Senior High School

General Mathematics
Quarter 1 – SLAS 4
Solving Real- Life Problems

FOR TANDAG NATIONAL SCIENCE HIGH SCHOOL USE ONLY

IDENTIFYING INFORMATION
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Learning Area: ___________________________ Quarter: 1 __

Name of Learner: _______________________________________________________

Grade Level: 11

School: _________________________________________________________________

LEARNING ACTIVITY DESCRIPTION

Week Covered: First Week

Learning Competency:

Solving Real-Life Problems Involving Functions

Objectives:
After going through this module, you are expected to:
1. represent situations as functions and evaluate functions to determine the
required quantity
2. apply concepts learned in solving real-life problems involving functions
3. solve problems involving functions
composition of functions

Materials

activity notebook, pen or pencil

Content Background:

This module was designed and written to help you solve problems involving
functions bearing in mind that you already know how to represent real – life
situation using functions including piece-wise functions, evaluate functions and
perform operations on functions. These skills will aid you in attaining success on
this module.
Solving problems involving functions is essential in predicting values that will help
in decision making process. This module covers varied situations that can be seen
in real life such as travel fares, monthly bills sales and the like. It is hoped that
upon

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exploring this learning kit, you will find the eager and enthusiasm in completing
the
task required.

SEE AND BE SEEN

Directions: Choose the letter of the best answer. Write the chosen letter on a
separate sheet of paper.

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For numbers 6 - 9 use the problem below:

Mark charges ₱100.00 for an encoding work. In addition, he charges ₱5.00 per page
of printed output.

6.Find a function f(x) where x represents the number of pages of printed out.

a. f(x) = 100 + 5x

b. f(x) = 100 - 5x

c. f(x) = 100x + 5

d. f(x) = 100x – 5

7.How much will Mark charge for 55-page encoding and printing work?

a. ₱275.00

b. ₱175.00

c. ₱375.00

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d. ₱475.00

8.How many pages were printed if Mark received a payment of ₱600.00?

a. 100 pages

b. 80 pages

c. 60 pages

d. 50 pages

9.If Mark offers a promo to loyal costumer that the first 20 pages of the printed
output will be free of charge; how much will he charge to a loyal customer who
printed 70 pages of output?

a. ₱250.00

b. ₱50.00

c. ₱350.00

d. ₱450.00

10. A proposed tricycle fare would charge ₱20.00 for the first 5 km of travel and
₱0.75 for each additional kilometer over the proposed fare. Find the fare function
f(x) where x represents the number of kilometers travelled.

a. f(x) = 20 + 0.75x

b. f(x) = 20 - 0.75x

c. f(x) =16.25 + 0.75x

d. f(x) = 6.25 - 0.75x

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1. Being able to understand a problem presented is the first thing that we learn on
how to solve problems in Mathematics. Careful reading leads you to thorough
analysis in the identification of given facts and in determining the required or the
unknown quantity. Precise label of the known and unknown quantities will help
you set up a direction towards the solution.

2. A function is a rule of correspondence between two non-empty sets, such that to

each element of the first set called domain, there corresponds one and only one
element of the second set called range.

3. Functions are used to model real life situations and in representing real – life
situations the quantity of one variable depends or corresponds to or mapped onto
another quantity.

4. Piece-wise function are functions that may be represented by a combination or of

equations.

5. If a function f is defined by y = f(x) and an independent variable x is found by

substituting x into the function rule then it undergoes a process of evaluating
function. Moreover, you also studied fundamental operation can be applied to two
or more functions to form a new function. Such operations are addition,
subtraction, multiplication and division.

Consider the examples below and reflect if you are confident enough to proceed

1. Write a function C that represent the cost of buying x facemask, if a facemask

cost ₱65.00

C(x) = 65x

2. A commuter pays ₱ 9.00 for a jeepney fare for the first 5 km and an additional ₱
0.75 for every succeeding distance d in kilometer. Represent the situation as
function

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F(d) = 9, if 0<d<5

F(d) = 9 + 0.75(d), if d>5

Activity 1: Performance Task

JEEPNEY OR TRICYCLE?

Read and analyze the problem below.

