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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. The squaring operation only produces
Multiplication
domain
nonnegative numbers
reflexive
2. Logarithm (Log)
then a < c
inverse operation of Exponentiation
Quadratic equations
system of linear equations
3. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Identity
system of linear equations
A functional equation
nonnegative numbers
4. Will have two solutions in the complex number system - but need not have any in the real number system.
All quadratic equations
An operation ?
commutative law of Multiplication
The simplest equations to solve
5. often express relationships between given quantities - the knowns - and quantities yet to be determined - the unknowns.
system of linear equations
Equations
two inputs
Solution to the system
6. 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
Reunion of broken parts
Pure mathematics
A functional equation
7. Is an equation where the unknowns are required to be integers.
A Diophantine equation
The logical values true and false
Unary operations
Binary operations
8. Is an equation of the form aX = b for a > 0 - which has solution
two inputs
exponential equation
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.
Identity
9. The process of expressing the unknowns in terms of the knowns is called
Solving the Equation
associative law of addition
scalar
Operations on sets
10. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
Unknowns
The relation of inequality (<) has this property
The operation of exponentiation
11. Can be defined axiomatically up to an isomorphism
system of linear equations
The real number system
logarithmic equation
nonnegative numbers
12. Include the binary operations union and intersection and the unary operation of complementation.
Associative law of Exponentiation
The relation of equality (=) has the property
Operations on sets
identity element of addition
13. Can be combined using the function composition operation - performing the first rotation and then the second.
A solution or root of the equation
Rotations
equation
symmetric
14. If a < b and c < 0
Pure mathematics
then bc < ac
Constants
Solution to the system
15. The value produced is called
operation
value - result - or output
the fixed non-negative integer k (the number of arguments)
unary and binary
16. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
operands - arguments - or inputs
range
Real number
Variables
17. The inner product operation on two vectors produces a
The relation of equality (=) has the property
scalar
nonnegative numbers
A polynomial equation
18. Is algebraic equation of degree one
Algebraic equation
Algebraic number theory
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 linear equation
19. Include composition and convolution
transitive
Operations
Operations on functions
Unary operations
20. Not associative
an operation
Associative law of Exponentiation
Reflexive relation
The operation of addition
21. If a = b and b = c then a = c
A binary relation R over a set X is symmetric
transitive
an operation
Number line or real line
22. An operation of arity k is called a
domain
k-ary operation
Associative law of Multiplication
identity element of addition
23. Are called the domains of the operation
The sets Xk
The relation of equality (=)
Reflexive relation
Addition
24. Division ( / )
Abstract algebra
Operations on sets
radical equation
inverse operation of Multiplication
25. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
Associative law of Multiplication
operation
Solution to the system
scalar
26. If a < b and c > 0
nonnegative numbers
then ac < bc
Binary operations
A linear equation
27. Is Written as a + b
Reunion of broken parts
Identity
Addition
commutative law of Addition
28. Is an equation involving integrals.
Polynomials
then a + c < b + d
A differential equation
A integral equation
29. 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.
A transcendental equation
Properties of equality
Linear algebra
Equation Solving
30. 0 - which preserves numbers: a + 0 = a
then ac < bc
substitution
identity element of addition
The operation of addition
31. 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.
Algebra
has arity one
Change of variables
Real number
32. 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
when b > 0
Solving the Equation
Expressions
Change of variables
33. Are denoted by letters at the beginning - a - b - c - d - ...
A polynomial equation
Algebraic geometry
Knowns
when b > 0
34. 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
A linear equation
an operation
Reunion of broken parts
The relation of equality (=)'s property
35. 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.
Knowns
The central technique to linear equations
A transcendental equation
then bc < ac
36. In which abstract algebraic methods are used to study combinatorial questions.
value - result - or output
Algebraic combinatorics
domain
Linear algebra
37. 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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38. Can be combined using logic operations - such as and - or - and not.
then ac < bc
Elimination method
A differential equation
The logical values true and false
39. The operation of multiplication means _______________: a
Repeated addition
when b > 0
Linear algebra
Identity
40. In which the specific properties of vector spaces are studied (including matrices)
symmetric
Identity
The operation of exponentiation
Linear algebra
41. Letters from the beginning of the alphabet like a - b - c... often denote
Constants
identity element of addition
then a + c < b + d
Repeated multiplication
42. () 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.
then a < c
Algebra
Abstract algebra
Solving the Equation
43. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Pure mathematics
The relation of inequality (<) has this property
Algebraic number theory
inverse operation of Exponentiation
44. Is an equation involving derivatives.
the fixed non-negative integer k (the number of arguments)
A differential equation
Identity
commutative law of Exponentiation
45. Symbols that denote numbers - is to allow the making of generalizations in mathematics
the fixed non-negative integer k (the number of arguments)
Equations
Operations
The purpose of using variables
46. Is an action or procedure which produces a new value from one or more input values.
transitive
commutative law of Multiplication
an operation
Conditional equations
47. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
A functional equation
Pure mathematics
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.
then ac < bc
48. Is Written as a
when b > 0
system of linear equations
Multiplication
The method of equating the coefficients
49. 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
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.
Constants
A transcendental equation
50. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
exponential equation
unary and binary
All quadratic equations