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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 an equation involving integrals.
Addition
substitution
Quadratic equations can also be solved
A integral equation
2. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Linear algebra
Vectors
The relation of equality (=)
the fixed non-negative integer k (the number of arguments)
3. Is Written as a
commutative law of Exponentiation
The method of equating the coefficients
Multiplication
Equation Solving
4. If a < b and c < d
identity element of addition
then a + c < b + d
Operations on sets
exponential equation
5. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
then bc < ac
inverse operation of addition
The simplest equations to solve
6. In which properties common to all algebraic structures are studied
A binary relation R over a set X is symmetric
A Diophantine equation
Change of variables
Universal algebra
7. Are called the domains of the operation
inverse operation of addition
then ac < bc
The sets Xk
A integral equation
8. Is an equation where the unknowns are required to be integers.
A Diophantine equation
radical equation
Operations can involve dissimilar objects
system of linear equations
9. 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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10. The values for which an operation is defined form a set called its
The relation of equality (=)'s property
Constants
domain
operation
11. 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
Conditional equations
Solution to the system
The real number system
Elimination method
12. The inner product operation on two vectors produces a
scalar
when b > 0
an operation
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.
13. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
nonnegative numbers
Knowns
Conditional equations
14. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
value - result - or output
The sets Xk
The simplest equations to solve
Elimination method
15. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
unary and binary
scalar
the set Y
16. The operation of exponentiation means ________________: a^n = a
Equation Solving
Repeated addition
when b > 0
Repeated multiplication
17. Are denoted by letters at the beginning - a - b - c - d - ...
commutative law of Multiplication
Knowns
A functional equation
The purpose of using variables
18. Operations can have fewer or more than
Elimination method
nonnegative numbers
two inputs
Binary operations
19. 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)
nullary operation
then a + c < b + d
Equations
The operation of exponentiation
20. The operation of multiplication means _______________: a
Equations
Properties of equality
Repeated addition
equation
21. Introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers - such as addition. This can be done for a variety of reasons - including equation solvi
Elementary algebra
Vectors
scalar
has arity one
22. Is called the codomain of the operation
Algebraic geometry
Unary operations
the set Y
operation
23. A binary operation
has arity two
Vectors
exponential equation
unary and binary
24. Are true for only some values of the involved variables: x2 - 1 = 4.
Knowns
Conditional equations
The operation of addition
associative law of addition
25. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
nonnegative numbers
Quadratic equations can also be solved
Categories of Algebra
Repeated addition
26. 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'.
two inputs
Change of variables
Reflexive relation
Unknowns
27. (a + b) + c = a + (b + c)
exponential equation
Algebraic geometry
A solution or root of the equation
associative law of addition
28. k-ary operation is a
The central technique to linear equations
Algebraic geometry
the fixed non-negative integer k (the number of arguments)
(k+1)-ary relation that is functional on its first k domains
29. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Variables
value - result - or output
Number line or real line
identity element of Exponentiation
30. Is Written as a + b
(k+1)-ary relation that is functional on its first k domains
A differential equation
Addition
Knowns
31. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Unknowns
Operations on functions
Operations can involve dissimilar objects
Identities
32. Is an equation in which a polynomial is set equal to another polynomial.
The relation of inequality (<) has this property
Variables
A polynomial equation
Equations
33. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
Conditional equations
A binary relation R over a set X is symmetric
radical equation
34. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Pure mathematics
Identity
Conditional equations
Algebraic equation
35. Subtraction ( - )
Associative law of Multiplication
inverse operation of addition
equation
Identities
36. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
logarithmic equation
system of linear equations
Identity element of Multiplication
Multiplication
37. 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.
then a + c < b + d
The relation of inequality (<) has this property
operands - arguments - or inputs
commutative law of Multiplication
38. Is algebraic equation of degree one
A linear equation
transitive
A polynomial equation
Polynomials
39. Referring to the finite number of arguments (the value k)
identity element of addition
finitary operation
the fixed non-negative integer k (the number of arguments)
radical equation
40. An operation of arity k is called a
Associative law of Multiplication
k-ary operation
Universal algebra
Difference of two squares - or the difference of perfect squares
41. Is an equation involving derivatives.
A transcendental equation
A binary relation R over a set X is symmetric
A differential equation
Algebraic geometry
42. Include composition and convolution
Variables
Number line or real line
Operations on functions
exponential equation
43. Can be defined axiomatically up to an isomorphism
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.
reflexive
A binary relation R over a set X is symmetric
The real number system
44. 1 - which preserves numbers: a
The logical values true and false
Identity element of Multiplication
Universal algebra
Quadratic equations can also be solved
45. Is an algebraic 'sentence' containing an unknown quantity.
Linear algebra
Polynomials
Unknowns
The relation of inequality (<) has this property
46. A
commutative law of Multiplication
finitary operation
Equation Solving
Exponentiation
47. If a < b and c < 0
Equation Solving
then bc < ac
symmetric
commutative law of Addition
48. 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).
Pure mathematics
Quadratic equations
then ac < bc
Equations
49. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Elementary algebra
symmetric
Solution to the system
reflexive
50. 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
All quadratic equations
Difference of two squares - or the difference of perfect squares
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.