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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. 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)
Reunion of broken parts
Identity
inverse operation of addition
The operation of addition
2. There are two common types of operations:
unary and binary
The relation of inequality (<) has this property
Multiplication
operation
3. Not associative
an operation
Associative law of Exponentiation
inverse operation of Multiplication
(k+1)-ary relation that is functional on its first k domains
4. Referring to the finite number of arguments (the value k)
finitary operation
transitive
The operation of addition
A differential equation
5. The squaring operation only produces
nonnegative numbers
Addition
Associative law of Exponentiation
the set Y
6. Is an equation involving integrals.
A integral equation
(k+1)-ary relation that is functional on its first k domains
A solution or root of the equation
Expressions
7. A distinction is made between the equality sign ( = ) for an equation and the equivalence symbol () for an
Operations can involve dissimilar objects
Identity
Associative law of Multiplication
Rotations
8. If a < b and c < d
then a + c < b + d
Algebraic combinatorics
A functional equation
Unary operations
9. b = b
unary and binary
Algebraic equation
Operations
reflexive
10. Is an equation involving derivatives.
Multiplication
A differential equation
Polynomials
operation
11. 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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12. Is an equation of the form aX = b for a > 0 - which has solution
unary and binary
Solving the Equation
A Diophantine equation
exponential equation
13. Parenthesis and other grouping symbols including brackets - absolute value symbols - and the fraction bar - exponents and roots - multiplication and division - addition and subtraction
A integral equation
Order of Operations
Algebraic combinatorics
The relation of equality (=)'s property
14. Together with geometry - analysis - topology - combinatorics - and number theory - algebra is one of the main branches of
Order of Operations
Pure mathematics
(k+1)-ary relation that is functional on its first k domains
the fixed non-negative integer k (the number of arguments)
15. Subtraction ( - )
(k+1)-ary relation that is functional on its first k domains
inverse operation of addition
Identity element of Multiplication
A Diophantine equation
16. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Algebraic equation
Solution to the system
Unary operations
commutative law of Multiplication
17. using factorization (the reverse process of which is expansion - but for two linear terms is sometimes denoted foiling).
(k+1)-ary relation that is functional on its first k domains
The operation of addition
operation
Quadratic equations can also be solved
18. In which properties common to all algebraic structures are studied
Universal algebra
operation
k-ary operation
The simplest equations to solve
19. Is an equation in which the unknowns are functions rather than simple quantities.
A functional equation
an operation
A transcendental equation
operands - arguments - or inputs
20. If an equation in algebra is known to be true - the following operations may be used to produce another true equation:
A integral equation
Elimination method
The method of equating the coefficients
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.
21. In an equation with a single unknown - a value of that unknown for which the equation is true is called
A solution or root of the 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.
Order of Operations
Operations
22. Elementary algebra - Abstract algebra - Linear algebra - Universal algebra - Algebraic number theory - Algebraic geometry - Algebraic combinatorics
transitive
Categories of Algebra
Quadratic equations
Reflexive relation
23. The codomain is the set of real numbers but the range is the
The real number system
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.
nonnegative numbers
Algebraic equation
24. Letters from the beginning of the alphabet like a - b - c... often denote
an operation
Constants
The method of equating the coefficients
operation
25. 1 - which preserves numbers: a^1 = a
logarithmic equation
then a < c
identity element of Exponentiation
Unknowns
26. The value produced is called
k-ary operation
value - result - or output
identity element of addition
Equations
27. A mathematical statement that asserts the equality of two expressions - this is written by placing the expressions on either side of an equals sign (=).
then a + c < b + d
equation
has arity two
when b > 0
28. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
associative law of addition
The simplest equations to solve
A functional equation
Knowns
29. Is algebraic equation of degree one
A linear equation
Elementary algebra
The sets Xk
Abstract algebra
30. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
system of linear equations
when b > 0
The operation of addition
Equation Solving
31. 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
Exponentiation
The relation of equality (=) has the property
Abstract algebra
32. Is Written as a + b
Variables
The method of equating the coefficients
Addition
Categories of Algebra
33. If it holds for all a and b in X that if a is related to b then b is related to a.
Algebraic combinatorics
Solving the Equation
A binary relation R over a set X is symmetric
operation
34. In which the specific properties of vector spaces are studied (including matrices)
Order of Operations
Linear algebra
Identities
radical equation
35. Can be combined using the function composition operation - performing the first rotation and then the second.
operation
scalar
Rotations
equation
36. 0 - which preserves numbers: a + 0 = a
A functional equation
Constants
identity element of addition
Algebraic equation
37. Can be added and subtracted.
Vectors
Equations
Equations
domain
38. The operation of multiplication means _______________: a
Repeated addition
A Diophantine equation
Quadratic equations
Variables
39. Division ( / )
(k+1)-ary relation that is functional on its first k domains
Algebraic geometry
inverse operation of Multiplication
domain
40. The inner product operation on two vectors produces a
commutative law of Multiplication
unary and binary
commutative law of Addition
scalar
41. The process of expressing the unknowns in terms of the knowns is called
substitution
Reflexive relation
Solving the Equation
operation
42. 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.
exponential equation
The central technique to linear equations
Operations can involve dissimilar objects
Universal algebra
43. 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 on functions
radical equation
operation
value - result - or output
44. 1 - which preserves numbers: a
A differential equation
operation
Identity element of Multiplication
when b > 0
45. A binary operation
Knowns
Repeated multiplication
has arity two
Solving the Equation
46. The values of the variables which make the equation true are the solutions of the equation and can be found through
equation
commutative law of Addition
Equation Solving
A differential equation
47. If a < b and c > 0
then ac < bc
finitary operation
The logical values true and false
Algebraic equation
48. The values combined are called
The relation of equality (=)
operands - arguments - or inputs
Identities
Conditional equations
49. 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
Reunion of broken parts
Addition
Multiplication
Change of variables
50. Reflexive: b = b; symmetric: if a = b then b = a; transitive: if a = b and b = c then a = c.
The relation of equality (=)
All quadratic equations
Binary operations
Conditional equations