Download Algebra 1 Review Questions 1. What is a right angle? A right angle

Algebra 1 Review Questions
1. What is a right angle?
A right angle is an angle whose measurement is 90º.
2. What is an acute angle?
An acute angle is an angle whose measurement is less than 90º.
3. What is an obtuse angle?
An obtuse angle is an angle whose measurement is greater than 90º.
4. What are parallel lines?
Parallel lines are two or more lines in the same plane which do not intersect.
5. What are perpendicular lines?
Perpendicular lines are lines whose angle of intersection are right angles.
6. How many degrees are there in a straight line?
There are 180º in a straight line.
7. How many degrees are there in a circle?
There are 360º in a circle.
8. What is a polygon?
A polygon is a simple, closed, flat geometric figure whose sides are line segments.
9. What is a triangle?
A triangle is a polygon which has three sides.
10. What is the sum of the measurements of the angles of a triangle?
The sum of the measurements of the angles of a triangle is 180º.
11. What is a right triangle?
A right triangle is a triangle which has a 90º angle.
12. What is an acute triangle?
An acute triangle is a triangle in which all the angles are less than 90º.
13. What is an obtuse triangle?
An obtuse triangle is a triangle in which one of the angles is greater than 90º.
14. What is an isosceles triangle?
An isosceles triangle is a triangle in which at least two sides are of equal length.
15. What is an equilateral triangle?
An equilateral triangle is a triangle in which all sides are of equal length.
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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16. What is a scalene triangle?
A scalene triangle is a triangle in which all the sides are of different length.
17. What is the measurement of the angles opposite sides of equal length in any triangle?
In any triangle, the angles opposite sides of equal length have equal measures.
18. What is a quadrilateral?
A quadrilateral is a polygon which has four sides.
19. What is a parallelogram?
A parallelogram is a quadrilateral which has two pairs of parallel sides.
20. What is a trapezoid?
A trapezoid is a quadrilateral which has two parallel sides.
21. What is a rectangle?
A rectangle is a parallelogram with four right angles.
22. What is a rhombus?
A rhombus is a parallelogram with four equal sides.
23. What is a square?
A square is a rhombus with four right angles.
24. What is the circumference of a circle?
The circumference of a circle is πd or 2πr .
25. What is the set of real numbers?
The set of real numbers is any number which can be located on the number line.
26. What is the set of natural numbers?
The set of natural numbers is {1, 2, 3, …}.
27. What is the set of whole numbers?
The set of whole numbers is {0, 1, 2, 3, …}.
28. What is the set of integers?
The set of integers is {…, -3, -2, -1, 0, 1, 2, 3, …}.
29. What is the formula for the area of a rectangle or a square?
The formula for the area of a rectangle or a square is (length )(width ) .
30. What is the formula for the area of a triangle?
(base)(height ) .
The formula for the area of a triangle is
2
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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31. What is the formula for the area of a circle?
The formula for the area of a circle is πr 2 .
32. What are inverse operations?
Inverse operations are operations which undo each other.
33. What is the inverse operation of addition?
The inverse operation of addition is subtraction.
34. What is the inverse operation of division?
The inverse operation of division is multiplication.
35. What is the indeterminate form of a fraction?
0
The indeterminate form of a fraction is .
0
36. What is the undefined form of a fraction?
n
The undefined form of a fraction is where n is any real or unreal number.
0
37. What is the reciprocal or multiplicative inverse property of multiplication?
1
The inverse property of multiplication is n ⋅ = 1 where n is any nonzero real number.
n
38. What is surface area?
Surface area is the total area of all the exposed surfaces of a geometric solid.
39. What is the lateral surface area of a geometric solid?
The lateral surface area of a geometric solid is the surface area of the geometric solid between the
bases.
40. What is a prism?
A prism is a geometric solid whose bases are identical and parallel polygons.
41. What is a cylinder?
A cylinder is a geometric solid whose bases are identical and parallel closed curves.
42. What is the formula for the volume of a prism or cylinder?
The formula for the volume of a right solid is (area of the base)(height).
( )( )
( )( ) ( )( )
43. What is the identity of x m x n ?
The identity of x m x n is x m x n = x m + n .
