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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. 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
then a < c
Exponentiation
inverse operation of Exponentiation
when b > 0
2. b = b
inverse operation of addition
reflexive
Repeated multiplication
Equations
3. A + b = b + a
commutative law of Addition
Reflexive relation
Operations on functions
then a < c
4. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
A transcendental equation
equation
Universal algebra
The relation of equality (=) has the property
5. The values for which an operation is defined form a set called its
A polynomial equation
Repeated multiplication
Operations on functions
domain
6. 1 - which preserves numbers: a^1 = a
The purpose of using variables
identity element of Exponentiation
Properties of equality
then bc < ac
7. 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)
The operation of exponentiation
Properties of equality
Knowns
Operations
8. Is algebraic equation of degree one
A linear equation
Elimination method
Expressions
Categories of Algebra
9. Is the claim that two expressions have the same value and are equal.
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
Elementary algebra
Equations
10. Operations can have fewer or more than
operation
Identities
A linear equation
two inputs
11. Is an equation involving a transcendental function of one of its variables.
then bc < ac
substitution
nullary operation
A transcendental equation
12. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
value - result - or output
Change of variables
commutative law of Multiplication
13. The values of the variables which make the equation true are the solutions of the equation and can be found through
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.
A Diophantine equation
Equation Solving
scalar
14. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
Equation Solving
Operations can involve dissimilar objects
Quadratic equations can also be solved
when b > 0
15. Applies abstract algebra to the problems of geometry
nonnegative numbers
Repeated addition
Algebraic geometry
commutative law of Multiplication
16. Is synonymous with function - map and mapping - that is - a relation - for which each element of the domain (input set) is associated with exactly one element of the codomain (set of possible outputs).
operation
symmetric
has arity two
Properties of equality
17. An operation of arity k is called a
Addition
commutative law of Multiplication
k-ary operation
A binary relation R over a set X is symmetric
18. A value that represents a quantity along a continuum - such as -5 (an integer) - 4/3 (a rational number that is not an integer) - 8.6 (a rational number given by a finite decimal representation) - v2 (the square root of two - an algebraic number that
nonnegative numbers
Conditional equations
Real number
Elimination method
19. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Identity
identity element of Exponentiation
Real number
Solution to the system
20. 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'.
scalar
then a < c
Reflexive relation
Expressions
21. The operation of exponentiation means ________________: a^n = a
operands - arguments - or inputs
Repeated multiplication
then ac < bc
inverse operation of Exponentiation
22. If a < b and c > 0
Multiplication
nullary operation
commutative law of Addition
then ac < bc
23. In which the specific properties of vector spaces are studied (including matrices)
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.
A transcendental equation
domain
Linear algebra
24. The values combined are called
operands - arguments - or inputs
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.
Linear algebra
Identity
25. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
The relation of equality (=) has the property
Algebraic equation
Pure mathematics
Algebra
26. There are two common types of operations:
Quadratic equations can also be solved
has arity two
unary and binary
The operation of addition
27. 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
commutative law of Multiplication
Algebra
Equations
28. If a < b and c < d
then a + c < b + d
Vectors
Elementary algebra
Equations
29. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Elimination method
(k+1)-ary relation that is functional on its first k domains
The relation of inequality (<) has this property
Variables
30. Not commutative a^b?b^a
commutative law of Exponentiation
Exponentiation
Binary operations
Algebra
31. If a < b and c < 0
Elementary algebra
Reunion of broken parts
then bc < ac
Abstract algebra
32. Is an equation involving integrals.
A integral equation
identity element of Exponentiation
reflexive
Repeated addition
33. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
Difference of two squares - or the difference of perfect squares
The method of equating the coefficients
Unknowns
Operations can involve dissimilar objects
34. 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.
Unknowns
The relation of equality (=) has the property
A linear equation
has arity one
35. 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
then ac < bc
All quadratic equations
The logical values true and false
36. Involve only one value - such as negation and trigonometric functions.
radical equation
Unary operations
operation
The real number system
37. Subtraction ( - )
inverse operation of addition
Categories of Algebra
nonnegative numbers
Unary operations
38. The value produced is called
Properties of equality
domain
value - result - or output
(k+1)-ary relation that is functional on its first k domains
39. 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.
has arity two
Change of variables
(k+1)-ary relation that is functional on its first k domains
an operation
40. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
the fixed non-negative integer k (the number of arguments)
Number line or real line
system of linear equations
The sets Xk
41. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
equation
All quadratic equations
The real number system
42. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
Operations
The sets Xk
range
Algebraic equation
43. The process of expressing the unknowns in terms of the knowns is called
(k+1)-ary relation that is functional on its first k domains
The relation of inequality (<) has this property
operation
Solving the Equation
44. 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).
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.
Quadratic equations
A binary relation R over a set X is symmetric
45. 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
range
Reunion of broken parts
domain
nonnegative numbers
46. Is Written as a
Solving the Equation
Multiplication
A binary relation R over a set X is symmetric
Operations on sets
47. Logarithm (Log)
Associative law of Multiplication
Rotations
inverse operation of Exponentiation
Quadratic equations can also be solved
48. In which abstract algebraic methods are used to study combinatorial questions.
The simplest equations to solve
Identities
An operation ?
Algebraic combinatorics
49. If a = b and b = c then a = c
then ac < bc
Equations
then bc < ac
transitive
50. 0 - which preserves numbers: a + 0 = a
Unary operations
identity element of addition
Real number
Categories of Algebra