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Test your basic knowledge |
CLEP College Algebra: Algebra Principles
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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. 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
Equation Solving
Elimination method
exponential equation
A differential equation
2. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s
the fixed non-negative integer k (the number of arguments)
substitution
identity element of Exponentiation
Repeated addition
3. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
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.
symmetric
Categories of Algebra
radical equation
4. 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)
The operation of addition
logarithmic equation
has arity two
reflexive
5. The squaring operation only produces
The relation of equality (=) has the property
Pure mathematics
nonnegative numbers
equation
6. Is an action or procedure which produces a new value from one or more input values.
Identity element of Multiplication
Binary operations
radical equation
an operation
7. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
All quadratic equations
Order of Operations
an operation
Binary operations
8. Is Written as a + b
Addition
An operation ?
A functional equation
inverse operation of Multiplication
9. 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
equation
Pure mathematics
then a + c < b + d
10. The values for which an operation is defined form a set called its
domain
Operations on functions
A Diophantine equation
A transcendental equation
11. 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
Equations
The simplest equations to solve
Linear algebra
12. The inner product operation on two vectors produces a
two inputs
then a < c
Identities
scalar
13. 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.
Change of variables
Quadratic equations
A functional equation
Solving the Equation
14. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
range
Universal algebra
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.
Number line or real line
15. Not associative
A solution or root of the equation
k-ary operation
domain
Associative law of Exponentiation
16. 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)
Reflexive relation
then a + c < b + d
The operation of exponentiation
range
17. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
finitary operation
radical equation
The sets Xk
18. Symbols that denote numbers - is to allow the making of generalizations in mathematics
Associative law of Multiplication
A integral equation
The purpose of using variables
domain
19. There are two common types of operations:
unary and binary
A transcendental equation
Repeated multiplication
Vectors
20. Is an equation in which the unknowns are functions rather than simple quantities.
Pure mathematics
inverse operation of Multiplication
(k+1)-ary relation that is functional on its first k domains
A functional equation
21. Is an equation involving a transcendental function of one of its variables.
commutative law of Exponentiation
Exponentiation
A transcendental equation
Rotations
22. Include the binary operations union and intersection and the unary operation of complementation.
nullary operation
Algebraic geometry
Operations on sets
operation
23. 0 - which preserves numbers: a + 0 = a
the set Y
(k+1)-ary relation that is functional on its first k domains
The logical values true and false
identity element of addition
24. The codomain is the set of real numbers but the range is the
nonnegative numbers
then bc < ac
Equations
Identities
25. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
identity element of Exponentiation
Exponentiation
Unknowns
the fixed non-negative integer k (the number of arguments)
26. Subtraction ( - )
logarithmic equation
Rotations
inverse operation of addition
A linear equation
27. An operation of arity zero is simply an element of the codomain Y - called a
Difference of two squares - or the difference of perfect squares
Quadratic equations can also be solved
nullary operation
nonnegative numbers
28. In which properties common to all algebraic structures are studied
Algebra
The sets Xk
logarithmic equation
Universal algebra
29. Logarithm (Log)
then ac < bc
A linear equation
inverse operation of Exponentiation
The relation of equality (=)'s property
30. 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
A binary relation R over a set X is symmetric
The method of equating the coefficients
identity element of Exponentiation
Polynomials
31. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
Linear algebra
Algebraic number theory
A linear equation
32. Operations can have fewer or more than
The operation of exponentiation
The method of equating the coefficients
two inputs
symmetric
33. Is called the type or arity of the operation
the fixed non-negative integer k (the number of arguments)
value - result - or output
range
logarithmic equation
34. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
scalar
nonnegative numbers
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 Exponentiation
35. Is Written as ab or a^b
A solution or root of the equation
commutative law of Addition
Order of Operations
Exponentiation
36. Are called the domains of the operation
The sets Xk
Quadratic equations can also be solved
Addition
Algebraic number theory
37. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
Associative law of Exponentiation
Identities
Real number
38. Is an equation involving derivatives.
A differential equation
Equation Solving
Linear algebra
Quadratic equations
39. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Identities
Operations on sets
associative 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.
40. Can be combined using logic operations - such as and - or - and not.
the fixed non-negative integer k (the number of arguments)
The logical values true and false
Conditional equations
has arity one
41. An operation of arity k is called a
identity element 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.
k-ary operation
Quadratic equations
42. May contain numbers - variables and arithmetical operations. These are conventionally written with 'higher-power' terms on the left
scalar
Operations on functions
has arity two
Expressions
43. 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
All quadratic equations
The relation of equality (=)
Universal algebra
Reunion of broken parts
44. Can be defined axiomatically up to an isomorphism
Elimination method
the set Y
The real number system
Operations can involve dissimilar objects
45. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Reflexive relation
when b > 0
Algebraic equation
Conditional equations
46. 1 - which preserves numbers: a
symmetric
Identity element of Multiplication
Multiplication
Abstract algebra
47. 1 - which preserves numbers: a^1 = a
Categories of Algebra
identity element of Exponentiation
identity element of addition
commutative law of Exponentiation
48. 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 equation
Operations on sets
The relation of inequality (<) has this property
Properties of equality
49. If a = b then b = a
Binary operations
Associative law of Exponentiation
symmetric
A linear equation
50. In which the specific properties of vector spaces are studied (including matrices)
inverse operation of Multiplication
Linear algebra
The relation of equality (=)'s property
Repeated multiplication