44. What are the roots of an equation?
The roots of an equation are the solutions of the equation.
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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45. What are equivalent equations?
Equivalent equations are equations that have the same solution set.
46. What is the identity of x − n ?
1
The identity of x − n is x − n = n , if n is any real number and x ≠ 0 .
x
47. What is the identity of x 0 ?
The identity of x 0 is x 0 = 1 , if x ≠ 0 .
48. What is a prime number?
A prime number is an integer greater than one whose only integer factors are one and the number
itself.
49. What is the greatest common factor (GCF)?
The GCF of two or more terms is the product of all prime algebraic factors common to every term,
each to the highest power that it occurs in all of the terms.
50. What is the solution set?
The solution set is the set of numbers that will satisfy a given equation or inequality.
xm
51. What is the identity of n ?
x
m
m
x
x
The identity of n is n = x m − n , if m and n are real numbers and x ≠ 0 .
x
x
52. What is the least common multiple (LCM)?
The LCM is the smallest number that can be divided evenly by each of a given set of numbers.
53. What is the range of a set of numbers?
The range of a set of numbers is the difference between the largest number and the smallest number.
54. What is the median of a set of numbers?
The median of a set of numbers is the middle number.
55. What is the mode of a set of numbers?
The mode of a set of numbers is the number that appears the greatest number of times.
56. What is the mean of a set of numbers?
The mean of a set of numbers is the average.
57. What is a conjunction?
A conjunction is a statement of two conditions which must both be true in order for the statement to be
true.
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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58. What is a disjunction?
A “disjunction” uses the word “or” and means that either condition may be met.
59. What is a polynomial?
A polynomial is an algebraic expression with one or more variables having only terms with real
number coefficients and whole number powers of the variables.
60. What is the degree of a term of a polynomial?
The degree of a term of a polynomial is the sum of the exponents of the variables in the term.
61. What is the degree of a polynomial?
The degree of a polynomial is the degree of its highest degree term.
62. What is an independent variable?
An independent variable, which is usually x, is the variable whose value is assigned.
63. What is a dependent variable?
A dependent variable, which is usually y, is the variable whose value depends on the value assigned to
another variable.
( )
The identify of (x ) is (x ) = x
n
64. What is the identity of x m ?
m n
m n
mn
.
65. What is a complex fraction?
A complex fraction is a fraction that has more than one division line in it. (a fraction in a fraction)
66. What is a finite set?
A finite set is a set with a finite number of members.
67. What is an infinite set?
An infinite set is a set with an infinite number of members.
68. What does the symbol ∈ mean?
The symbol ∈ means “is a member of.”
69. What does the symbol ∉ mean?
The symbol ∉ means “is not a member of.”
70. What is a subset?
A subset is when all the members of one set are also members of another set.
71. What does the symbol ⊂ mean?
The symbol ⊂ means “is a subset of.”
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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72. What does the symbol ⊄ mean?
The symbol ⊄ means “is not a subset of.”
73. What are equal sets?
Equal sets are set that have the same members.
74. When are sets proper subsets of one another?
Set are proper subsets of one another when all the members of one set are also members of a second
set.
75. What is the empty or null set?
The empty or null set is a set that has no members and is symbolized by {} or φ .
76. What is the set of natural numbers?
The set of natural numbers is N={1, 2, 3, …}
77. What is the set of whole numbers?
The set of whole numbers is W={0, 1, 2, 3, …}
78. What is the set of integers?
The set of integers is J={…, -3, -2, -1, 0, 1, 2, 3, …}
79. What is the set of real numbers?
The set of real numbers, symbolized by ℜ , is any number which can be located on the number line.
80. What is the set of rational numbers?
The set of rational numbers, symbolized by Q, are all real numbers that can be expressed as a fraction
of integers.
81. What is the set of irrational numbers?
The set of irrational numbers, symbolized by P, are all real number that cannot be expressed as a
fraction of integers.
82. What is the square root of a number?
The square root of a number, symbolized as
( x)
2
x , is the unique positive real number such that
= x , for all x ≥ 0 .
83. What is the general definition of a nth root of a number?
The general definition of a nth root of a number is
( x)
n
n
=x
84. What is a quadratic equation?
A quadratic equation is an equation with one unknown in which the highest power of the variable is 2.
