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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 vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
Repeated addition
inverse operation of Exponentiation
Operations on sets
2. Is Written as a
A differential equation
Rotations
Multiplication
Operations
3. Is an equation of the form aX = b for a > 0 - which has solution
The operation of addition
equation
exponential equation
Pure mathematics
4. b = b
Algebraic number theory
reflexive
has arity two
Algebraic equation
5. Operations can have fewer or more than
two inputs
substitution
radical equation
Reunion of broken parts
6. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
radical equation
Operations on functions
Equations
Multiplication
7. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
two inputs
Variables
transitive
operation
8. (a
two inputs
Associative law of Multiplication
inverse operation of addition
Reunion of broken parts
9. Is an equation of the form log`a^X = b for a > 0 - which has solution
Operations on functions
logarithmic equation
Binary operations
operands - arguments - or inputs
10. If a < b and c > 0
Rotations
then ac < bc
Quadratic equations can also be solved
The purpose of using variables
11. 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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12. The inner product operation on two vectors produces a
The real number system
Reunion of broken parts
Unary operations
scalar
13. Letters from the beginning of the alphabet like a - b - c... often denote
The logical values true and false
Constants
A differential equation
Repeated addition
14. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
operation
Knowns
Difference of two squares - or the difference of perfect squares
Multiplication
15. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
The method of equating the coefficients
Constants
Unknowns
Addition
16. 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.
k-ary operation
The relation of equality (=)
Conditional equations
The central technique to linear equations
17. If a < b and c < d
The operation of addition
unary and binary
then a + c < b + d
Knowns
18. Logarithm (Log)
commutative law of Multiplication
inverse operation of Exponentiation
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.
associative law of addition
19. A
commutative law of Multiplication
Binary operations
Addition
The purpose of using variables
20. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
finitary operation
Variables
Quadratic equations
Number line or real line
21. There are two common types of operations:
unary and binary
associative law of addition
The sets Xk
identity element of Exponentiation
22. Is an algebraic 'sentence' containing an unknown quantity.
Categories of Algebra
finitary operation
Polynomials
Order of Operations
23. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Identities
Equation Solving
commutative law of Exponentiation
Binary operations
24. If it holds for all a and b in X that if a is related to b then b is related to a.
Associative law of Exponentiation
Identity element of Multiplication
A binary relation R over a set X is symmetric
Vectors
25. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
A integral equation
Order of Operations
identity element of Exponentiation
k-ary operation
26. That 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.
Associative law of Multiplication
associative law of addition
A polynomial equation
The relation of equality (=) has the property
27. Not commutative a^b?b^a
Associative law of Exponentiation
inverse operation of Multiplication
commutative law of Exponentiation
an operation
28. Is a function of the form ? : V ? Y - where V ? X1
A functional equation
An operation ?
Repeated addition
Equations
29. Are called the domains of the operation
Identity
logarithmic equation
The sets Xk
Operations on functions
30. 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
Elementary algebra
A integral equation
Addition
31. Is called the type or arity of the operation
Repeated addition
the fixed non-negative integer k (the number of arguments)
value - result - or output
Elementary algebra
32. k-ary operation is a
(k+1)-ary relation that is functional on its first k domains
Unknowns
scalar
then a < c
33. Not associative
Constants
The real number system
Associative law of Exponentiation
Categories of Algebra
34. Is Written as ab or a^b
The simplest equations to solve
Exponentiation
nullary 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.
35. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
reflexive
Solving the Equation
Variables
36. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
Reunion of broken parts
A Diophantine equation
Quadratic equations can also be solved
equation
37. 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).
Operations
Quadratic equations
Linear algebra
Change of variables
38. The values combined are called
Categories of Algebra
operands - arguments - or inputs
commutative law of Multiplication
Equation Solving
39. The values of the variables which make the equation true are the solutions of the equation and can be found through
Expressions
A linear equation
The real number system
Equation Solving
40. Are denoted by letters at the beginning - a - b - c - d - ...
Addition
value - result - or output
has arity two
Knowns
41. In which the specific properties of vector spaces are studied (including matrices)
Properties of equality
A integral equation
Linear algebra
Quadratic equations
42. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Equations
reflexive
substitution
Abstract algebra
43. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
substitution
A functional equation
Solution to the system
transitive
44. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Equations
Identity element of Multiplication
Equation Solving
Quadratic equations can also be solved
45. A binary operation
has arity two
The purpose of using variables
Change of variables
Operations can involve dissimilar objects
46. The squaring operation only produces
nonnegative numbers
A binary relation R over a set X is symmetric
k-ary operation
scalar
47. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Algebraic equation
Pure mathematics
reflexive
identity element of addition
48. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Reunion of broken parts
Algebraic equation
Order of Operations
Algebraic combinatorics
49. Applies abstract algebra to the problems of geometry
Expressions
when b > 0
Equations
Algebraic geometry
50. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Linear algebra
Universal algebra
The relation of equality (=)
Algebraic number theory