Math10 curriculum map docx

CURRICULUM MAP
Subject: MATHEMATICS
Grade Level: Grade 10
Teacher: Melvin B. Sandro
Time Content Content Standard Performance
Standard
Learning
Competencies
Assessment Activities Resources Instructional
Core Values
1st Grading
Period
Patterns
and Algebra
The learner
demonstrates
understanding of
key concepts of
sequences,
polynomials and
polynomial
equations.
The learner is able
to formulate and
solve problems
involving
sequences,
polynomials and
polynomial
equations in
different
disciplines
through
appropriate and
accurate
representations.
The learner…
1.generates patterns
(M10AL-Ia-1)
2. illustrates an
arithmetic sequence
(M10AL-Ib-1)
Identification-identifying the
sequence and series defined
Direction: Think of as many as you
can that begin with 3, 6, ... and have
pattern. For each sequence,write the
next five terms. If possible,write a
formula for the nth term of the
Problem solving- Sequences and
series
Magic Box-students will answer the
problems contained in the box.
Let’s try it.
A. Use patterns to complete the table
below.
Figurate
number
1st 2nd 3rd 4th
Triangular 1 3 6 10
Square 1 4 9 16
Pentagonal 1 5 12 22
Hexagonal 1 6 15
Heptagonal 1 7
Octagonal 1
B. Find the first five terms in the
sequence given by the formula :
an = 3n +2
Discussion:
1. Did you complete the table? How?
2. Did you find any pattern?
3. How did you get the next term in each
pattern?
Boardwork.
List all the indicated terms of each finite
sequence.
1. an = 2n2 – 1 for 1 ≤ n ≥ 5
2. an = 1/n+1 for 1 ≤ n ≤ 4
GIVE MY FORMULA-students will
recite the formula of the presented terms
Integration: Arts
Sketching
A Real Step to Sequence
Use the situation below to answer the
questions that follow
E-Math10
M.Esparrago
et.al (pp. 2-
43)
E-Math10
(Teacher’s
Wraparound
Edition) (p2-
54)
develop self-
esteemand
independence
promote
reliability with
regards to their
mathematical
skills

Standard
Learning
Competencies
Core Values
3. determines
arithmetic means and
nth term of an
arithmetic sequence.
(M10AL-Ib-c-1)
Completion-solving for the missing
terms in the presented sets of
sequence
Seatwork.
A. Find the nth term of the
given arithmetic sequence.
1. Find the 15th term of the
arithmetic sequence 18,
22, 26, 30, 34, ...
2. In the arithmetic
sequence 8, 14, 20, 26,
32, ... , which term is
122?
3. Find the 18th term of
the arithmetic sequence
whose first term is 11
Situation: Mr. Lorenzo’s daughter is
graduating from elementary school this
year. To prepare his daughter’s college
education he is thinking of either taking an
education plan for her, or save a fixed
amount in a bank. He has already saved
PhP8,000 for this purpose. He decided to
save PhP500 monthly in a bank starting this
year.
Think about it. Make a graphical
representation for the problem.
Discussion:
1. How much will he have saved
after one year?
2. Let’s include the already saved
PhP8,000 to his savings after a
year, what is the total savings?
3. How much will he have saved
after two years? three years? four
years?
4. How much money will he have
saved when his daughterenrolls
in college?
Mr. Lorenzo estimates that his daughter
will need P30,000 for her four years in
college. Will he have saved this amount
by the time his daughterreaches the last
year in college?
Board works-Solving sequences and
series
Competency: Determine arithmetic
means and nth term of an arithmetic
sequence
Discussion:
1. What is a5 ? a20 ? a50 ?
2. What is the formula for
determining the number of
matchsticks needed to form n
squares?
3. How did you find the activity?
How are we going to write a formula for
the nth term of a sequence?
E-Math10
M.Esparrago
et.al (pp. 68-
93)
exhibit the
importance of
being attentive
during class
discussion

Standard
Learning
Competencies
Core Values
4. find the sumof the
terms of a given
arithmetic sequence.
(M10AL-Ic-2)
and whose 17th term is
59.
4. Insert 4 arithmetic
means between 5 and
25.
5. Find x, if the sequence
m, x, n is an arithmetic.
B. In the arithmetic sequence
9, 11, 13, 15, 17, ...,
1. Write a formula for the
nth term,
2. Find its 12th term, and
Which term is 47?
Answer the following.
1. Find the sumof the first 25
multiples of 8.
2. Find the sumof the first 12 terms
of the arithmetic sequence whose
general term is an = 3n+5.
FILL ME – students will complete the
missing terms in the presented table
The Secretof Karl
What is 1 + 2 + 3 + ... + 50 + 51 + ... + 98
+ 99 + 100?
A famous story tells that this was the
problem given by an elementary school
teacher to a famous mathematician to keep
him busy.Do you know that he was able
to get the sum within seconds only? Can
you beat that? His name was Karl
Friedrich Gauss (1777-1885). Do you
know how he did it? Let us find out by
doing the activity below.
Think-Pair-Share
Determine the answer to the above
problem. Then look for a partner and
compare your answer with his/her answer.
Discuss with him/her your technique (if
any) in getting the answer quickly. Then
with your partner, answer the questions
E-Math10
(Teacher’s
Wraparound
Edition)
pp.69-73
develop their
camaraderie in
group activities

Standard
Learning
Competencies
Core Values
5. illustrates a
geometric sequence.
(M10AL-Id-1)
Book activity: Problem solving
Oral Recitations
Missing You
Find the missing terms in each
geometric sequence.
1. 3, 12, 48, __, __
2. __, __, 32, 64, 128, ...
3. 120, 60, 30, __, __, __
4. 5, __, 20, 40, __, __
5. __, 4, 12, 36, __, __
6. -2, __, __, -16, -32,-64
7. 256, __, __,-32,16,...
8. 27,9,__,__,64,256
9.1,4 __, __, __, 64, 256
10. 5x2 __, 5x6, 5x8 __ , ...
Find the first five terms of each
sequence and state whether the given
below and see if this is similar to your
technique.
1. What is the sumof each of the pairs 1
and 100, 2 and 99, 3 and 98, ..., 50 and 51?
2. How many pairs are there in #1?
3. From youranswers in #1 and #2, how
do you get the sum of the integers from 1
to 100? 4. What is the sum of the integers
from 1 to 100?
Group activity- groups will solve problems
composed by the opponent group
Activity:
The Rule of Geometric Sequence
Form a group of 3 members and answer the
guide questions using the table.
Problem: What are the first 5 terms of a
geometric sequence whose first term
is 2 and whose common ratio is 3?
Term Other Ways to Write the
Terms
In Factored
Form
In Exponential
Form
A1 = 2 2 2x30
A2 = 6 2x3 2x31
A3 =
18
2x3x3 2x32
A4 =
54
2x3x3x3 2x33
A5 =
162
2x3x3x3x3 2x34
... ... ...
An ?
Guide Questions:
1. Look at the two ways of writing the
terms. What does 2 represent?
2. For any two consecutive terms, what
does 3 represent?
3. What is the relationship between the
exponent of 3 and the position of
the term?
E-Math10
M.Esparrago
et.al (pp. 100-
117)
enhance their
critical skills in
solving math
problems

