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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. The operation of exponentiation means ________________: a^n = a
Repeated multiplication
identity element of addition
the fixed non-negative integer k (the number of arguments)
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.
2. 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.
The central technique to linear equations
A differential equation
Rotations
commutative law of Exponentiation
3. Are denoted by letters at the beginning - a - b - c - d - ...
Abstract algebra
symmetric
the fixed non-negative integer k (the number of arguments)
Knowns
4. Is a binary relation on a set for which every element is related to itself - i.e. - a relation ~ on S where x~x holds true for every x in S. For example - ~ could be 'is equal to'.
Operations on functions
Reunion of broken parts
has arity two
Reflexive relation
5. Is the claim that two expressions have the same value and are equal.
Change of variables
A linear equation
Equations
The operation of exponentiation
6. 1 - which preserves numbers: a
Identity element of Multiplication
has arity one
Linear algebra
Algebraic combinatorics
7. If a < b and c < 0
The relation of equality (=)
Associative law of Multiplication
Solving the Equation
then bc < ac
8. Two equations in two variables - it is often possible to find the solutions of both variables that satisfy both equations.
A Diophantine equation
system of linear equations
Order of Operations
Pure mathematics
9. Is an equation of the form X^m/n = a - for m - n integers - which has solution
radical equation
reflexive
The method of equating the coefficients
Algebraic equation
10. Not commutative a^b?b^a
Unknowns
identity element of addition
commutative law of Exponentiation
The relation of inequality (<) has this property
11. If a < b and b < c
operation
Conditional equations
then a < c
nonnegative numbers
12. Applies abstract algebra to the problems of geometry
inverse operation of Multiplication
value - result - or output
Constants
Algebraic geometry
13. Is an algebraic 'sentence' containing an unknown quantity.
Polynomials
Unknowns
Equations
then a < c
14. (a
Associative law of Multiplication
Identity element of Multiplication
transitive
Number line or real line
15. The inner product operation on two vectors produces a
nonnegative numbers
scalar
system of linear equations
A differential equation
16. The squaring operation only produces
nonnegative numbers
symmetric
Equations
The central technique to linear equations
17. The values combined are called
operands - arguments - or inputs
A polynomial equation
Knowns
reflexive
18. 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 operation of exponentiation
Elimination method
Identity
has arity one
19. 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)
then a + c < b + d
(k+1)-ary relation that is functional on its first k domains
Associative law of Exponentiation
The operation of addition
20. Involve only one value - such as negation and trigonometric functions.
Elementary algebra
A binary relation R over a set X is symmetric
Expressions
Unary operations
21. Are true for only some values of the involved variables: x2 - 1 = 4.
operands - arguments - or inputs
Repeated multiplication
Conditional equations
Quadratic equations can also be solved
22. Is an equation in which a polynomial is set equal to another polynomial.
A polynomial equation
then a < c
A Diophantine equation
The relation of equality (=)
23. Is called the type or arity of the operation
A integral equation
Quadratic equations
the fixed non-negative integer k (the number of arguments)
The sets Xk
24. Is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
Binary operations
Quadratic equations
Pure mathematics
Algebraic equation
25. A + b = b + a
Quadratic equations can also be solved
inverse operation of Exponentiation
commutative law of Addition
A functional equation
26. 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)
then a < c
Associative law of Exponentiation
Elementary algebra
The operation of exponentiation
27. 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.
then bc < ac
A Diophantine equation
The relation of inequality (<) has this property
The method of equating the coefficients
28. Is called the codomain of the operation
The real number system
Knowns
the set Y
Multiplication
29. Include the binary operations union and intersection and the unary operation of complementation.
the fixed non-negative integer k (the number of arguments)
Operations on sets
nonnegative numbers
Algebraic combinatorics
30. Are linear equations that have only one variable. They contain only constant numbers and a single variable without an exponent. For example:
unary and binary
The simplest equations to solve
Elimination method
The operation of addition
31. The value produced is called
A integral equation
value - result - or output
associative law of addition
Multiplication
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
inverse operation of Multiplication
when b > 0
has arity two
Order of Operations
33. Can be combined using logic operations - such as and - or - and not.
Addition
value - result - or output
operation
The logical values true and false
34. A unary operation
has arity one
The relation of inequality (<) has this property
equation
Quadratic equations
35. Can be added and subtracted.
operation
Vectors
Difference of two squares - or the difference of perfect squares
has arity one
36. The operation of multiplication means _______________: a
Unknowns
Exponentiation
Quadratic equations
Repeated addition
37. Will have two solutions in the complex number system - but need not have any in the real number system.
The relation of inequality (<) has this property
All quadratic equations
Identity element of Multiplication
The central technique to linear equations
38. Include composition and convolution
The operation of addition
Exponentiation
Operations on functions
Addition
39. 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.
Identities
nullary operation
identity element of addition
The relation of equality (=) has the property
40. Take two values - and include addition - subtraction - multiplication - division - and exponentiation.
Variables
The relation of equality (=)'s property
Binary operations
nullary operation
41. An operation of arity k is called a
k-ary operation
symmetric
Associative law of Exponentiation
identity element of addition
42. Is algebraic equation of degree one
The real number system
A linear equation
Universal algebra
Change of variables
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).
scalar
A linear equation
operation
A Diophantine equation
44. Is Written as a + b
nullary operation
A Diophantine equation
Solving the Equation
Addition
45. 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 Addition
Solving the Equation
substitution
the set Y
46. Implies that the domain of the function is a power of the codomain (i.e. the Cartesian product of one or more copies of the codomain)
operation
Unknowns
A transcendental equation
Vectors
47. 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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48. 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).
nonnegative numbers
Quadratic equations
nonnegative numbers
Operations can involve dissimilar objects
49. The values of the variables which make the equation true are the solutions of the equation and can be found through
Equation Solving
finitary operation
scalar
Pure mathematics
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 (=)
Knowns
The operation of addition
Order of Operations