GENERAL MATHEMATICS
Major Performance Task
Name: _____________________________________ Section: ____________________________
“Solving Exponential and Logarithmic Equations and Inequalities”
Topics Covered: Exponential and Logarithmic Functions
Target skills:
The students will be able to:
1. solve problem involving exponential functions, equations, and inequalities M11GM-Ig-2; and
2. solve problems involving logarithmic functions, equations, and inequalities M11GM-Ij-2
PT Description:
In this major performance task, students are challenged to solve exponential and logarithmic equations and inequalities using
only the specified number of steps. For each step, they must indicate the law or property applied. Additionally, they will be required to
answer a reflective question related to the topics covered.
General Instructions:
1. Secure a hard copy of this worksheet.
2. Even though there are various ways to solve exponential and logarithmic equations and inequalities, I challenge you to solve
each of the following items using the specified number of steps.
3. In the adjacent column, indicate what method, math operation, property, or law is applied for each step.
4. Then, answer the reflective question and use the given rubric as your guide.
5. All your answers must be handwritten. No need to place your major PT in a folder. Just make sure to staple it if you have
multiple pages.
6. Deadline of submission: October 21, 2024 (Monday)
Solving (10 points for each item)
53𝑥+2−(1−𝑥) = 1252𝑥−1−𝑥 Given
Step 1:
Step 2:
Step 3:
1
Step 4:
Step 5:
Final Answer: 𝒙 = _____________
1 2𝑥+3 1 𝑥−1
( ) >( ) Given
4 2
Step 1:
Step 2:
Step 3:
2
Step 4:
Step 5:
Step 6:
Final Answer: _____________
𝑙𝑜𝑔(3𝑥 2 + 1) − 𝑙𝑜𝑔(3 + 𝑥) = 𝑙𝑜𝑔(3𝑥 − 2) Given
Step 1.
Step 2.
Step 3:
Step 4:
3
Step 5:
Step 6:
−𝟕𝒙 = −𝟕 Combine like terms
Step 7:
Final Answer: 𝒙 = _____________
𝑙𝑜𝑔(200) + 𝑙𝑜𝑔(5) − 𝑙𝑜𝑔(100) Given
Step 1:
Step 2:
4 Step 3:
Step 4:
Final Answer: _____________
Reflective Essay (20 points)
How can the laws and properties of exponents and logarithms be applied to real-life situations? Why is it important to follow
these mathematical principles to avoid making mistakes in practical contexts? Answer in 8-10 sentences. Refer to the rubric below
on how you will be graded.
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“Take delight in the Lord, and he will give you the desires of your heart.”
Psalm 37:4
Analytic Rubric for the Reflective Essay
Exemplary Proficient Developing Needs Improvement
Criteria
(4𝑝𝑜𝑖𝑛𝑡𝑠) (3𝑝𝑜𝑖𝑛𝑡𝑠) (2𝑝𝑜𝑖𝑛𝑡𝑠) (1𝑝𝑜𝑖𝑛𝑡)
Understanding of Demonstrates a deep and Demonstrates a good Shows some Shows minimal or no
Concepts clear understanding of understanding of the understanding of the understanding of
exponents and logarithms, concepts, with adequate concepts but with unclear exponents and logarithms,
explaining how they apply examples. Addresses the example(s). Partially with no real-life examples
to real-life situations. importance of laws but addresses the importance or incorrect applications.
Shows advanced insight lacks depth in explanation. of the laws. Does not address the
into the importance of importance of laws.
laws.
Real-life Application Provides detailed, Provides relevant and Provides limited or basic Provides irrelevant
relevant, and creative adequate example(s) but example(s), which may be example(s), with little or
example(s) of how lacks creativity or depth in vague and loosely no connection to real-
exponents and logarithms the application of connected to real-life world applications.
are used in everyday life. concepts. contexts.
Clarity of Explanation Explanations are precise, Explanations are generally Explanations are Explanations are unclear
clear, and easy to follow. clear, but there may be sometimes unclear or or disorganized, with little
occasional confusion or confusing. to no logical flow between
gaps in reasoning. ideas.
Importance of Following Thoroughly explains why Adequately explains the Attempts to explain the Fails to explain the
Laws it’s important to follow the importance of following importance of following importance of following
laws and properties of the laws and properties of the laws but with loose the laws and does so in
exponents and logarithms, exponents and logarithms connection to real-life an incorrect manner.
connecting this to avoiding but lacks strong consequences.
errors in real life. connection to real-life
consequences.
Mechanics (Grammar, Essay is free from Essay has minor errors in Essay contains several Essay has frequent errors
Syntax, Structure) grammar, spelling, and grammar, spelling, or grammatical, spelling, or in grammar, spelling, or
punctuation errors. The punctuation but is still punctuation errors that punctuation that make it
structure is well organized. easy to understand. occasionally interfere with difficult to follow. Structure
Structure is generally understanding. Structure is disorganized.
good. is inconsistent.
Total _____/𝟐𝟎