Standard
Learning
Competencies
Core Values
6. differentiates a
geometric sequence
from an arithmetic
sequence.(M10AL-
Id-1)
7. differentiates a
finite geometric
sequence from an
infinite geometric
sequence.(M10AL-
Id-3)
8. determines
geometric means and
nth term of a
geometric sequence.
(M10AL-Ie-1)
sequence is arithmetic, geometric, or
neither.
1. An = 3n + 8
2. An = n2 + 2
3. An = 5 . 2n
4. An = 4 – 7n
5. An = (n2 + 2) / n
Consider the infinite geometric
sequence 5, -25, 125, -625, ...
Complete the table below by finding
the indicated partial sums. Answer
the questions that follow.
S1 S2 S3 S4 S5
Guide Questions:
1. What is the common ratio of the
given sequence?
2. What happens to the values of n S
as n increases?
3. Does the given infinite sequence
have a finite sum?
Find the indicated number of
geometric means between each pair
of numbers.
1. 16 and 81 [3]
2. 256 and 1 [3]
3. –32 and 4 [2]
4. 1/3 and 64/3 [1]
5. 2xy and 16xy4 [2]
4. If the position of the term is n, what must
be the exponent of 3?
5. What is n a for this sequence?
6. In general, if the first term of a geometric
sequence is a1 and the
common ratio is r, what is the nth term of
the sequence?
State whether the given sequence is
arithmetic, geometric, or neither. If it is
arithmetic, give the common difference. If
it is geometric, give the common ratio.
1. 11, 14, 17, 20, ...
2. 4, 8, 16, 32, ...
3. 5, 8, 12, 17, 26, ...
4. 32, 28, 24, 20, ...
5. 1, 8, 27, 64, ...
6. 7, 10, 15, 22, 31, ...
7. 1, -3, 5, -7, ...
8. 80, 40, 20, 10, ..
9. 20, 30, 36, 42, ...
10. 100, -50, 25, -12.5, ...
Consider the infinite geometric sequence
2, 4, 8, 16, 32, 64, ... Complete the table
below by finding the indicated partial
sums. Answer the questions that follow.
S1 S2 S3 S4 S5
Guide Questions:
1. What is the common ratio of the given
sequence?
2. What happens to the values of n S as n
increases?
3. Does the given infinite sequence have a
finite sum?
1. Insert 3 terms between 2 and 32 of a
geometric sequence.
E-Math10
(Teacher’s
Wraparound
Edition) pp.
76-93
E-Math10
M.Esparrago
et.al (pp. 128-
138)
E-Math10
(Teacher’s
Wraparound
promote
independence in
doing individual
works
boost their
confidence in
answering
develop their
willingness in
learning

Standard
Learning
Competencies
Core Values
9. finds the sum of the
terms of a given finite
or infinite geometric
sequence.(M10AL-
Ie-2)
10. illustrates other
types of sequences
(e.g., harmonic,
Fibonacci). (M10AL-
If-1)
Group presentation will be graded
using a rubric.
Presentation 10
Clarity 10
Correctnes 20
Discsipline 10
TOTAL 50 points
State whether the given sequence is
harmonic, part of a Fibonacci or
neither. Then, give the next term of
the sequence.
1. 8, 16, 24, 32, ...
2. 1/3, 1/9, 1/27, 1/81, ...
3. 1296, 216, 36, 6, ...
4. 8, 13, 21, 34, 55, ...
5. ¾, 1, 5/4, 3/2, ...
2. Find the value of x if the geometric
mean of 2x and 19x – 2 is 7x – 2.
Group Activity
Let the students be grouped into three.
Each will be given a situation to analyze,
illustrate and solve.
1. The mathematics in Banking
Suppose Miguel saves 100 pesos
in January and that each amount
thereafter he manages to save
one-half more than what he has
saved in the previous month.
How much is Miguel’s total
savings after 10 months?
2. the Music of Math
Julian sees a new band at the
concert. He emails a link for the
band’s website to five of their
friends. The link is forwarded
again following the same pattern.
What is the total number of
emails sent if there are eight
rounds?
3. population of fruit flies
A population of fruit flies is growing in
such a way that each generation is 1.5
times as large as the last generation.
Suppose there were 100 insects in the first
generation. How many would there be in
the fourth generation?
1. Given the Fibonacci sequence 5, 8, 13,
21, 34, ... , find the next 6 terms.
Solution: Since each new term in a
Fibonacci sequence can be obtained by
adding its two preceding terms, then the
Edition)
pp.104-114
show
attentiveness in
classroom
discussion and
activities

Standard
Learning
Competencies
Core Values
11. solves problems
involving sequences.
(M10AL-If-2)
next 6 terms are 55, 89, 144, 233, 377, and
610
2. Given the arithmetic sequence ½, 1, 3/2,
2, ... ,find the 10th term of the
corresponding harmonic sequence.
Solution: Getting the 10th term of the
given sequence which is 5, then the 10th
term of the harmonic sequence is 1/5.
May the Best Man Win
Do the following by group.
Imagine that you were one of the
people in the Human Resource group of a
fast growing company in the Philippines.
All of you were asked by the management
to create a salary scheme for a very
important job that the company would
offer to the best IT graduates this year.
The management gave the salary range
good for 2 years, telling everyone in your
group that whoever could give a salary
scheme that would best benefit both the
employer and the would-be employees
would be given incentives.
1. Form groups of 5. In your respective
groups,make use of all the concepts
you learned on geometric sequences
considering the starting salary, the rate
of increase, the time frame, etc. in
making different salary schemes and in
deciding which one will be the best for
both the employer and the would-be
employees.
2. Prepare a visual presentation of your
chosen salary scheme with the different
data that were used,togetherwith the
formulas and all the computations done.
You may include one or two salary
schemes that you have prepared in your
group for comparison.
3. In a simulated board meeting, show
your visual presentation to your classmates

