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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 the claim that two expressions have the same value and are equal.
Unary operations
Equations
The operation of exponentiation
finitary operation
2. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
Abstract algebra
value - result - or output
Algebra
inverse operation of Multiplication
3. Involve only one value - such as negation and trigonometric functions.
Categories of Algebra
Unary operations
Difference of two squares - or the difference of perfect squares
Algebraic combinatorics
4. 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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5. Include composition and convolution
A polynomial equation
Algebraic geometry
Operations on functions
Vectors
6. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
transitive
then a < c
The central technique to linear equations
Identity
7. If a < b and c > 0
the fixed non-negative integer k (the number of arguments)
then ac < bc
Vectors
The relation of inequality (<) has this property
8. Is called the type or arity of the operation
Operations can involve dissimilar objects
domain
Number line or real line
the fixed non-negative integer k (the number of arguments)
9. Applies abstract algebra to the problems of geometry
Constants
Associative law of Multiplication
Algebraic geometry
Change of variables
10. Is an equation involving a transcendental function of one of its variables.
A transcendental equation
then bc < ac
Constants
commutative law of Exponentiation
11. 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)
A integral equation
Algebraic combinatorics
Equation Solving
The operation of addition
12. Symbols that denote numbers - is to allow the making of generalizations in mathematics
The purpose of using variables
Number line or real line
then ac < bc
Operations on functions
13. Division ( / )
Vectors
inverse operation of Multiplication
when b > 0
commutative law of Exponentiation
14. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
finitary operation
Difference of two squares - or the difference of perfect squares
Linear algebra
then ac < bc
15. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
A linear equation
value - result - or output
Order of Operations
domain
16. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
the set Y
then a < c
inverse operation of addition
17. Is an equation involving integrals.
Exponentiation
A integral equation
equation
Unknowns
18. If a < b and b < c
then a < c
Abstract algebra
Solution to the system
domain
19. 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
has arity one
Real number
Algebraic equation
All quadratic equations
20. Is an equation involving derivatives.
Equations
Algebra
value - result - or output
A differential equation
21. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Pure mathematics
Abstract algebra
Elimination method
The relation of equality (=)
22. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
The central technique to linear equations
Difference of two squares - or the difference of perfect squares
commutative law of Exponentiation
23. In which the specific properties of vector spaces are studied (including matrices)
Difference of two squares - or the difference of perfect squares
Real number
Linear algebra
Equations
24. Is an equation where the unknowns are required to be integers.
All quadratic equations
A Diophantine equation
value - result - or output
inverse operation of Multiplication
25. The operation of multiplication means _______________: a
when b > 0
An operation ?
Repeated addition
The relation of inequality (<) has this property
26. Subtraction ( - )
Conditional equations
inverse operation of addition
The relation of equality (=)
The method of equating the coefficients
27. In an equation with a single unknown - a value of that unknown for which the equation is true is called
the set Y
Associative law of Exponentiation
associative law of addition
A solution or root of the equation
28. The squaring operation only produces
nonnegative numbers
Expressions
The method of equating the coefficients
then a + c < b + d
29. 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
Equations
Knowns
when b > 0
Algebraic geometry
30. Include the binary operations union and intersection and the unary operation of complementation.
Operations on functions
Rotations
Equations
Operations on sets
31. The codomain is the set of real numbers but the range is the
The relation of equality (=)'s property
nonnegative numbers
identity element of addition
Reflexive relation
32. (a + b) + c = a + (b + c)
substitution
Algebra
inverse operation of addition
associative law of addition
33. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
when b > 0
an operation
Algebra
34. k-ary operation is a
Unknowns
inverse operation of Exponentiation
The relation of inequality (<) has this property
(k+1)-ary relation that is functional on its first k domains
35. 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
The method of equating the coefficients
Reflexive relation
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.
Vectors
36. Operations can have fewer or more than
two inputs
Operations
(k+1)-ary relation that is functional on its first k domains
identity element of addition
37. An operation of arity zero is simply an element of the codomain Y - called a
Identity
Number line or real line
nullary operation
inverse operation of Exponentiation
38. Are denoted by letters at the beginning - a - b - c - d - ...
The simplest equations to solve
A binary relation R over a set X is symmetric
Knowns
finitary operation
39. 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
Real number
All quadratic equations
Reunion of broken parts
Identities
40. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Binary operations
Expressions
The relation of equality (=)'s property
The method of equating the coefficients
41. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Multiplication
Pure mathematics
A transcendental equation
inverse operation of addition
42. 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 purpose of using variables
The relation of equality (=)
commutative law of Exponentiation
43. 0 - which preserves numbers: a + 0 = a
identity element of addition
then bc < ac
Algebra
range
44. Is an equation of the form aX = b for a > 0 - which has solution
exponential equation
Rotations
The relation of equality (=)'s property
inverse operation of Exponentiation
45. May not be defined for every possible value.
Expressions
Operations
The logical values true and false
Elementary algebra
46. The values of the variables which make the equation true are the solutions of the equation and can be found through
value - result - or output
identity element of addition
reflexive
Equation Solving
47. () is the branch of mathematics concerning the study of the rules of operations and relations - and the constructions and concepts arising from them - including terms - polynomials - equations and algebraic structures.
Algebra
Operations can involve dissimilar objects
Quadratic equations
Pure mathematics
48. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Number line or real line
then a < c
Order of Operations
Repeated addition
49. The values combined are called
operands - arguments - or inputs
Algebraic geometry
Reflexive relation
transitive
50. The inner product operation on two vectors produces a
A functional equation
Reunion of broken parts
domain
scalar