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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. Letters from the beginning of the alphabet like a - b - c... often denote
Solving the Equation
Expressions
Constants
Properties of equality
2. Is an equation involving derivatives.
A differential equation
unary and binary
the fixed non-negative integer k (the number of arguments)
finitary operation
3. Are denoted by letters at the end of the alphabet - x - y - z - w - ...
substitution
Unknowns
when b > 0
Equation Solving
4. The codomain is the set of real numbers but the range is the
A functional equation
The operation of exponentiation
Identities
nonnegative numbers
5. 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
Change of variables
k-ary operation
Rotations
when b > 0
6. 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).
Exponentiation
The relation of equality (=)
Quadratic equations
commutative law of Addition
7. Is an equation in which the unknowns are functions rather than simple quantities.
an operation
scalar
A solution or root of the equation
A functional equation
8. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
A solution or root of the equation
Quadratic equations can also be solved
Constants
logarithmic equation
9. Is an action or procedure which produces a new value from one or more input values.
The operation of addition
equation
an operation
Difference of two squares - or the difference of perfect squares
10. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
The logical values true and false
Order of Operations
operation
Exponentiation
11. 0 - which preserves numbers: a + 0 = a
inverse operation of addition
operation
identity element of addition
Operations
12. Is a function of the form ? : V ? Y - where V ? X1
Equation Solving
The relation of inequality (<) has this property
nonnegative numbers
An operation ?
13. If a < b and c < 0
The method of equating the coefficients
inverse operation of Exponentiation
Unknowns
then bc < ac
14. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
has arity two
substitution
Quadratic equations can also be solved
15. Is algebraic equation of degree one
The sets Xk
radical equation
A linear equation
unary and binary
16. Can be defined axiomatically up to an isomorphism
Difference of two squares - or the difference of perfect squares
The real number system
equation
commutative law of Exponentiation
17. Can be combined using logic operations - such as and - or - and not.
inverse operation of addition
Reunion of broken parts
inverse operation of Multiplication
The logical values true and false
18. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Categories of Algebra
Binary operations
Properties of equality
A polynomial equation
19. Are called the domains of the operation
commutative law of Addition
The sets Xk
then a < c
substitution
20. In which the specific properties of vector spaces are studied (including matrices)
inverse operation of Exponentiation
Linear algebra
Abstract algebra
Equations
21. If it holds for all a and b in X that if a is related to b then b is related to a.
A differential equation
The sets Xk
A binary relation R over a set X is symmetric
Algebraic combinatorics
22. The values for which an operation is defined form a set called its
The purpose of using variables
domain
scalar
then a + c < b + d
23. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
identity element of Exponentiation
Repeated multiplication
Elimination method
The simplest equations to solve
24. (a
The operation of exponentiation
scalar
Associative law of Multiplication
operation
25. Will have two solutions in the complex number system - but need not have any in the real number system.
The central technique to linear equations
All quadratic equations
The logical values true and false
has arity one
26. If a < b and b < c
The operation of addition
Algebraic equation
Multiplication
then a < c
27. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
substitution
commutative law of Multiplication
Difference of two squares - or the difference of perfect squares
radical equation
28. 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.
Change of variables
Difference of two squares - or the difference of perfect squares
The relation of inequality (<) has this property
Expressions
29. Include composition and convolution
Elementary algebra
Identity
Operations on functions
inverse operation of Multiplication
30. 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)
substitution
The operation of addition
commutative law of Multiplication
Unary operations
31. Are denoted by letters at the beginning - a - b - c - d - ...
Knowns
when b > 0
The operation of exponentiation
A differential equation
32. The operation of multiplication means _______________: a
Repeated addition
The operation of exponentiation
Algebra
Associative law of Multiplication
33. In which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
A Diophantine equation
Algebraic number theory
Addition
The method of equating the coefficients
34. An operation of arity k is called a
k-ary operation
The relation of inequality (<) has this property
Expressions
The relation of equality (=)
35. 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).
Operations can involve dissimilar objects
inverse operation of Multiplication
A binary relation R over a set X is symmetric
operation
36. Is the claim that two expressions have the same value and are equal.
The central technique to linear equations
Equations
The relation of inequality (<) has this property
Conditional equations
37. Some equations are true for all values of the involved variables (such as a + b = b + a); such equations are called
nullary operation
Polynomials
Identities
range
38. The value produced is called
when b > 0
value - result - or output
Identity
The operation of addition
39. The process of expressing the unknowns in terms of the knowns is called
system of linear equations
The relation of equality (=)
The simplest equations to solve
Solving the Equation
40. Applies abstract algebra to the problems of geometry
then bc < ac
Algebraic geometry
Exponentiation
Operations on functions
41. () 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.
The relation of equality (=)
The relation of equality (=) has the property
Exponentiation
Algebra
42. A binary operation
operands - arguments - or inputs
A transcendental equation
The central technique to linear equations
has arity two
43. Can be combined using the function composition operation - performing the first rotation and then the second.
A differential equation
The real number system
then a + c < b + d
Rotations
44. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
Algebraic equation
the fixed non-negative integer k (the number of arguments)
The relation of equality (=)
Expressions
45. Logarithm (Log)
operands - arguments - or inputs
The operation of addition
Difference of two squares - or the difference of perfect squares
inverse operation of Exponentiation
46. Is an equation in which a polynomial is set equal to another polynomial.
commutative law of Exponentiation
identity element of Exponentiation
A polynomial equation
Associative law of Exponentiation
47. In which properties common to all algebraic structures are studied
The logical values true and false
Universal algebra
The real number system
The relation of equality (=) has the property
48. Can be added and subtracted.
Vectors
A transcendental equation
Unknowns
k-ary operation
49. A vector can be multiplied by a scalar to form another vector
Operations can involve dissimilar objects
Polynomials
Identity element of Multiplication
transitive
50. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
Solution to the system
Algebraic number theory
Identity
system of linear equations