1
Q
A
2
Q
When adding integers with the same sign, what do you do to the absolute values and the sign?
A
Add absolute values; keep common sign
This rule applies when both integers are either positive or negative.
3
Q
When adding integers with different signs, subtract the smaller absolute value from the larger and keep the sign of the number with the larger ________.
A
absolute value
This helps determine the result when combining integers of different signs.
4
Q
Rule for multiplying/dividing signed numbers: same signs give a ________ result.
A
positive
This applies to both multiplication and division.
5
Q
Rule for multiplying/dividing signed numbers: different signs give a ________ result.
A
negative
This rule is consistent for both multiplication and division.
6
Q
Which property is TRUE for addition of integers: a) Commutative b) Not commutative c) Undefined d) None?
A
a – Commutative
The commutative property states that changing the order of the addends does not change the sum.
7
Q
Which operation is NOT commutative for integers: a) Addition b) Multiplication c) Subtraction d) Both a and b?
A
c – Subtraction
Subtraction does not yield the same result when the order of the numbers is changed.
8
Q
Which property is TRUE: x + 0 = x is the ________ property (addition).
A
Identity
The identity property states that adding zero to any number does not change the number.
9
Q
Which property is TRUE: x × 1 = x is the ________ property (multiplication).
A
Identity
The identity property for multiplication indicates that multiplying any number by one does not change the number.
10
Q
Which property states: if x and y are integers, then x + y is an integer?
A
Closure (addition)
The closure property indicates that the sum of two integers is always an integer.
11
Q
For integers, x ÷ y is generally NOT in Z; this violates which property?
A
Closure (division)
Division of integers does not always yield an integer result.
12
Q
Which property: x(y + z) = xy + xz?
A
Distributive property
The distributive property allows multiplication to be distributed over addition.
13
Q
Divisibility by 2: a number is divisible by 2 if its last digit is ________.
A
even
Even numbers end with 0, 2, 4, 6, or 8.
14
Q
Divisibility by 4: a number is divisible by 4 if its last ________ digits form a number divisible by 4.
A
two
This rule applies to the last two digits of the number.
15
Q
Divisibility by 8: a number is divisible by 8 if its last ________ digits form a number divisible by 8.
A
three
This rule applies to the last three digits of the number.
16
Q
Divisibility by 3: a number is divisible by 3 if the sum of its digits is divisible by ________.
A
3
This is a quick way to check for divisibility by 3.
17
Q
Divisibility by 9: a number is divisible by 9 if the sum of its digits is divisible by ________.
A
9
Similar to the rule for 3, but applies to 9.
18
Q
Divisibility by 6: a number is divisible by 6 if it is even and divisible by ________.
A
3
A number must meet both criteria to be divisible by 6.
19
Q
Divisibility rule for 5: last digit is 0 or ________.
A
5
This indicates that the number can be evenly divided by 5.
20
Q
In the handout’s table, divisibility by 7 uses: Double the last digit, then ________ it from the rest.
A
subtract
This method helps determine if a number is divisible by 7.
21
Q
GCF means the ________ number that divides two or more numbers exactly.
A
highest
The greatest common factor is the largest factor shared by the numbers.
22
Q
LCM means the ________ number that is a multiple of two or more integers.
A
smallest
The least common multiple is the smallest multiple shared by the numbers.
23
Q
A ratio is a comparison between two positive quantities a and b; it can be written as a:b or a/______.
A
b
Ratios express the relative sizes of two quantities.
24
Q
A proportion is written as equality of two ratios: a/b = ________.
A
c/d
Proportions indicate that two ratios are equivalent.
25
Law of exponents: xa · xb = x______.
a+b
## Footnote
This rule applies when multiplying powers with the same base.
26
Law of exponents: xa / xb = x______.
a−b
## Footnote
This rule applies when dividing powers with the same base.
27
Law of exponents: (xa)b = x______.
ab
## Footnote
This rule applies when raising a power to another power.
28
Negative exponent rule: x^(−a) = 1/x______.
a
## Footnote
Negative exponents indicate the reciprocal of the base raised to the positive exponent.