Miguel is a senior high school student who commutes from home to school which is

15 km apart. There are two modes of transportation the first one is through jeep
and

the other one is through tricycle. In riding a jeepney the fare charge ₱9.00 for the

first 4 km travel and ₱0.75 for each additional kilometer. Meanwhile in riding a

tricycle the fare would be ₱10.00 for the first km travel and ₱1 for each additional

kilometer. Will you help Miguel analyze his situation?

Questions

1. If you are Miguel and decided to ride in a jeepney, how much will be your
fare? _____________________________________________________________

Hint: You may use the table below to compute the fare

2. If you decided to ride in a tricycle how much will be your fare? ____________

Hint: You may use the strategy in no. 2

3. What characteristics does Miguel possess if he chose to ride a jeepney?

_______________________________________________________________

4. Is there any advantage in riding a jeepney instead of tricycle? Or riding a tricycle

instead of jeepney? What would it be?

___________________________________________________________________________

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5. If you are Miguel which between the two modes of transportation will you choose?
Why? ____________________________________________________

Activity 2. Performance Task

BINGE WATCH

1. Lucena Network charges ₱450.00 monthly cable connection fee plus ₱130.00
for each hour of pay-per-view (PPV) event regardless of a full hour or a
fraction of an hour.

a. Find payment function f(x) where x represents the number of PPV hours.

b. What is the monthly bill of a customer who watched 25 hours of PPV events?

c. What is the monthly bill of a customer who watched 0.5 hour of PPV events?

Activity 3. Multiple Choice.

Choose the letter of the best answer. Write the chosen letter on a separate sheet of
paper.

For numbers 1- 5 use the problem below: Emmanuel decided to put up a candy
shop that sells a dairy chocolate that cost ₱135.00 per pack. The cost of making
the chocolate is ₱90.00 and the operating expense is ₱4,500.00

1. Which of the following pertains to the profit function?

a. P(x) = 45x – 4,500

b. P(x) = 225x – 4,500

c. P(x) = 45x + 4,500

d. P(x) = 225x + 4,500

2. How many packs of dairy chocolate must be sold to break even?

a. 50

b. 100

c. 150

d. 200

3. Which value of x will make Emmanuel’s candy shop suffer loss for selling packs
of chocolates?

a. X> 100

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b. x≤ 100

c. x< 100

d. x≥ 100

4. How many chocolate bars must be sold if Emmanuel wanted to earn a profit of
₱6,750.00?

a. 100

b. 150

c. 250

d. 350

5. How much is the gain if Emmanuel sold 350 packs of chocolates?

a. ₱6,750.00

b. ₱9,750.00

c. ₱11.250.00

d. ₱15,250.00

REFLECTIONS
Directions: Explain what you have learned and what you need to know more in this
learning activity sheets. Write your reflections using the following paragraph starters
on your paper.

Concepts Learned:

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I learned that…
______________________________________________________________________________

Concepts Unlearned:

I need to know more about…

______________________________________________________________________________

REFERENCES

Books:
CHED. General Mathematics Learner's Materials. Pasig City: Department of
Education - Bureau of Learning Resources, 2016.
Orines, Fernando B. Next Cantury Mathematics 11. Quezon City: Phoenix
Publishing House, 2016.
Oronce, Orlando A. General Mathematics, 1st Ed. Quezon City: Rex Book Store Inc.,
2016.
Online Sources:
https://courses.lumenlearning.com/waymakercollegealgebra/chapter/piecewisedefined-
functions/

ANSWER KEY

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Tasks.
your Performance
This will serve as
REFLECTION
 Development Team of School-based Learning Activity Sheets (LAS)

Writer: Angelo F. Racho, T –II; Tandag National Science High School

Editor: Ella Mae V. Pasuhil , T –II
Reviewer: Mia O. Laorden, MT-II; Joeyconsly L. Valeroso, MT – I
Illustrator: Mia O. Laorden, MT-II
Management Team: Romulo T. Laorden, P – I
Mia O. Laorden, MT – II

For inquiries or feedback, please write or call:

TANDAG NATIONAL SCIENCE HIGH SCHOOL

LEARNING RESOURCE MANAGEMENT TEAM - TNSHS

Tabon – tabon, Quezon, Tandag City, Surigao del Sur

Telephone: 214-5827

Email Address: sciencehighschool.tandag@gmail.com

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