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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85. What is the identity for mn ?
The identity for mn is mn = m n for any real numbers such that m > 0 and n > 0 .
86. What is the domain?
The domain is the set of all permissible numbers which may be used as the replaced values in an
equation.
87. What is a monomial?
A monomial is a single expression in the form of ax n where a is a real number and n is any positive
integer.
88. What is a binomial?
A binomial is an algebraic expression that is the sum or difference of two monomials.
89. What is a trinomial?
A trinomial is an algebraic expression that is the sum or difference of three monomials.
90. What is a polynomial?
A polynomial is the general description of monomials, binomials, trinomials or four or more algebraic
expressions.
91. How is probability determined?
number of outcomes of the event
.
Probability is determined by
number of outcomes in the sample space
92. How are odds determined?
Odds in favor of an event occurring are determined by
probability event will occur
.
probability event will not occur
93. What is a pyramid?
A pyramid is a geometric solid with one face a polygon (called the “base”) and the other faces
triangles (called “lateral faces”) with a common vertex that is not on the plane of the base.
94. What is a cone?
A cone is a geometric solid with one face a closed curve (called the “base”) with a curved surface
(called the “lateral surface”) and a common vertex that is not on the plane of the base.
95. What is the formula for the volume of a pyramid and cone?
1
The formula for the volume of a pyramid and cone is (area of the base )(height ) .
3
96. What is the formula for the volume of a sphere?
4
The formula for the volume of a sphere is πr 2 .
3
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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97. How is the difference of squares such as x 2 − y 2 factored?
The difference of squares such as x 2 − y 2 is factored as (x + y )( x − y ) .
98. What is the slope-intercept form of a linear equation?
The slope-intercept form or a linear equation is y = mx + b where m is the slope and b is the
y-intercept.
99. What is the point-slope form of a linear equation?
The point-slope form or a linear equation is y − y1 = m( x − x1 ) where m is the slope and (x1,y1) is a
point on the line.
100. What is the slope of a line?
rise y 2 − y1
The slope of the line is m =
.
=
run x 2 − x1
101. What are consistent equations?
Consistent equations are equations which have one or more solutions.
102. What are inconsistent equations?
Inconsistent equations are equations which have no common solution.
103. What are dependent solutions?
Dependent equations are equations whose solutions sets are equal.
104. What is a function?
A function is a set of ordered pairs for which each value of the independent variable (often x) in the
domain has only one corresponding value of the dependent variable (often y) in the range.
105. What is a relation?
A relation is any set of ordered pairs.
106. What is the domain of a function?
The domain of a function is the values which the independent variable may equal.
107. What is the range of a function?
The range of a function is the values which the dependent variable may equal.
108. What is the standard form of a quadratic equation?
The standard form of a quadratic equation is ax 2 + bx + c = 0 where a, b and c are constants.
109. What is the multiplicative property of inequality?
The multiplicative property of inequality states that − x > 1 is equivalent to x < −1 and − x < 1 is
equivalent to x > −1 .
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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110. What is the identity of p 2 = q ?
The identity of p 2 = q is p = ± q , if p and q are real numbers.
111. What is the Pythagorean theorem?
The Pythagorean theorem states that for any right triangle, c 2 = a 2 + b 2 where c is the length of the
hypotenuse.
112. What are Pythagorean triples?
Pythagorean triples describe the three sides of a right triangle whose lengths are integers.
113. What is the formula for the distance between two points?
The formula for the distance between two points is d =
(x 2 − x1 )2 + ( y 2 − y1 )2 .
114. What is the formula for the statement, “A varies directly with B”?
The formula for the statement, “A varies directly with B” is AB = k or A = kB .
115. What is the formula for the statement, “A varies inversely with B” or “A varies proportionally
with B”?
k
The formula for the statement, “A varies inversely with B” is A ⋅ B = k or A = .
B
116. What is the general equation for exponential growth functions?
The general equation for exponential growth functions is P(t ) = P0 y t where t is time, P0 is the initial
amount, and y is the growth multiplier.
Algebra 1 Review Questions (adapted from work by Jim Brooks)
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