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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. 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
Algebraic equation
Real number
The real number system
Operations
2. Will have two solutions in the complex number system - but need not have any in the real number system.
The operation of exponentiation
Operations on functions
then a < c
All quadratic equations
3. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Rotations
Number line or real line
The operation of exponentiation
A Diophantine equation
4. Referring to the finite number of arguments (the value k)
Binary operations
has arity one
Repeated addition
finitary operation
5. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
The real number system
nonnegative numbers
The simplest equations to solve
identity element of Exponentiation
6. 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
k-ary operation
operation
A Diophantine equation
7. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
Identity
Order of Operations
substitution
The simplest equations to solve
8. The inner product operation on two vectors produces a
commutative law of Addition
unary and binary
Operations can involve dissimilar objects
scalar
9. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
operation
domain
system of linear equations
An operation ?
10. Can be defined axiomatically up to an isomorphism
Reunion of broken parts
Exponentiation
The real number system
Quadratic equations can also be solved
11. In which the specific properties of vector spaces are studied (including matrices)
Linear algebra
Addition
Unary operations
Repeated multiplication
12. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
Equations
Quadratic equations can also be solved
reflexive
13. 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).
Repeated multiplication
operation
Operations on sets
The purpose of using variables
14. Is an equation in which a polynomial is set equal to another polynomial.
Addition
Repeated multiplication
A polynomial equation
A solution or root of the equation
15. Not associative
Associative law of Exponentiation
nonnegative numbers
Elimination method
nonnegative numbers
16. Applies abstract algebra to the problems of geometry
inverse operation of Exponentiation
Algebraic geometry
A polynomial equation
Reunion of broken parts
17. Is an equation involving derivatives.
A differential equation
Unknowns
A functional equation
then a < c
18. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
k-ary operation
Equation Solving
Algebraic number theory
The logical values true and false
19. Is algebraic equation of degree one
Operations on functions
equation
radical equation
A linear equation
20. In which abstract algebraic methods are used to study combinatorial questions.
Algebraic combinatorics
nonnegative numbers
exponential equation
inverse operation of Multiplication
21. 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
Vectors
finitary operation
the set Y
Elimination method
22. If a = b then b = a
Reflexive relation
symmetric
an operation
the set Y
23. 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.
The relation of equality (=) has the property
has arity one
commutative law of Addition
The relation of equality (=)
24. Can be combined using the function composition operation - performing the first rotation and then the second.
value - result - or output
Rotations
nonnegative numbers
Conditional equations
25. Not commutative a^b?b^a
Algebraic number theory
commutative law of Exponentiation
operands - arguments - or inputs
Exponentiation
26. The squaring operation only produces
Quadratic equations can also be solved
nonnegative numbers
Difference of two squares - or the difference of perfect squares
Operations
27. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebra
Repeated addition
Algebraic equation
Real number
28. Involve only one value - such as negation and trigonometric functions.
inverse operation of addition
then a + c < b + d
inverse operation of Multiplication
Unary operations
29. 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'.
The relation of equality (=) has the property
Operations
Reflexive relation
symmetric
30. 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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31. 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)
A integral equation
Number line or real line
operation
Reunion of broken parts
32. 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
Change of variables
nonnegative numbers
Identity
33. 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
The sets Xk
Exponentiation
Algebraic combinatorics
34. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Pure mathematics
Reflexive relation
Algebraic combinatorics
All quadratic equations
35. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
two inputs
The purpose of using variables
Number line or real line
36. The process of expressing the unknowns in terms of the knowns is called
Quadratic equations
Solving the Equation
nullary operation
associative law of addition
37. 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.
Solving the Equation
A polynomial equation
The central technique to linear equations
then bc < ac
38. 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 can involve dissimilar objects
Quadratic equations
Binary operations
k-ary operation
39. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
two inputs
equation
A linear equation
40. If a < b and c < 0
Pure mathematics
Quadratic equations
The sets Xk
then bc < ac
41. An operation of arity zero is simply an element of the codomain Y - called a
The method of equating the coefficients
Quadratic equations can also be solved
nullary operation
Solution to the system
42. May not be defined for every possible value.
Expressions
Solution to the system
Operations
commutative law of Exponentiation
43. Division ( / )
Algebra
inverse operation of Multiplication
domain
unary and binary
44. 1 - which preserves numbers: a
Categories of Algebra
Reflexive relation
Identity element of Multiplication
Solution to the system
45. Are called the domains of the operation
Knowns
The sets Xk
Identity
reflexive
46. If it holds for all a and b in X that if a is related to b then b is related to a.
Reunion of broken parts
A binary relation R over a set X is symmetric
A functional equation
Pure mathematics
47. Is an equation of the form aX = b for a > 0 - which has solution
nullary operation
Vectors
Identity
exponential equation
48. Logarithm (Log)
then ac < bc
Operations on functions
inverse operation of Exponentiation
the fixed non-negative integer k (the number of arguments)
49. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
Quadratic equations can also be solved
Number line or real line
Identities
Algebraic equation
50. Letters from the beginning of the alphabet like a - b - c... often denote
commutative law of Addition
operation
Constants
value - result - or output