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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. Is an equation in which the unknowns are functions rather than simple quantities.
then a + c < b + d
A functional equation
The relation of inequality (<) has this property
two inputs
2. Is an equation of the form log`a^X = b for a > 0 - which has solution
logarithmic equation
Solving the Equation
Operations on functions
Pure mathematics
3. 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
The sets Xk
Binary operations
Elimination method
associative law of addition
4. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
identity element of addition
Algebraic equation
Identity
Addition
5. 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)
identity element of addition
equation
Exponentiation
The operation of exponentiation
6. If a = b and b = c then a = c
then a + c < b + d
The relation of equality (=)
transitive
Solving the Equation
7. If a < b and b < c
A Diophantine equation
The relation of equality (=)
commutative law of Multiplication
then a < c
8. Not associative
Pure mathematics
Associative law of Exponentiation
A Diophantine equation
An operation ?
9. Is an equation where the unknowns are required to be integers.
the fixed non-negative integer k (the number of arguments)
associative law of addition
A Diophantine equation
The relation of equality (=) has the property
10. If an equation in algebra is known to be true - the following operations may be used to produce another true 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.
Linear algebra
Variables
Equations
11. The squaring operation only produces
nonnegative numbers
then bc < ac
Difference of two squares - or the difference of perfect squares
The sets Xk
12. May not be defined for every possible value.
finitary operation
Real number
Operations
has arity one
13. The values combined are called
Algebraic equation
operands - arguments - or inputs
then a + c < b + d
Reflexive relation
14. Symbols that denote numbers - letters from the end of the alphabet - like ...x - y - z - are usually reserved for the
Identity
Variables
Reflexive relation
A polynomial equation
15. Are true for only some values of the involved variables: x2 - 1 = 4.
substitution
Conditional equations
Linear algebra
operation
16. Include the binary operations union and intersection and the unary operation of complementation.
Operations on sets
inverse operation of Exponentiation
radical equation
Algebraic number theory
17. 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
The operation of addition
when b > 0
The real number system
operation
18. 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
Algebra
Repeated addition
Knowns
19. Are called the domains of the operation
The simplest equations to solve
Unknowns
Operations can involve dissimilar objects
The sets Xk
20. Logarithm (Log)
The operation of exponentiation
Polynomials
inverse operation of Exponentiation
scalar
21. 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
associative law of addition
Linear algebra
22. An equivalent for y can be deduced by using one of the two equations. Using the second equation: Subtracting 2x from each side of the equation: and multiplying by -1: Using this y value in the first equation in the original system: Adding 2 on each s
commutative law of Exponentiation
then ac < bc
Repeated addition
substitution
23. 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).
Quadratic equations
range
transitive
Unknowns
24. Is Written as a
Polynomials
when b > 0
Multiplication
Identity element of Multiplication
25. The codomain is the set of real numbers but the range is the
A Diophantine equation
inverse operation of Exponentiation
nonnegative numbers
associative law of addition
26. Is an equation involving integrals.
A integral equation
Operations on sets
Universal algebra
inverse operation of Multiplication
27. 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)
Vectors
The operation of addition
inverse operation of Exponentiation
has arity two
28. In which the specific properties of vector spaces are studied (including matrices)
Real number
Number line or real line
Linear algebra
operands - arguments - or inputs
29. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
A transcendental equation
The simplest equations to solve
Equation Solving
Identities
30. Is a squared (multiplied by itself) number subtracted from another squared number. It refers to the identity
identity element of Exponentiation
Difference of two squares - or the difference of perfect squares
Associative law of Multiplication
then ac < bc
31. Involve only one value - such as negation and trigonometric functions.
Unary operations
system of linear equations
Operations on sets
Multiplication
32. Are denoted by letters at the beginning - a - b - c - d - ...
The simplest equations to solve
Knowns
inverse operation of Exponentiation
Addition
33. The inner product operation on two vectors produces a
Identity element of Multiplication
then a < c
(k+1)-ary relation that is functional on its first k domains
scalar
34. In which properties common to all algebraic structures are studied
Order of Operations
Universal algebra
Quadratic equations can also be solved
nullary operation
35. Sometimes also called modern algebra - in which algebraic structures such as groups - rings and fields are axiomatically defined and investigated.
The operation of exponentiation
An operation ?
Abstract algebra
Associative law of Exponentiation
36. An operation of arity zero is simply an element of the codomain Y - called a
nullary operation
substitution
A functional equation
Order of Operations
37. Is an assignment of values to all the unknowns so that all of the equations are true. also called set simultaneous equations.
k-ary operation
Solution to the system
(k+1)-ary relation that is functional on its first k domains
scalar
38. Subtraction ( - )
The logical values true and false
inverse operation of addition
Associative law of Exponentiation
A polynomial equation
39. The set which contains the values produced is called the codomain - but the set of actual values attained by the operation is its
an operation
range
Pure mathematics
The purpose of using variables
40. 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
unary and binary
then a < c
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.
41. A binary operation
has arity two
The relation of equality (=)
The logical values true and false
A differential equation
42. 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 functional equation
Quadratic equations
Addition
Reunion of broken parts
43. 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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44. Can be added and subtracted.
All quadratic equations
Vectors
then a + c < b + d
A differential equation
45. Is an equation in which a polynomial is set equal to another polynomial.
Universal algebra
A polynomial equation
then ac < bc
Reflexive relation
46. Real numbers can be thought of as points on an infinitely long line where the points corresponding to integers are equally spaced called the
Linear algebra
Operations
Exponentiation
Number line or real line
47. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
Categories of Algebra
equation
Identity
then bc < ac
48. If a < b and c < 0
when b > 0
then bc < ac
k-ary operation
The operation of exponentiation
49. 1 - which preserves numbers: a^1 = a
then bc < ac
k-ary operation
identity element of Exponentiation
Equation Solving
50. 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.
Linear algebra
Order of Operations
Difference of two squares - or the difference of perfect squares
Properties of equality