Standard
Learning
Competencies
Core Values
12. performs division
of polynomials using
long division and
synthetic
division.(M10AL-Ig-
1)
13. proves the
Remainder Theorem
and the Factor
Theorem. (M10AL-
Ig-2)
A. Use the Remainder Theorem to
find the remainder R in each of the
following.
1. (x4 – x3 + 2)  (x + 2)
2. (x3 – 2x2 + x + 6)  (x – 3)
3. (x4 – 3x3 + 4x2 – 6x + 4)  (x – 2)
4. (x4 – 16x3 + 18x2 – 128)  (x + 2)
5. (3x2 + 5x3 – 8)  (x – 4)
B. Use the Factor Theorem to
determine whether or not the first
polynomial is a factor of the second.
Then, give the remainder if the
second polynomial is divided by the
first polynomial.
1. x – 1; x2 + 2x + 5
2. x – 1; x3 – x – 2
3. x – 4; 2x3 – 9x2 + 9x – 20
who will act as the company’s human
resource administrative officers.
Apply Your Skills
Solve the problem. Show your complete
solutions.
If one ream of bond paper costs (3x – 4)
pesos,how many reams can you buy for
(6x4 – 17x3 + 24x2 – 34x + 24) pesos?
A. Use the Factor Theorem to determine
whether or not the first polynomial is a
factor of the second.Then,give the
remainder if the second polynomial is
divided by the first polynomial.
1. x – 1; x2 + 2x + 5
2. x – 1; x3 – x – 2
3. x – 4; 2x3 – 9x2 + 9x – 20
4. a – 1; a3 – 2a2 + a – 2
5. y + 3; 2y3 + y2 – 13y + 6
B. Applying the Remainder Theorem
Answer each of the following problems.
1. What is the remainder when 5x234 + 2 is
divided by
a. x – 1?
b. x + 1?
2. What is the remainder when 4x300 –
3x100 – 2x25 + 2x22 – 4 is divided by
a. x – 1?
b. x + 1?
Factoring Polynomials
Find the missing factor in each of the
following. Write your answers in your
notebook.
1. x3 – 8 = (x – 2)(__________)

Standard
Learning
Competencies
Core Values
14. factors
polynomials.
(M10AL-Ih-1)
15. illustrates
polynomials
equations.(M10AL-
Ii-1)
4. a – 1; a3 – 2a2 + a – 2
5. y + 3; 2y3 + y2 – 13y + 6
“Bussiness Math”
Read and analyze the situation.
Students individually perform the
following steps:
a. Consider the polynomial
30x3 – 48x2 + 1758x + 10
000 as the annual
representation of DVD sales
in million pesos where x is
the number of years since
2010.
b. Use the polynomial in step a
to estimate the year where
DVD sales will be about 9
billion pesos.
c. Considering the
mathematical model in a for
the DVD sales,would you
consider this business
feasible? Why?
2. 2x3 + x2 – 23x + 20 = (x +
4)(__________)
3. 3x3 + 2x2 – 37x + 12 = (x –
3)(__________)
4. x3 – 2x2 – x + 2 = (x – 2)(__________)
5. 2x3 – x2 – 2x + 1 = (2x –
1)(__________)

Standard
Learning
Competencies
Core Values
16. proves Rational
Root Theorem.
(M10AL-Ii-2)
17. solves polynomial
equations.(M10AL-
Ij-1)
Find all the possible rational roots of
1. 2x3 + 3x2 – 8x + 3 = 0
2. x3 + 2x2 – 5x - 6 = 0
3. 6x3 – 25x2 – 31x + 30 = 0
4. 3x3 – 2x2 + 8x + 5
A. Find all the roots of each
equation.
1. x3 + 3x2 – 10x – 24 = 0
2. 3x3 + x2 – 12x – 4 = 0
3. 2x3 – 5x2 – 14x + 8 = 0
B. Find a polynomial equation of
least degree with integral coefficients
that have the given roots.
1. – 4, - 2 , 3
2. – 3 , 2
3. -1, 2, 3, 5
What is a Polynomial Equation?
Complete the Frayer Model using the word
POLYNOMIAL EQUATION/
FUNCTION.
Definition Facts/Characteristics
Examples Non-examples
Process Questions:
1. How did you determine the
examples and non-examples of a
polynomial equation/function?
2. How does the polynomial
equation/function differ from the
other equation/function?
3. What makes an equation a
polynomial equation/function?
Reflection Log
1. What difficulties did you
encounter while finding the
rational roots of the polynomial
equation?
2. How did you overcome these
difficulties?
A. Completing the List of Roots of
Polynomial Equations
One of the roots ofthe polynomial equation
is given. Find the other roots.
1. – 2x4 + 13x3 – 21x2 + 2x + 8 = 0;
x1 =  ½
2. x4 – 3x2 + 2 = 0;
x1 = 1
3. x4 – x3 – 7x2 + 13x – 6 = 0;
x1 = 1
4. x5 – 5x4 – 3x3 + 15x2 – 4x + 20 = 0;
x1 = 2
PE

Standard
Learning
Competencies
Core Values
18. solves problems
involving
polynomials and
polynomials
equations.(M10AL-
Ij-2)
5. 2x4 – 17x3 + 13x2 + 53x + 21 = 0;
x1 = –1
How did you find the activity?
B. Creating Polynomial Equation
For each item below, give a polynomial
equation with integer coefficients that has
the following roots.
1. –1, 3, –6
2. ±2, ±7
3. 0, –4, –5, ±1
4. ±2, 3, 5 3
5. ±2, 3 1  , 7 2 , 3
Modeling through Polynomial Equati ons
Do the following by group.
Set up a polynomial equation that models
each problem below. Then solve the
equation, and state the answer to each
problem.
1. One dimension of a cube is increased by
1 inch to form a rectangular block. Suppose
that the volume of the new block is 150
cubic inches. Find the length of an edge of
the original cube.
2. The dimensions of a rectangular metal
box are 3 cm, 5 cm, and 8 cm. If the first
two dimensions are increased by the same
number of centimeters, while the third
dimension remains the same, the new
volume is 34 cm3 more than the original
volume. What is the new dimension of the
enlarged rectangular metal box?
3. The diagonal of a rectangle is 8 m longer
than its shorter side. If the area of the
rectangle is 60 square m, find its
dimensions.
4. Identical squares are cut from each
corner of an 8 inch by 11.5 inch
rectangular piece of cardboard. The sides
are folded up to make a box with no top. If

Standard
Learning
Competencies
Core Values
the volume of the resulting box is 63.75
cubic inches, how long is the edge of each
square that is cut off?
2nd Grading
Period
Patterns
and Algebra
The learner
demonstrates
understanding of
key concepts of
polynomial
function.
The learner is able
to conduct
systematically a
mathematical
investigation
involving
polynomial
functions in
different fields.
19. illustrates
polynomial functions.
(M10AL-IIa-1)
Give Me More Companions
Work with your friends. Determine
the x-intercept/s and the y-intercept
of each given polynomial function.
To obtain other points on the graph,
find the value of y that corresponds
to each value of x in the table.
1. y = (x + 4)(x + 2)(x – 1)(x – 3)
x-intercepts: __ __
__ __
y-intercept: __
List all your answers above as
ordered pairs.
2. . y = –(x + 5)(2x + 3)(x – 2)(x – 4)
x-intercepts: __ __
__ __
y-intercept: __
A. Did you miss me? Here i am again
Factor each polynomial completely using
any method. Enjoy working with your
seatmate using the Think-Pair-Share
strategy.
1. (x – 1) (x2 – 5x + 6)
2. (x2 + x – 6) (x2 – 6x + 9)
3. (2x2 – 5x + 3) (x – 3)
4. x3 + 3x2 – 4x – 12
5. 2x4 + 7x3 – 4x2 – 27x – 18
E-Math10
M.Esparrago
et.al (pp. 161-
201)
enhance their
efficiency and
reliability