29
Zero exponent rule: x^0 = ________.
1
## Footnote
Any non-zero number raised to the power of zero equals one.
30
One exponent rule: x^1 = ________.
x
## Footnote
Any number raised to the power of one equals itself.
31
Adding polynomials: always add ________ terms.
like
## Footnote
Like terms have the same variable raised to the same power.
32
Subtracting polynomials is like addition, except for the operation being ________.
subtraction
## Footnote
When subtracting, change the signs of the terms being subtracted.
33
Multiplying polynomials generally results in a polynomial of ________ degree (than either factor).
higher
## Footnote
The degree of the resulting polynomial is the sum of the degrees of the factors.
34
Polynomial long division Step 1: write the polynomial in ________ order of degree.
descending
## Footnote
This helps in organizing the terms for division.
35
Factoring is described as the reverse process of ________.
expansion
## Footnote
Factoring breaks down a polynomial into simpler components.
36
Common-factor factoring pattern: ax + ay = a(______)
x + y
## Footnote
This shows how to factor out the common term.
37
An equality true for all variable values is called an ________.
identity
## Footnote
Identities hold true regardless of the values of the variables involved.
38
Identity: (a + b)^2 = a^2 + 2ab + b^2 is called the square of a ________.
binomial
## Footnote
This identity expands the square of a sum.
39
Identity: (a − b)^2 = a^2 − 2ab + b^2 is the square of a ________.
binomial
## Footnote
This identity expands the square of a difference.
40
Identity: a^2 − b^2 = (a + b)(a − b) is the difference of two ________.
squares
## Footnote
This identity factors the difference of squares into a product.
41
Translate: “Three times the sum of a number and five” → 3(______)
x + 5
## Footnote
This expression represents the mathematical translation of the phrase.
42
Translate: “Ten more than a number” → x + ________.
10
## Footnote
This expression indicates an increase by ten.
43
Translate: “Nine less a number” → ________.
9 − x
## Footnote
This expression indicates a decrease by nine.
44
Translate: “Eight times a number” → ________.
8x
## Footnote
This expression indicates multiplication by eight.
45
Translate: “Three-fourths of a number” → (3/4)______.
x
## Footnote
This expression indicates a fraction of the number.
46
Translate: “The quotient of a number and seven” → x/______.
7
## Footnote
This expression indicates division by seven.
47
Translate: “The ratio of a number to fifteen” → x/______.
15
## Footnote
This expression indicates a comparison to fifteen.
48
Translate: “The square of a number” → x^______.
2
## Footnote
This expression indicates raising the number to the second power.
49
Translate: “The cube of a number” → x^______.
3
## Footnote
This expression indicates raising the number to the third power.
50
Graphical method for linear systems: solution is the point of ________ of the graphs.
intersection
## Footnote
The intersection point represents the solution to the system of equations.
51
Elimination method: add/subtract equations to ________ a variable.
eliminate
## Footnote
This method simplifies the system of equations to find the solution.
52
Substitution method Step 2: solve one equation for either ________ or y.
x
## Footnote
This step allows for substitution into the other equation.
53
Cross-multiplication method uses two equations in standard form: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0; denominator is (b2a1 − b1a2) and it must not equal ________.
0
## Footnote
A zero denominator indicates that the equations are dependent or inconsistent.
54
Matrix method writes linear equations as A X = ________.
B
## Footnote
This method uses matrices to represent and solve systems of equations.
55
Euclid’s way of presenting geometry is called the ________ method.
axiomatic method
## Footnote
This method is based on a set of axioms or postulates.
56
The three undefined terms in geometry: point, line, and ________.
plane
## Footnote
These terms form the foundation of geometric concepts.
57
Statements describing the system that require no proof are called ________.
postulates
## Footnote
Postulates are accepted as true without proof.
58
Statements required to be proved from postulates/definitions are called ________.
theorems
## Footnote
Theorems are derived from established postulates.
59
A theorem that is an immediate consequence of another theorem is a ________.
corollary
## Footnote
Corollaries follow directly from previously proven theorems.
