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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. k-ary operation is a
nullary operation
system of linear equations
(k+1)-ary relation that is functional on its first k domains
Solving the Equation
2. The inner product operation on two vectors produces a
commutative law of Exponentiation
Associative law of Multiplication
nullary operation
scalar
3. If a < b and c > 0
Reunion of broken parts
The relation of inequality (<) has this property
commutative law of Exponentiation
then ac < bc
4. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
Properties of equality
k-ary operation
Unknowns
Order of Operations
5. Is an equation of the form X^m/n = a - for m - n integers - which has solution
Properties of equality
radical equation
commutative law of Multiplication
Algebraic equation
6. Involve only one value - such as negation and trigonometric functions.
then a + c < b + d
Equation Solving
Unary operations
finitary operation
7. 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.
A integral equation
radical equation
Change of variables
Reunion of broken parts
8. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
Unary operations
nullary operation
A linear equation
9. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The logical values true and false
The relation of equality (=)
two inputs
A integral equation
10. The squaring operation only produces
the set Y
Quadratic equations
Solving the Equation
nonnegative numbers
11. Can be added and subtracted.
operation
Vectors
Equation Solving
logarithmic equation
12. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Knowns
Elementary algebra
Variables
Solution to the system
13. Will have two solutions in the complex number system - but need not have any in the real number system.
Rotations
operation
The purpose of using variables
All quadratic equations
14. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Identity
Abstract algebra
identity element of Exponentiation
Operations can involve dissimilar objects
15. 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
The simplest equations to solve
Elementary algebra
Number line or real line
16. If a = b then b = a
The purpose of using variables
Algebraic equation
Variables
symmetric
17. Subtraction ( - )
then a < c
then bc < ac
Binary operations
inverse operation of addition
18. Is Written as a + b
substitution
finitary operation
Addition
The method of equating the coefficients
19. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
The operation of exponentiation
Repeated multiplication
nonnegative numbers
20. 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.
The relation of inequality (<) has this property
inverse operation of addition
A solution or root of the equation
Repeated multiplication
21. The operation of multiplication means _______________: a
Repeated addition
operation
Universal algebra
range
22. May not be defined for every possible value.
Elimination method
value - result - or output
Polynomials
Operations
23. Include the binary operations union and intersection and the unary operation of complementation.
value - result - or output
Number line or real line
A polynomial equation
Operations on sets
24. 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.
Associative law of Multiplication
Properties of equality
operation
Knowns
25. A binary operation
Linear algebra
has arity two
has arity one
The sets Xk
26. A + b = b + a
Associative law of Exponentiation
The sets Xk
commutative law of Addition
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.
27. 1 - which preserves numbers: a
An operation ?
Algebraic combinatorics
Identity element of Multiplication
Equations
28. If a = b and b = c then a = c
Variables
A transcendental equation
transitive
The central technique to linear equations
29. 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
(k+1)-ary relation that is functional on its first k domains
Identity element of Multiplication
Algebraic equation
30. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Conditional equations
Reflexive relation
Order of Operations
The relation of equality (=) has the property
31. A
Polynomials
commutative law of Multiplication
then ac < bc
then a + c < b + d
32. 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
identity element of addition
A polynomial equation
A solution or root of the equation
Reunion of broken parts
33. In which abstract algebraic methods are used to study combinatorial questions.
Polynomials
Algebraic combinatorics
associative law of addition
the fixed non-negative integer k (the number of arguments)
34. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Binary operations
The relation of equality (=) has the property
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.
system of linear equations
35. Not commutative a^b?b^a
scalar
commutative law of Exponentiation
Solving the Equation
Unknowns
36. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
inverse operation of addition
Quadratic equations can also be solved
Solution to the system
Identity
37. 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)
Elementary algebra
The operation of exponentiation
Binary operations
scalar
38. 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.
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39. Symbols that denote numbers - is to allow the making of generalizations in mathematics
then a < c
The purpose of using variables
The logical values true and false
Difference of two squares - or the difference of perfect squares
40. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Algebra
Binary operations
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.
inverse operation of Multiplication
41. 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
Associative law 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.
Elimination method
A differential equation
42. 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
operation
Algebraic equation
then a + c < b + d
43. Applies abstract algebra to the problems of geometry
Multiplication
Universal algebra
Algebraic geometry
(k+1)-ary relation that is functional on its first k domains
44. 0 - which preserves numbers: a + 0 = a
The relation of equality (=)
The operation of addition
identity element of addition
Algebraic combinatorics
45. 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
system of linear equations
The method of equating the coefficients
The relation of inequality (<) has this property
46. Are called the domains of the operation
Associative law of Multiplication
The sets Xk
reflexive
finitary operation
47. The value produced is called
Multiplication
value - result - or output
A integral equation
Addition
48. Is an equation involving derivatives.
A integral equation
A differential equation
the set Y
A solution or root of the equation
49. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
when b > 0
Equations
identity element of Exponentiation
A linear equation
50. Logarithm (Log)
Elimination method
inverse operation of Exponentiation
nonnegative numbers
commutative law of Addition