Standard
Learning
Competencies
Core Values
20. graphs polynomial
functions.(M10AL-
IIa-b-1)
21. solves problems
involving polynomial
functions.(M10AL-
IIb-2)
Follow My Path (part II. )
1. The graph on the right is defined
by y = -x5 + 3x4 + x3 – 7x2 + 4 or, in
factored form, y = - (x+1)2 (x-1)(x-
2)2.
Questions:
a. Is the leading coefficient a positive
or a negative number?
b. Is the polynomial of even degree
or odd degree?
c. Observe the end behaviors of the
graph on both sides. Is it rising or
falling to the left or to the right?
2. The graph on the right is defined
by y = x4 – 7x2 + 6x or, in factored
form, y = x(x+3)(x-1)(x-2).
For each given polynomial function,
describe or determine the following,
then sketch the graph. You may need
a calculator in some computations.
a. number of turning points
b. sketch
1. y = -x3 + 2x2 – 2x +4
2. y = x2 (x2 – 7)(2x+3)
B. Seize and Intercept Me
Determine the intercepts of the graphs of
the following polynomial functions:
1. y = x3 + x2 – 12x
2. y = (x – 2)(x – 1)(x + 3)
3. y = 2x4 + 8x3 + 4x2 – 8x – 6
4. y = –x4 + 16
5. y = x5 + 10x3 – 9x
It’s Your Turn, Show Me
For each given polynomial function,
describe or determine the following, then
sketch the graph. You may need a
calculator in some computations.
a. number of turning points
b. sketch
1. y = -(x+3)(x+1)2(2x-5)
2. y = (x2 – 5)(x-1)2(x-2)3
E-Math10
(Teachers
Wraparound
Edition) pp.
137-172
develop their
critical thinking
in solving
mathematical
problems
Geometry The learner
demonstrates
understanding of
key concepts of
circles and
coordinate
geometry.
The learner is able
to formulate and
find solutions to
challenging
solutions
involving circles
and otherrelated
22. derives
inductively the
relations among
chords,arcs, central
angles, and inscribed
angles. (M10GE-IIc-
1)
Find My Degree Measure
In ʘA below, m 42,   LAM m 30,
  HAG and KAH is a right
angle. Find the following measure of
an angle or an arc, and explain how
you arrived at your answer.
Use ʘA below to identify and name the
following. Then, answer the questions that
follow.
E-Math10
M.Esparrago
et.al (208-245)
develop their
comprehension in
solving
mathematical
problems

Standard
Learning
Competencies
Core Values
terms in different
disciplines
through
appropriate and
accurate
representations.
The learner is able
to formulate and
solve problems
involving
geometric figures
on the rectangular
coordinate plane
with perseverance
and accuracy. 23. proves theorems
related to chords,
arcs, central angles,
and inscribed angles.
(M10GE-IIc-d-1)
24. illustrates secants,
tangents,segments,
and sectors ofa circle.
(M10GE-IIe-1)
1. mLAK 6. mLK
2. mJAK 7. mJK
3. mLAJ 8. mLMG
4. mJAH 9. mJH
5. mKAM 10. mKLM
Answer.
1. Do you agree that if two lines
intersect at the center of a circle, then
the lines intercept two pairs of
congruent arcs? Explain your answer.
2. The length of an arc of a circle is
6.28 cm. If the circumference of the
circle is 37.68 cm, what is the degree
measure of the arc? Explain how you
arrived at your answer.
From One Place to Another
Use the figure and the given
information to answer the questions
that follow. Explain how you arrived
at your answer.
1. If mADC = 160 and mEF = 80,
what is m ? ABC
2. If mPR = 45 and mQS = 49,
what is m ? PTR m ?
My Real World
1. 2 semicircles in the
figure
2. 4 minor arcs and their
corresponding major arcs
3. 4 central angles
Questions:
a. How did you identify and name the
semicircles? How about the minor arcs and
the major arcs? central angles?
b. Do you think the circle has more
semicircles, arcs,and central angles? Show.
Find My Arc Length
The radius of ʘ O below is 5 units. Find the
length of each of the following arcs given
the degree measure. Answer the questions
that follow.
1. m𝑃𝑉
̂ = 45; length of 𝑃𝑉
̂ = ________
2. m𝑃𝑄
̂ = 60; length of 𝑃𝑄
̂ = ________
3. m𝑄𝑅
̂ = 90; length of 𝑄𝑅
̂ = ________
Questions:
a. How did you find the length of each arc?
b. What mathematics concepts orprinciples
did you apply to find the length of each arc?
Tangents or Secants?
In the figure below, KL, KN, MP, and ML
intersect Q at some points.Use the figure
to answer the following qestions.
1. Which lines are tangent to the circle?
Why?
2. Which lines are secants? Why?
3. At what points does each secant
intersect the circle? How about the
tangents?
4. Which angles are formed by two secant
lines? two tangents? a tangent and a
secant?
E-Math10
(Teachers
Wraparound
Edition) pp.
174-211
E-Math10
M.Esparrago
et.al (pp. 260-
297)
showactiveness
during class
discussion and
activities
develop team
works

Standard
Learning
Competencies
Core Values
25. proves theorems
on secants,tangents,
and segments.
(M10GE-IIe-f-1)
26. solves problems
on circles. (M10GE-
IIf-2)
You will be given a practical task
which will demonstrate your
understanding of the different
geometric relationships involving
tangents and secants.
Answer the following. Use the rubric
provided to rate your work for
evaluation purposes.
1. The chain and gears of bicycles or
motorcycles or belt around two
pulleys are some real-life illustrations
of tangents and circles. Using these
real-life objects or similar ones,
formulate problems involving
tangents, then solve.
2. The picture below shows a bridge
in the form of an arc. It also shows
how secant is illustrated in real life.
Using the bridge in the picture and
other reallife objects, formulate
problems involving secants, then
solve them.
Fly Me To Your World!
questions that follow.
You are in a hot air balloon and your
eye level is 60 meters over the ocean.
Suppose your line of sight is tangent
to the radius of the earth like the
illustration shown below.
1. How far away is the farthest point
you can see over the ocean if the
radius of the earth is approximately
6378 kilometers?
2. What mathematics concepts would
you apply to find the distance from
where you are to any point on the
horizon?
A Map of my Own
Perform the following activities.
5. Name all the intercepted arcs in the
figure. Which angles intercept each of
these arcs?
6. Suppose m KOM  50 and m 130, 
 KQM what is mKLM equal to? How
about mNP?
Prove!
1. If a secant and a tangent intersect at the
point of tangency,then the measure of each
angle formed is one-half the measure of its
intercepted arc.
Given:
MP and LN are secant and tangent,
respectively, and intersect at C at the point
of tangency, M.
Prove: mNMP m ½ (mMP) and
m<LMP ½ (mMKP)
Were you able to prove the different
geometric relationships involving tangents
and secants? Were you convinced that
these geometric relationships are true? I
know you were! Find out by yourself how
these geometric relationships are
illustrated or applied in the real world.
My True World!
Divide the class in four groups. Let the
students read, analyze and perform the
activity.
Make a design of an arch bridge that
would connect two places which are
separated by a river, 20 m wide. Indicate on
the design the different measurements of
the parts of the bridge. Out of the design
and the measurements of its parts,
E-Math10
(Teachers
Wraparound
Edition)
pp.226-263
exhibit their
willingness in
learning
mathematical
skills
improve their
critical thinking

