another vector
An operation ?
Operations can involve dissimilar objects
The real number system
Quadratic equations can also be solved
14. If it holds for all a and b in X that if a is related to b then b is related to a.
Solution to the system
A binary relation R over a set X is symmetric
then a + c < b + d
logarithmic equation
15. If a = b then b = a
symmetric
Algebraic geometry
Algebraic equation
Operations on sets
16. 1 - which preserves numbers: a^1 = a
substitution
Reflexive relation
identity element of Exponentiation
then ac < bc
17. The codomain is the set of real numbers but the range is the
nonnegative numbers
All quadratic equations
A transcendental equation
operation
18. The value produced is called
the fixed non-negative integer k (the number of arguments)
value - result - or output
Identity element of Multiplication
operands - arguments - or inputs
19. The values of the variables which make the equation true are the solutions of the equation and can be found through
Knowns
k-ary operation
Equation Solving
Identity element of Multiplication
20. The inner product operation on two vectors produces a
range
scalar
identity element of Exponentiation
Binary operations
21. If a < b and b < c
A linear equation
then a < c
commutative law of Multiplication
Categories of Algebra
22. 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
Difference of two squares - or the difference of perfect squares
Reunion of broken parts
Vectors
operands - arguments - or inputs
23. In which abstract algebraic methods are used to study combinatorial questions.
Number line or real line
Algebraic combinatorics
Associative law of Exponentiation
A binary relation R over a set X is symmetric
24. Include composition and convolution
inverse operation of Exponentiation
The logical values true and false
range
Operations on functions
25. A binary operation
Number line or real line
The relation of equality (=) has the property
the set Y
has arity two
26. Is an equation of the form log`a^X = b for a > 0 - which has solution
Universal algebra
Binary operations
Equation Solving
logarithmic equation
27. Operations can have fewer or more than
A differential equation
two inputs
nonnegative numbers
A transcendental equation
28. 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)
inverse operation of addition
Multiplication
The operation of exponentiation
Repeated multiplication
29. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
range
Quadratic equations can also be solved
nonnegative numbers
The method of equating the coefficients
30. Are denoted by letters at the beginning - a - b - c - d - ...
Polynomials
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
Knowns
31. 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)
an operation
range
The method of equating the coefficients
The operation of addition
32. 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
A differential equation
domain
Linear algebra
33. Is an equation in which the unknowns are functions rather than simple quantities.
An operation ?
A functional equation
Unary operations
commutative law of Exponentiation
34. A unary operation
has arity one
An operation ?
Solution to the system
then ac < bc
35. Can be combined using the function composition operation - performing the first rotation and then the second.
Elementary algebra
Linear algebra
symmetric
Rotations
36. The operation of exponentiation means ________________: a^n = a
An operation ?
Repeated multiplication
scalar
value - result - or output
37. 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'.
identity element of Exponentiation
Reflexive relation
commutative law of Addition
Elementary algebra
38. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Variables
substitution
Algebraic geometry
Universal algebra
39. 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.
identity element of Exponentiation
A integral equation
domain
The relation of inequality (<) has this property
40. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Order of Operations
Quadratic equations can also be solved
Multiplication
Algebra
41. Will have two solutions in the complex number system - but need not have any in the real number system.
then a < c
The real number system
Polynomials
All quadratic equations
42. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
The operation of exponentiation
A linear equation
Exponentiation
Identities
43. Is Written as a
then ac < bc
All quadratic equations
Pure mathematics
Multiplication
44. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
The method of equating the coefficients
Solving the Equation
Solution to the system
Difference of two squares - or the difference of perfect squares
45. Can be combined using logic operations - such as and - or - and not.
Reunion of broken parts
domain
Unary operations
The logical values true and false
46. 0 - which preserves numbers: a + 0 = a
Quadratic equations can also be solved
nonnegative numbers
identity element of addition
operation
47. Is algebraic equation of degree one
Knowns
The operation of exponentiation
The purpose of using variables
A linear equation
48. Division ( / )
Reunion of broken parts
inverse operation of Multiplication
substitution
system of linear equations
49. In an equation with a single unknown - a value of that unknown for which the equation is true is called
commutative law of Exponentiation
exponential equation
finitary operation
A solution or root of the equation
50. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
logarithmic equation
the set Y
A solution or root of the equation