60
Two or more lines having a common point are ________ lines.
intersecting
## Footnote
Intersecting lines cross at one or more points.
61
Two angles whose sum is 90° are ________ angles.
complementary
## Footnote
Complementary angles add up to a right angle.
62
Two angles whose sum is 180° are ________ angles.
supplementary
## Footnote
Supplementary angles form a straight line when combined.
63
Lines that do not share a common point are ________ lines.
parallel
## Footnote
Parallel lines run in the same direction and never meet.
64
Lines that intersect to form 90° angles are ________ lines.
perpendicular
## Footnote
Perpendicular lines create right angles at their intersection.
65
An angle formed inside a polygon is an ________ angle.
interior
## Footnote
Interior angles are located within the boundaries of the polygon.
66
An angle located outside a polygon is an ________ angle.
exterior
## Footnote
Exterior angles are formed by extending one side of the polygon.
67
Perimeter is the ________ of all sides of a polygon.
sum
## Footnote
The perimeter measures the total distance around the polygon.
68
Area is the amount of space covered by a ________ figure.
plane
## Footnote
Area quantifies the surface within the boundaries of a shape.
69
Volume is the amount of space covered by a ________ figure.
solid
## Footnote
Volume measures the three-dimensional space occupied by an object.
70
A triangle with one right angle is a ________ triangle.
right
## Footnote
Right triangles have one angle measuring 90 degrees.
71
The longest side of a right triangle is the ________.
hypotenuse
## Footnote
The hypotenuse is opposite the right angle.
72
A quadrilateral with two pairs of parallel sides is a ________.
parallelogram
## Footnote
Parallelograms have opposite sides that are equal in length.
73
A parallelogram with right angles is a ________.
rectangle
## Footnote
Rectangles have four right angles and opposite sides that are equal.
74
A parallelogram with all sides equal is a ________.
rhombus
## Footnote
Rhombuses have equal-length sides and opposite angles that are equal.
75
A regular quadrilateral; a rhombus with right angles is a ________.
square
## Footnote
Squares have equal sides and four right angles.
76
A quadrilateral with one pair of parallel sides is a ________.
trapezoid
## Footnote
Trapezoids have at least one pair of parallel sides.
77
A quadrilateral with two pairs of congruent adjacent sides is a ________.
kite
## Footnote
Kites have two pairs of equal-length sides that are adjacent.
78
Circumference formula in the handout: C = ________.
2πr
## Footnote
This formula calculates the distance around a circle.
79
Area of a circle: A = πr^______.
2
## Footnote
This formula calculates the space within a circle.
80
Area of a triangle: A = (b×h)/______.
2
## Footnote
This formula calculates the area based on the base and height.
81
Area of a rectangle: A = l × ______.
w
## Footnote
This formula calculates the area based on length and width.
82
Perimeter of a rectangle: P = 2l + 2______.
w
## Footnote
This formula measures the total distance around a rectangle.
83
Area of a square: A = l^______.
2
## Footnote
This formula calculates the area of a square based on the length of its sides.
84
Perimeter of a square: P = ______.
4l
## Footnote
This formula measures the total distance around a square.
85
Area of a trapezoid: A = ((B + b)×h)/______.
2
## Footnote
This formula calculates the area based on the lengths of the bases and height.
86
Volume of a cube: V = a^______.
3
## Footnote
This formula calculates the space within a cube.
87
Volume of a rectangular prism: V = l × w × ______.
h
## Footnote
This formula calculates the volume based on length, width, and height.
88
Volume of a cylinder: V = π × r^2 × ______.
h
## Footnote
This formula calculates the volume of a cylinder.
89
Volume of a cone: V = (1/3) × π × r^2 × ______.
h
## Footnote
This formula calculates the volume of a cone.
90
Volume of a sphere: V = (4/3) × π × r^______.
3
## Footnote
This formula calculates the volume of a sphere.
91
In probability, the set of all possible outcomes is the ________ space.
sample
## Footnote
The sample space includes every possible result of a random experiment.
92
An event is a ________ of outcomes of a random experiment.
set
## Footnote
Events can consist of one or more outcomes.