Standard
Learning
Competencies
Core Values
27. derives the
distance formula.
(M10GE-IIg-1)
28. applies the
distance formula to
prove some geometric
properties. (M10GE-
IIg-2)
1. Have a copy of the map of your
municipality, city, or province then
make a sketch of it on a coordinate
plane. Indicate on the sketch some
important landmarks, then determine
their coordinates.Explain why the
landmarks you have indicated are
significant in your community. Write
also a paragraph explaining how you
selected the coordinates of these
important landmarks.
2. Using the coordinates assigned to
the different landmarks in item #1,
formulate then solve problems
involving the distance formula,
midpoint formula, and the coordinate
proof.
Prove That This is True
Write a coordinateproof to prove
each of the following.
1. The diagonals of an isosceles
trapezoid arecongruent.
Given: Trapezoid PQRS with PS 
QR
Prove: PR  QS
2. The medians to the legs of an
isosceles trianglearecongruent.
Given: Isosceles triangleABC with
AB AC  . BT and CS are the
medians.
Prove: BT  CS
formulate problems involving tangent and
secant segments, and then solve.
Use the rubric provided to rate your
work.
How far are we from each other?
Find the distance between each pair of
points on the coordinate plane. Answer the
1. M(2, –3) and N(10, –3)
2. C(–3, 2) and D(9, 7)
3. P(3, –7) and Q(3, 8)
4. S(–4, –2) and T(1, 7)
5. R(4, 7) and S(–6, –1)
1. The coordinates of the endpoints of ST
are (-2, 3) and (3, y), respectively.
Suppose the distance between Sand T is
13 units.What value/s ofy would satisfy
the given condition? Justify your
answer.

Standard
Learning
Competencies
Core Values
29. illustrates the
center-radius form of
the equation of a
circle. (M10GE-IIh-
1)
Turn Me into a General!
Write each equation of a circle in
general form. Show your solutions
completely.
1. (x-2)2 + (y-4)2=36
2. (x+ 4)2 + (y-9)2=144
3. (x-6)2 + (y-1)2=81
4. (x-8)2 + (y+ 7)2=225
5. x 2 + (y-5)2= 36
2. The length of MN  15units. Suppose the
coordinates of M are (9, –7) and the
coordinates of N are (x, 2).
a. What is the value of x if N lies on the
first quadrant? second quadrant?
Explain your answer.
b. What are the coordinates of the
midpoint ofMN if N lies in the second
quadrant? Explain your answer.
3. The midpoint of CS has coordinates (2, –
1). If the coordinates of C are (11, 2),
what are the coordinates of S? Explain
your answer.
4. A tracking device attached to a kidnap
victim prior to his abduction indicates
that he is located at a point whose
coordinates are (8, 10). In the tracking
device, each unit on the grid is
equivalent to 10 kilometers. How far is
the tracker from the kidnap victim if he
is located at a point whose coordinates
are (1, 3)?
5. F  d,a , A d,c  , S  b,c , and T b,a 
are distinct points on the coordinate
plane.
a. Is FS  AT ? Justify your answer.
b. What figure will be formed when you
connect consecutive points by a line
segment? Describe the figure.
Is there a traffic in the air?
An air traffic controller (the person who
tells the pilot where a plane needs to go
using coordinates on the grid) reported that
the airport is experiencing air traffic due to
the big number of flights that are scheduled
to arrive. He advised the pilot of one of the
airplanes to move around the airport for the
meantime to give way to the other planes to
land first. The air traffic controller further
told the pilot to maintain its present altitude

Standard
Learning
Competencies
Core Values
30. determines the
center and radius of a
circle given its
equation and vice
versa. (M10GE-IIh-
2)
31. graphs a circle
and othergeometric
figures on the
coordinate plane.
(M10GE-IIi-1)
Find Out More!
1. A line passes through the centerof
a circle and intersects it at points (2,
3) and (8, 7). What is the equation of
the circle?
2. The diameter of a circle is 18 units
and its centeris at (–3, 8). What is
the equation of the circle?
3. Write an equation of the circle with
a radius of 6 units and is tangent to the
line y  1 at (10, 1).
Graph! Graph! Graph!
Graph the following circles in a
graphing paper, with the specified
center and radius, using a compass.
1. Center (5,1); radius : 2 units
2. Center (4,6); radius : 3 unit
3. Center (-1,-6); radius : 4
units
4. Center (5,0); radius : 5 units
5. Center (-4, 0); radius : 1 unit
or height from the ground and its horizontal
distance from the origin, point P(0, 0).
Questions:
1. Suppose the plane is located at a point
whose coordinates are (30, 40) and
each unit on the air traffic controller’s
grid is equivalent to 1 km. How far is
the plane from the air traffic
controller? Explain your answer.
2. What would be the y-coordinate of the
position of the plane at a particular
instance if its x-coordinate is 5? 10?
15? -20? -30? Explain your answer.
3. Suppose that the pilot strictly follows
the advice of the air traffic controller.
Is it possible for the plane to be at a
point whose xcoordinate is 60? Why?
4. How would you describe the path of the
plane as it goes around the airport? What
equation do you think would define this
path?
Don’t Treat This as a Demotion!
In numbers 1 to 6, a general equation of a
circle is given. Transform the equation to
standard form, then give the coordinates of
the center and the radius. Answer the
1. x2 + y2 - 2x – 8y – 47 = 0
2. x2 + y2 + 4x – 4y – 28 = 0
3. x2 + y2 + 8y – 84 = 0
Try This!
Answer the following problem. Make a
grpahical representation of the problem.
The Provincial Disaster and Risk
Reduction Management Committee
(PDRRMC) advised the residents living
within the 10 km radius critical area to

Standard
Learning
Competencies
Core Values
32. solves problems
involving geometric
figures on the
coordinate plane.
(M10GE-Iii-j-1)
1. The diameter of a circle is 18
units and its center is at (–3, 8).
What is the equation of the circle?
2. Write an equation of the circle
with a radius of 6 units and is
tangent to the line y  1 at (10, 1).
3. A circle defined by the equation
( x – 6 )2
+ ( y – 9 )2
= 34 is tangent
to a line at the point (9, 4). What is
the equation of the line?
4. A line passes through the center
of a circle and intersects it at
points (2, 3) and (8, 7). What is the
equation of the circle?
5. The Provincial Disaster and
Risk Reduction Management
Committee (PDRRMC) advised
the residents living within the 10
km radius critical area to evacuate
due to eminent eruption of a
volcano. On the map that is drawn
on a coordinate plane, the
coordinates corresponding to the
location of the volcano is (3, 4).
a. If each unit on the
coordinate plane is equivalent to 1
km, what is the equation of the
circle enclosing the critical area?
b. Suppose you live at
point (11, 6). Would you follow
the advice of the PDRRMC?
Why?
c. In times of eminent
disaster, what precautionary
measures should you take to be
safe?
d. Suppose you are the
leader of a two-way radio team
evacuate due to eminent eruption of a
volcano. On the map that is drawn on a
coordinate plane, the coordinates
corresponding to the location of the
volcano is (3, 4).
a. If each unit on the coordinate
plane is equivalent to 1 km, what
is the equation of the circle
enclosing the critical area?
b. Suppose you live at point (11, 6).
Would you follow the advice of
the PDRRMC? Why?
c. In times of eminent disaster,
what precautionary measures
should you take to be safe?
Suppose you are the leader of a two-way
radio team with 15 members that is tasked
to give warnings to the residents living
within the critical area. Where would you
position each member of the team who is
tasked to inform the other members as
regards the current situation and to warn
the residents living within his/her assigned
area? Explain your answer.

