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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. 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.
Expressions
Properties of equality
Change of variables
when b > 0
2. The process of expressing the unknowns in terms of the knowns is called
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.
operands - arguments - or inputs
Solving the Equation
Knowns
3. 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.
Algebraic geometry
two inputs
The operation of addition
Properties of equality
4. If a < b and c > 0
Algebraic equation
Solving the Equation
Operations
then ac < bc
5. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Rotations
The relation of equality (=)
operation
Algebraic equation
6. Are denoted by letters at the beginning - a - b - c - d - ...
operation
Equations
Knowns
has arity two
7. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
equation
the set Y
Addition
Associative law of Exponentiation
8. 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.
Algebra
Repeated multiplication
The relation of inequality (<) has this property
The logical values true and false
9. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Quadratic equations can also be solved
Equations
Variables
transitive
10. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
A transcendental equation
Reflexive relation
The simplest equations to solve
logarithmic equation
11. 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
Reflexive relation
two inputs
when b > 0
domain
12. 1 - which preserves numbers: a^1 = a
Operations
identity element of Exponentiation
Binary operations
Conditional equations
13. 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 method of equating the coefficients
Solving the Equation
then a + c < b + d
then ac < bc
14. Referring to the finite number of arguments (the value k)
Repeated multiplication
finitary operation
Constants
value - result - or output
15. A vector can be multiplied by a scalar to form another vector
k-ary operation
The logical values true and false
associative law of addition
Operations can involve dissimilar objects
16. Can be added and subtracted.
Vectors
Algebra
Elimination method
domain
17. If a = b then b = a
Unary operations
commutative law of Addition
system of linear equations
symmetric
18. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
The operation of addition
A transcendental equation
The relation of equality (=)
19. The inner product operation on two vectors produces a
scalar
identity element of addition
an operation
Identity
20. Is an equation of the form X^m/n = a - for m - n integers - which has solution
A Diophantine equation
radical equation
The purpose of using variables
scalar
21. Is an equation involving a transcendental function of one of its variables.
inverse operation of addition
A transcendental equation
Linear algebra
operation
22. (a
Associative law of Multiplication
Vectors
when b > 0
The real number system
23. Is an equation of the form aX = b for a > 0 - which has solution
The simplest equations to solve
exponential equation
Exponentiation
Equation Solving
24. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
value - result - or output
Quadratic equations can also be solved
system of linear equations
Identity element of Multiplication
25. Is called the codomain of the operation
Exponentiation
the set Y
The logical values true and false
Addition
26. A
then bc < ac
commutative law of Multiplication
Identities
Unknowns
27. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
range
Difference of two squares - or the difference of perfect squares
Solution to the system
Knowns
28. Subtraction ( - )
Identities
associative law of addition
Exponentiation
inverse operation of addition
29. Logarithm (Log)
value - result - or output
Expressions
has arity two
inverse operation of Exponentiation
30. Are called the domains of the operation
The method of equating the coefficients
reflexive
The sets Xk
identity element of Exponentiation
31. Are true for only some values of the involved variables: x2 - 1 = 4.
Conditional equations
Operations on functions
(k+1)-ary relation that is functional on its first k domains
A differential equation
32. 1 - which preserves numbers: a
Equations
A linear equation
Binary operations
Identity element of Multiplication
33. Is an equation involving integrals.
then a + c < b + d
A integral equation
has arity one
Operations can involve dissimilar objects
34. The operation of exponentiation means ________________: a^n = a
Equation Solving
A solution or root of the equation
Repeated multiplication
Addition
35. 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
k-ary operation
then a < c
Real number
36. Will have two solutions in the complex number system - but need not have any in the real number system.
Categories of Algebra
scalar
All quadratic equations
the fixed non-negative integer k (the number of arguments)
37. Is Written as a + b
commutative law of Multiplication
Addition
A polynomial equation
radical equation
38. Is an equation where the unknowns are required to be integers.
Quadratic equations can also be solved
Elimination method
Solution to the system
A Diophantine equation
39. 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)
associative law of addition
The operation of exponentiation
Knowns
Pure mathematics
40. An operation of arity k is called a
k-ary operation
Operations can involve dissimilar objects
Operations on functions
The central technique to linear equations
41. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
Equations
Polynomials
Solving the Equation
Real number
42. The value produced is called
value - result - or output
finitary operation
Algebraic combinatorics
A binary relation R over a set X is symmetric
43. Is a function of the form ? : V ? Y - where V ? X1
Change of variables
A solution or root of the equation
An operation ?
has arity two
44. Can be combined using logic operations - such as and - or - and not.
Reflexive relation
Knowns
The logical values true and false
Reunion of broken parts
45. Is an equation in which a polynomial is set equal to another polynomial.
The operation of exponentiation
Unary operations
Algebraic combinatorics
A polynomial equation
46. The operation of multiplication means _______________: a
Multiplication
inverse operation of Exponentiation
Repeated addition
Change of variables
47. A unary operation
The operation of exponentiation
domain
An operation ?
has arity one
48. The values combined are called
The method of equating the coefficients
then a < c
The purpose of using variables
operands - arguments - or inputs
49. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Unary operations
range
Associative law of Multiplication
Operations
50. 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).
A binary relation R over a set X is symmetric
A functional equation
inverse operation of Exponentiation
Quadratic equations