93
Probability formula: P(x) = E(x)/S(x); E(x) is the number of ________ outcomes.
preferred
## Footnote
This formula calculates the likelihood of a specific event occurring.
94
Factorial definition: x! = 1×2×3×…×n, and 0! = ________.
1
## Footnote
The factorial of zero is defined as one.
95
Fundamental Counting Principle: if there are a ways and b ways, total ways = a×______.
b
## Footnote
This principle helps calculate the total number of outcomes.
96
Permutation formula: nPr = n!/(n−r)!. Order matters.
Order matters
## Footnote
Permutations consider the arrangement of items.
97
Combination formula: nCr = n!/((n−r)! r!). Order does NOT matter.
Order does NOT matter
## Footnote
Combinations consider the selection of items without regard to arrangement.
98
Fibonacci sequence base terms: F1 = 1 and F2 = ________.
1
## Footnote
The Fibonacci sequence starts with these two base values.
99
Fibonacci recursive rule (for n ≥ 3): Fn = Fn−1 + Fn−______.
2
## Footnote
This rule defines how to calculate subsequent Fibonacci numbers.
100
Triangular number formula: Tn = n(n+1)/______.
2
## Footnote
This formula calculates the nth triangular number.
101
Square number nth-term formula: Sn = ________.
n^2
## Footnote
This formula calculates the nth square number.
102
Pentagonal number formula: Pn = n(3n−1)/______.
2
## Footnote
This formula calculates the nth pentagonal number.
103
Mathematical language characteristics: precise, concise, and ________.
powerful
## Footnote
Mathematical language effectively conveys complex ideas.
104
Mathematical language is a ________ language.
symbolic
## Footnote
It uses symbols to represent numbers and operations.
105
“ℝ + ℝ = ℝ” expresses that the sum of any two real numbers is also a ________ number.
real
## Footnote
This property indicates closure under addition for real numbers.
106
An expression is like an English noun; it does NOT have a truth value (true/false): it is not a complete ________.
thought
## Footnote
Expressions represent quantities or relationships but do not assert truth.
107
A mathematical sentence states a complete thought and can be true or ________.
false
## Footnote
Mathematical sentences can be evaluated for truth.
108
A proposition is a declarative sentence that is either true or false, but never ________.
both
## Footnote
Propositions are clear statements with definitive truth values.
109
Which is NOT a proposition: a) 1+2=3 b) Ouch! c) If you study hard, you get good grades d) Tarlac City is in Region II?
b – Ouch!
## Footnote
This statement does not assert a truth value.
110
Negation is equivalent to the English word “________.”
not
## Footnote
Negation reverses the truth value of a proposition.
111
Conjunction uses “and” and is true only if both propositions are ________.
true
## Footnote
Conjunctions require both statements to be true for the overall statement to be true.
112
Disjunction uses “or” and is true if at least one proposition is ________.
true
## Footnote
Disjunctions allow for one or both statements to be true.
113
A conditional p → q is false only when p is true and q is ________.
false
## Footnote
This defines the truth conditions for a conditional statement.
114
A biconditional p ↔ q is read as “if and only ________.”
if
## Footnote
Biconditionals are true when both statements are either true or false.
115
A truth table involving n propositions has ________^n rows.
2
## Footnote
The number of rows corresponds to the combinations of truth values.
116
A proposition that is always true is a ________.
tautology
## Footnote
Tautologies hold true under all circumstances.
117
A proposition that is always false is a ________.
contradiction
## Footnote
Contradictions cannot be true under any circumstances.
118
A proposition that is neither tautology nor contradiction is a ________.
contingency
## Footnote
Contingencies can be true in some cases and false in others.
119
Converse of p → q is ________.
q → p
## Footnote
The converse switches the hypothesis and conclusion.
120
Inverse of p → q is ________.
(~p) → (~q)
## Footnote
The inverse negates both the hypothesis and conclusion.
121
Contrapositive of p → q is ________.
(~q) → (~p)
## Footnote
The contrapositive negates and switches the hypothesis and conclusion.