Standard
Learning
Competencies
Core Values
with 15 members that is tasked to
give warnings to the residents
living within the critical area.
Where would you position each
member of the team who is tasked
to inform the other members as
regardsthe current situation and to
warn the residents living within
his/her assigned area? Explain
your answer.
6. Cellular phone networks use
towers to transmit calls to a
circular area. On a grid of a
province, the coordinates that
correspond to the location of the
towers and the radius each covers
are as follows: Wise Tower is at (–
5, –3) and covers a 9 km radius;
Global Tower is at (3, 6) and
covers a 4 km radius; and Star
Tower is at (12, –3) and covers a 6
km radius.
a. What equation
represents the transmission
boundaries of each tower?
b. Which tower transmits
calls to phones located at
(12, 2)? (–6, –7)? (2, 8)?
(1, 3)?
c. If you were a cellular
phone user,which cellular
phone network will you
subscribe to? Why?
3rd Grading
Period
Statistics
and
Probability
The learner
demonstrates
understanding of
key concepts of
combinations and
probability
The learner is able
to use precise
counting
technique and
probability in
formulating
conclusions and
making decisions.
33. illustrates the
permutation of
objects.(M10SP-
IIIa-1)
Tell whether the situation is a
permuation or not.If it is a
permutation, solve.
1. . A teacher wants to assign 4
different tasks to her 4 students.In
how many possible ways can she do
it?
Permutation or Not?
Choose a partner. Tell whether the
situation is a permuation or not. If it is a
permutation, solve. The first one is done
for you.
1. Given the 4-letter word READ. In
how many ways can we arrange its
letters, 3 at a time?
E-Math10
M.Esparrago
et.al (pp. 320-
344)
realize the
importance of
permutation and
combination in
real life situation

Standard
Learning
Competencies
Core Values
34. derives the
formula for finding
the number of
permutations of n
objects taken r at a
time. (M10SP-IIIa-2)
2. In a certain general assembly, three
major prizes are at stake. In how
many ways can the first, second,and
third prizes be drawn from a box
containing 120 names?
3. In how many different ways can 5
bicycles be parked if there are 7
available parking spaces?
4. There are 8 basketball teams
competing for the top 4 standings in
order to move up to the semi-finals.
Find the number of possible rankings
of the four top teams.
people occupy the 12 seats in a front
row of a mini-theater?
Answer.
1. In how many ways can 5 people
arrange themselves in a row for
picture taking?
be seated around a circular
table?
be seated around a circular
table?
4. If there are 12 teams in a
basketball tournament and each
team must play every other team
in the eliminations, how many
elimination games will there be?
5. If there are 7 distinct points on a
plane with no three of which are
collinear, how many different
polygons can be possibly
formed?
Evaluate the following:
1. 13P6 =
2. 8P8 =
3. 15P13 =
4. 10! / 2!3!2! =
5. 6! /3! =
2. In a schoolclub, there are 5 possible
choices for the president,a secretary,
a treasurer, and an auditor. Assuming
that each of them is qualified for any
of these positions,in how many ways
can the 4 officers be elected?
3. How many different sets of 5 cards
each can be formed from a standard
deck of 52 cards?
4. In a 10-item Mathematics problem-
solving test,how many ways can you
select 5 problems to solve?
5. In how many ways can a committee
of 5 be formed from 5 juniors and 7
seniors if the committee must have 3
seniors?
Answer:
bicycles be parked if there are 7
available parking spaces?
2. How many distinguishable
permutations are possible with all the
letters of the word ELLIPSES?
people occupy the 12 seats in a front
row of a mini-theater?
4. Find the number of different ways that
a family of 6 can be seated around a
circular table with 6 chairs.
Mission Possible
E-Math10
(Teachers
Wraparound
Edition) pp.
334-359)
E-Math10
develop
camaraderie

Standard
Learning
Competencies
Core Values
35. solves problems
involving
permutations.
(M10SP-IIIb-1)
36. illustrates
combination of
objects.(M10SP-
IIIc-1)
37. differentiates
permutation from
combination of n
time. (M10SP-IIIc-2)
38. derives the
formula for finding
the number of
combinations of n
time. (M10SP-IIId-1)
39. solves problems
involving
Answer the problem.
There are 12 people in a dinner
gathering. In how many ways can the
host (one of the 12) arrange his
guests around a dining table if a. they
can sit on any of the chairs? b. 3
people insist on sitting beside each
other? c. 2 people refuse to sit beside
each other?
Direction: Solve the problem
involving combination
1. How many possible outcomes
are there if we choose a
committee that consist of 4 boys
and 2 girls from a group of 5
boys and 8 girls?
Direction: Make a Venn Diagram for
both combination and permutation
and discuss their simillarities and
differences.
Situation:
You have four colored shirts.You
can only bring two shirts every day.
In how many days can you provide a
two-colored shirt combination?
Answer the following question:
Using the Formula nCr = (n
r) = n! /
r! (n-r)! . what is your answer to the
given situation?
In a certain general assembly, three major
prizes are at stake. In how many ways can
the first, second, and third prizes be drawn
from a box containing 120 names?
Aside from the given situation, can you
cite anotherexample where the concept of
permutation is needed?
How Useful is This?
The 8 members of the board of Directors
of the cooperative is having a round table
meeting. In how many ways can the
secretary arranged them?
How important is permutation (circular,
linear) in life?
Activity: Oral Recitation
What is combination? Cite give an
example of it.
Make a venn diagram to showthe
difference between permutations and
combinations
Choose Wisely, Choose Me!
Solve the following problems completely.
Divide the class into 10 groups.Each
group will be given one problem to solve
and discuss to the class.
1. If there are 12 teams in a basketball
tournament and each team must play
every other team in the eliminations,
M.Esparrago
et.al (pp. 347-
371)
E-Math10
(Teachers
Wraparound
Edition) pp.
372- 386
E-Math10
M.Esparrago
et.al (pp. 372-
391)
E-Math10
(Teachers
Wraparound
Edition)
pp.387-407
exhibit activeness
in solving
mathematical
problems
improve their
comprehen-
sion in solving
problems.
develop their
critical thinking
in solving
exhibit teamwork
in doing group
activities
showactiveness

Standard
Learning
Competencies
Core Values
permutations and
combinations.
(M10SP-IIId-e-1)
Oral Recitation:
Define, then illustrate the following
words or phrase:
1. event
2. experiment
3. outcome
4. sample space
5. simple event
6. compound event
how many elimination games will
there be?
2. If there are 7 distinct points on a plane
with no three of which are collinear,
how many different polygons can be
possibly formed?
3. How many different sets of 5 cards
each can be formed from a standard
deck of 52 cards?
4. In a 10-item Mathematics problem-
solving test,how many ways can you
select 5 problems to solve?
5. In problem number 4, how many ways
can you select the 5 questions if you
are required to answer question
number 10?
6. In how many ways can a committee of
5 be formed from 5 juniors and 7
seniors if the committee must have 3
seniors?
7. From a population of 50 households,in
how many ways can a researcher
select a sample with a size of 10?
8. A box contains 5 red balls, 7 green
balls, and 6 yellow balls. In how many
ways can 6 balls be chosen if there
should be 2 balls of each color?
9. From 7 Biology books and 6 Chemistry
books, in how many ways can one
select 2 Biology and 2 Chemistry
books to buy if all the said books are
equally necessary?
10. Mrs. Rivera’s business is gown rental
and sale. She decided one day that she
would display her 10 newest gowns in
her shop’s window to attract
customers. If she only had 5
mannequins and planned to change the
set of gowns every 2 days,how many
days will have to pass before she runs
out of a new set to display?
DESCRIPTION: Find the union and
intersection of events A and B defined by
the following.

Standard
Learning
Competencies
Core Values
40. illustrates events
and union and
intersection of events.
(M10SP-IIIf-1)
41. illustrates the
probability of a union
of two events.
(M10SP-IIIg-1)
A Chance to Further Understand
(Group Work)
Answer the following questions.Be
ready to present youranswers in the
class.
1. How does a simple event differ
from a compound event?
2. Differentiate mutually exclusive
events from non-mutually exclusive
events.
3. Suppose there are three events A,
B, and C that are not mutually
exclusive. List all the probabilities
you would need to consider in order
to calculate P(A or B or C). Then,
write the formula you would use to
calculate the probability.
4. Explain why subtraction is used
when finding the probability of two
events that are not mutually
exclusive.
1. A 3-section spinnermarked red, green,
blue is spun once and a coin is tossed
once. A is event of spinning a red and B is
the event iof getting a head.
2. A die is tossed twice. A is the event of
getting equal dots and B is the event of
getting a sumof 11.
3. A coin is tossed three times. A is the
event that atleast 2 heads come up and B is
the event that only one head comes up.
1. Give the samplespaceof combination
of rice,viand,and drink.How many
possibleoutcomes are there?
2. List the outcomes of selecting a lunch
with pineapplejuice.
3. How many outcomes are there for
selectingany lunch with pineapplejuice?
selectinga lunch with steamed riceand
with pineapplejuice?
selectinga lunch with chicken adobo and
a pineapplejuice?
selectinga lunch with pinakbet and an
orange juice? A student taking lunch in
the canteen is selected atrandom.
7. What is the probability thatthe student
chose pineapplejuiceas a drink?
8. What is the probability thatthe student
chose steamed riceand pineapplejuice?

Standard
Learning
Competencies
Core Values
42. finds the
probability of (𝐴 ∪
𝐵). (M10SP-IIIg-h-
1)
Where in the Real World? (Group
Work)
Answer the following questions.
Write a report of youranswers using
a minimum of 120 words. Be ready
to present youranswers in the class.
1. Describe a situation in your life
that involves events which are
mutually exclusive or not
mutually exclusive. Explain why
the events are mutually exclusive
or not mutually exclusive.
2. Think about yourdaily experience.
How is probability utilized in
newspapers,television shows,and
radio programs that interest you?
What are your general
impressions of the ways in which
probability is used in the print
media and entertainment industry?
Mutually Exclusive or Not?
Consider each problem below. Draw
a Venn diagram for each. Determine
whether the events are mutually
exclusive or not mutually exclusive.
Then, find the probability.
1. Mario has 45 red chips, 12 blue
chips, and 24 white chips. What is
the probability that Mario
randomly selects a red chip or a
white chip?
2. Of 240 students,176 are on the
honorroll, 48 are members of the
varsity team, and 36 are in the
honorroll and are also members of
the varsity team. What is the
9. What is the probability that the student
chose chicken adobo and orange juice?
10. What is the probability thatthe
student chosepinakbet and pineapple
juice?
Reflect:
a. What does the tree diagramtell you?
b. How did you determine the sample
space?
c. Differentiate an outcome from a
samplespace.Give another example of an
outcome.
d. Aside from the tree diagram,how else
can you find the total number of possible
outcomes?
Counting Techniques and Probabillity
of Compound Events
Consider the situation below and answer
the questions that follow. There are a total
of 48 students in Grade 10 Charity.
Twenty are boys and 28 are girls.
1. If a teacher randomly selects a student to
represent the class in a schoolmeeting,
what is the probability that a a. boy is
chosen? b. girl is chosen?
2. If a committee of 3 students is formed,
what is the probability that a. all are
girls? b. two are boys and one is a girl?
3. Suppose that a team of 3 students is
formed such that it is composed of a
team leader, a secretary, and a
spokesperson.What is the probability
that a team formed is composed of a girl
secretary?

Standard
Learning
Competencies
Core Values
43. illustrates
mutually exclusive
events.(M10SP-IIIi-
1)
probability that a randomly
selected student is on the honor
roll or is a member of the varsity
team?
3. Ruby’s dog has 8 puppies.The
puppies include white females, 3
mixed-color females, 1 white
male, and 2 mixed-color males.
Ruby wants to keep one puppy.
What is the probability that she
randomly chooses a puppy that is
female and white?
4. Carl’s basketball shooting records
indicate that for any frame, the
probability that he will score in a
two-point shoot is 30%, a three-point
shoot,45%, and neither, 25%. What
is the probability that Cindy will
score either in a two-point shoot or in
a three-point shoot?
Solving Problems Involving
Conditional Probability
1. A family has two children. What is
the probability that the younger
child is a girl, given that at least
one of the children is a girl?
2. At a basketball game, 80% of the
fans cheered for team A. In the same
crowd, 20% of the fans were waving
banners and cheering for team A.
What is the probability that a fan
waved a banner given that the fan
cheered for team A?
More Exercises on Mutually Exclusive
and Not Mutually Exclusive Events
Consider the situation below and answer
the questions that follow.
1. A restaurant serves a bowl of candies to
their customers. The bowl of candies
Gabriel receives has 10 chocolate
candies, 8 coffee candies, and 12
caramel candies.After Gabriel chooses
a candy, he eats it. Find the probability
of getting candies with the indicated
flavors.
a. P (chocolate or coffee)
b. P (caramel or not coffee)
c. P (coffee or caramel)
d. P (chocolate or not caramel)
2. Rhian likes to wear colored shirts. She
has 15 shirts in the closet. Five of these
are blue, four are in different shades of
red, and the rest are of different colors.
What is the probability that she will
wear a blue or a red shirt?
3. Mark has pairs of pants in three
different colors, blue, black, and brown.
He has 5 colored shirts: a white, a red, a
yellow, a blue, and a mixed-colored
shirt. What is the probability that Mark
wears a black pair of pants and a red
shirt on a given day?
4. A motorcycle licence plate has 2 letters
and 3 numbers. What is the probability
that a motorcycle has a licence plate
containing a double letter and an even
number?