122
Inductive reasoning is usually based on ________.
observation
## Footnote
Inductive reasoning draws general conclusions from specific examples.
123
Deductive reasoning produces ________ conclusions (if premises are true).
necessary
## Footnote
Deductive reasoning guarantees the truth of the conclusion if the premises are true.
124
Polya’s 4 steps start with: ________ the problem.
Understand
## Footnote
This step emphasizes grasping the problem before attempting to solve it.
125
Polya’s 4 steps end with: ________ back.
Look
## Footnote
This final step involves reviewing the solution for accuracy.
126
Nominal scale is concerned with ________ data (labels).
categorical
## Footnote
Nominal scales classify data without a specific order.
127
Ordinal scale is concerned with ________ data.
ranked
## Footnote
Ordinal scales classify data with a meaningful order.
128
Interval scale assigns numbers with meaning and weight on values between ________.
intervals
## Footnote
Interval scales have equal distances between values but no true zero.
129
Ratio scale is like interval but includes an absolute ________.
zero
## Footnote
Ratio scales allow for meaningful comparisons of magnitude.
130
Population refers to an entire group of people/things/events with at least one trait in ________.
common
## Footnote
Populations are the complete set from which samples can be drawn.
131
A measure obtained from the population is a ________.
parameter
## Footnote
Parameters describe characteristics of the entire population.
132
A small number of observations taken from a population is a ________.
sample
## Footnote
Samples are used to infer characteristics about the population.
133
A measure obtained from a sample is a ________.
statistic
## Footnote
Statistics provide estimates of population parameters based on sample data.
134
Mean formula (ungrouped): x̄ = (∑x)/______.
N
## Footnote
This formula calculates the average of a set of values.
135
Median is the ________ value when data are arranged.
middle
## Footnote
The median represents the central value in a data set.
136
Mode is the value with the greatest ________.
frequency
## Footnote
The mode indicates the most common value in a data set.
137
Grouped mean formula: x̄ = (∑fx)/(∑______)
f
## Footnote
This formula calculates the mean for grouped data.
138
Range formula: R = highest score − ________ score.
lowest
## Footnote
The range measures the spread of values in a data set.
139
z-score (population): z = (x − μ)/______.
σ
## Footnote
The z-score indicates how many standard deviations a value is from the mean.
140
Normal distribution is symmetric about a vertical line through the ________.
mean
## Footnote
In a normal distribution, the mean, median, and mode are all equal.
141
In a normal distribution, mean, median, and mode are ________.
equal
## Footnote
This property characterizes the shape of the normal distribution curve.
142
Standard normal distribution has mean 0 and standard deviation ________.
1
## Footnote
This standardization allows for comparison across different normal distributions.
143
Linear regression equation: ŷ = a + ________.
bx
## Footnote
This equation models the relationship between two variables.
144
Modular arithmetic is also called ________ arithmetic.
clock
## Footnote
Modular arithmetic involves calculations with a fixed set of values.
145
Congruence notation: 13 ≡ 1 (mod 12) means the remainder when 13 is divided by 12 is ________.
1
## Footnote
This notation indicates equivalence in modular arithmetic.
146
Caesar cipher encryption: ek(x) ≡ (x + k) mod m; here m equals the alphabet size (A–Z) which is ________.
26
## Footnote
This cipher shifts letters by a fixed number in the alphabet.
147
Apportionment definition: dividing a fixed number of items among groups of different ________.
sizes
## Footnote
Apportionment ensures fair distribution based on group sizes.
148
Standard divisor = total population / number of people to ________.
apportion
## Footnote
This calculation determines how many items each group receives.
149
Father of Mathematics (commonly cited).
Archimedes
## Footnote
Archimedes made significant contributions to mathematics and physics.
150
Father of Algebra (commonly cited).
Al-Khwarizmi
## Footnote
Al-Khwarizmi is known for his work in algebra and algorithms.
151
Pythagorean Theorem for a right triangle.
a^2 + b^2 = c^2
## Footnote
This theorem relates the lengths of the sides of a right triangle.
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