Standard
Learning
Competencies
Core Values
44. solves problems
involving probability.
(M10SP-IIIi-j-1)
Probability in Real Life
Make a research report. Choose your
own topic of study orchoose from any of
the four recommended topics given below.
Focus on the question that follows:
How can I use statisticsand probability
to help others make informed decisions
regarding my chosen topic?
Recommended Topics:
1. Driving and cell phone use
2. Diet and health
3. Professional athletics
4. Costs associated with a college
education
4th Grading
Period
Statistics
and
Probability
The learner
demonstrates
understanding of
key concepts of
measures of
position.
The learner is able
to conduct
systematically a
mini-research
applying the
different statistical
methods.
45. illustrates the
following measures of
position: quartiles,
deciles and
percentiles. (M10SP-
Iva-1)
Find Out!
1. Find the average of the lower
quartile and the upperquartile of the
data.
Component Quantity
hard disk 290
monitors 370
keyboards 260
mouse 180
speakers 430
2. Mrs. Marasigan isa veterinarian.
One morning, sheasked her
secretary to record the servicetime
for 15 customers. The followingare
servicetimes in minutes. 20, 35, 55,
28, 46, 32, 25,56, 55, 28, 37, 60, 47,
Example.
1. The owner of a coffee shop recorded the
number of customers who came into his
café each hourin a day. The results were
14, 10, 12, 9, 17, 5, 8, 9, 14, 10, and 11.
Find the lower quartile and upperquartile
of the data.
Solution:
 In ascending order, the data are 5, 8, 9,
9, 10, 10, 11, 12, 14, 14, 17
 The least value in the data is 5 and the
greatest value in the data is 17.
 The middle value in the data is 10.
 The lower quartile is the value that is
between the middle value and the
least value in the data set.
 So, the lower quartile is 9.
 The upper quartile is the value that is
between the middle value and the
greatest value in the data set.
 So, the upper quartile is 14.
Try this! ( Seatwork)
E-Math10
M.Esparrago
et.al (pp. 402-
424)
show
participation in
class

Standard
Learning
Competencies
Core Values
46. calculates a
specified measure of
position (e.g. 90th
percentile) of a set of
data. (M10SP-IVb-1)
52, 17 Find the valueof the 2nd
decile,6th decile,and 8th decile
3. Given a test in Calculus,the 75th
percentile scoreis 15.What does it
mean? What is its measureof
position in relation to the other
data? Interpret the result and justify.
Aqua Running
Aqua Running has been
promoted as a method for
cardiovascular conditioning for the
injured athlete as well as for others
who desire a low impact aerobic
workout. A study reported in the
Journal of Sports Medicine
investigated the relationship between
exercise cadence and heart rate by
measuring the heart rates of 20
healthy volunteers at a cadence of 48
cycles per minute (a cycle consisted
of two steps).
The data are listed here:
87 109 79 80 96 95 90 92
96 98
101 91 78 112 94 98 94 107
81 96
Find the lower and upperquartiles of
the data using:
a. Mendenhall and Sincich Method
b. Linear Interpolation
Go, Investigate!
Given 50 multiple-choice
items in their final test in
Mathematics, the scores of 30
students are the following:
23 38 28 46 22 20 18 34 36 35
Go, Investigate!
Given 50 multiple-choice items in
their final test in Mathematics, the scores
of 30 students are the following:
23 38 28 46 22 20 18 34 36 35 45
48 16 22 27
25 29 31 30 25 44 21 18 43 21 26
37 29 13 37
Calculate the following using the given
data.
1. D2 6. P7
2. D3 7. P8
3. D4 8. P9
4. D5 9. P20
5. D6 10. P90
You’re My World!
The scores of Miss World
candidates from seven judges were
recorded as follows:
8.45, 9.20, 8.56, 9.13, 8.67, 8.85,
and 9.17.
Guide Quuestions:
1. Find the value of 2nd decile.
2. Find the value of 6th decile.
3. Find the value of 8th decile.
4. Find the 60th percentile or P60
of the judges’ scores.
5. What is the P35 of the judges’scores?
Find Me!
Find the first quartile (Q1), second
quartile (Q2), and the third quartile (Q3),
given the scores of 10 students in their
Mathematics activity :
4 9 7 14 10 8 12 15 6 11
a. using Mendenhall and Sincich Method.
b. using Linear Interpolation.
E-Math10
(Teachers
Wraparound
Edition) pp.
410-433
exhibit their
willingness to
learn

Standard
Learning
Competencies
Core Values
47. interprets
measures of position.
(M10SP-IVc-1)
48. solves problems
involving measures of
position. (M10SP-
IVd-e-1)
45 48 16 22 27 25 29 31 30 25
44 21 18 43 21 26 37 29 13 37
1. Calculate the following using the
given data.
1. D2 4. P25
2. D3 5. P75
3. P8
2. Interpret the result.
Find the percentile rank of 109 and
120 for the following distribution.
Class
Interval
Frequency
151-
160
8
141-
150
12
131-
140
6
121-
130
10
111-
120
7
101-
110
11
91-100 13
81-90 9
71-80 4
I. Time to Record!
Mrs. Marasigan is a veterinarian. One
morning, she asked her secretary to record
the service time for 15 customers. The
following are service times in minutes.
20, 35, 55, 28, 46, 32, 25, 56, 55, 28,
37, 60, 47, 52, 17
1. Find the value of the 2nd decile, 6th
decile, and 8th decile.
2. Interpret the result.
II. Your my World!
The scores of Miss World candidates
from seven judges were recorded as
follows:
8.45, 9.20, 8.56, 9.13, 8.67, 8.85, and
9.17.
1. Find the 60th percentile or P60 and
P35of the judges’scores.2. How will
interpret the result.
E-Math10
M.Esparrago
et.al (pp.439-
464)
develop
camaraderie
develop
independence in
doing individual
works

Standard
Learning
Competencies
Core Values
49. formulates
statistical mini-
research. (M10SP-
IVf-g-1)
50. uses appropriate
measures of position
and otherstatistical
methods in analyzing
and interpreting
research data.
(M10SP-IVh-j-1)
Mini-research!
Interview your classmates and find
the score distribution in the activity
That’s My Place. Compute for the
1st quartile, 7th decile and 80th
percentile for the scores distribution.
Finally, interpret the result.
Prepared by:
MELVIN B. SANDRO
Mathematics 10 Teacher
Checked by:
ANNA LIZA MANALO
Academic Coordinator

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