Application of Linear and Quadratic Equations

Grade 12 · Mathematics

Semester 1 | Period 2 | Week 10

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Subject: Mathematics

Semester: 1

Period: 2

Week: 10

WEEK 10

Class: Grade 12
Age: 17 years
Duration: 40 minutes per period (5 periods)
Subject: Mathematics
Topic: Application of Linear and Quadratic Equations
Focus: Solving word problems involving linear equations, simultaneous linear equations, one linear and one quadratic equation, and applying them to the capital market.

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Revise and solve simultaneous linear equations and quadratic equations.
  2. Interpret and solve word problems involving linear equations.
  3. Interpret and solve word problems involving simultaneous linear equations.
  4. Interpret and solve word problems involving simultaneous equations (one linear, one quadratic).
  5. Apply the knowledge of equations to the capital market.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Practice exercises
  • Real-life connections and discussion

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating the solution of simultaneous linear and quadratic equations
  • Example word problems on linear, quadratic, and simultaneous equations

 

PERIOD 1 & 2: Revision of Simultaneous Linear and Quadratic Equations

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces word problems involving linear equations. Guides students in translating word problems into algebraic equations.

Students listen attentively and ask clarifying questions.

Step 2 - Guided Example

Demonstrates solving a word problem involving linear equations. Example: "A car rental company charges a flat fee of $30 plus $0.20 per mile. If the total cost for a rental is $50, how many miles were driven?"

Students observe the process of translating the problem into an equation and solving it.

Step 3 - Student Practice

Assigns practice word problems for students to solve independently. Encourages pair work to discuss solutions.

Students solve problems and discuss their approaches in pairs.

NOTE ON BOARD:

Example Problem:
"A theater charges a flat rate of $10 for admission, plus $2 per snack. If a person spends $26 in total, how many snacks did they buy?"
Translation to equation:
10 + 2x = 26
Solve for x.

 

EVALUATION (5 exercises):

  1. A man spends $100 on a shopping trip. The amount spent on clothes is $60 more than the amount spent on shoes. How much was spent on each item?
  2. A store sells pens at $5 each and pencils at $2 each. If a customer buys 6 pens and 8 pencils, what is the total cost?
  3. A car rental company charges a flat fee of $20 plus $0.15 per mile. If a customer is charged $50, how many miles did they drive?
  4. A woman buys 3 shirts and 2 pairs of shoes for $80. The shirts cost $20 each. How much does each pair of shoes cost?
  5. A baker sells cakes for $15 each and cookies for $2 each. If the total revenue from selling 4 cakes and 5 cookies is $70, how much did he earn from each item?

 

PERIOD 5: Word Problems on Simultaneous Linear Equations and One Linear, One Quadratic

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Explains the interpretation and solution of word problems involving simultaneous linear and quadratic equations. Demonstrates how to set up such problems.

Students listen carefully and ask clarifying questions.

Step 2 - Simultaneous Linear and Quadratic

Solves a combined word problem, such as: "A person invests in two types of bonds. One type pays 5% interest and the other pays 7%. The total investment is $10,000. The amount invested in the 7% bonds is $2000 more than the amount invested in the 5% bonds. How much is invested in each?"

Students watch the step-by-step solution, taking notes and asking questions.

Step 3 - Practice

Provides several word problems for students to solve individually or in pairs. Mixes linear, quadratic, and simultaneous equations.

Students work on the problems, applying the learned methods to solve them.

 

EVALUATION (5 exercises):

  1. A person invests $4000 in two accounts, one paying 5% interest and the other 7%. If the total interest earned in one year is $240, how much was invested in each account?
  2. A farmer sells two types of crops. One type yields 20 tons per hectare, and the other yields 15 tons per hectare. The farmer sold 150 tons of crops. How many hectares did he plant of each crop?
  3. A student has 3 times as many dimes as nickels. If the total value of the coins is $5.30, how many of each coin does the student have?
  4. A theater sells adult tickets for $12 and children’s tickets for $8. If the total revenue from ticket sales is $480, how many adult and children’s tickets were sold?
  5. A person invests $5000 in two bonds. One bond earns 5% interest and the other earns 8%. The total interest earned is $320. How much is invested in each bond?

 

CLASSWORK (5 questions):

  1. Solve the word problem: "A bank account has a balance of $3000. One part earns 3% interest, and the other part earns 5%. After one year, the total interest is $120. How much is in each part?"
  2. Solve: "A customer buys 5 apples and 3 oranges for $8. The next day, the same customer buys 2 apples and 7 oranges for $7. How much is one apple and one orange?"
  3. Solve: "A person buys a car for $12,000 and finances it with a loan. After 2 years, the loan balance is reduced to $8,000. How much was paid off each year?"
  4. Solve: "A student spends $50 on books and supplies. One part is spent on notebooks at $3 each, and the rest is spent on pens at $1 each. How many notebooks and pens were bought?"
  5. Solve: "A person invests in two types of stocks. One stock earned 6% return, and the other earned 9%. If the total return is $400, how much was invested in each stock?"

 

ASSIGNMENT (5 tasks):

  1. Solve: "A man buys 2 shirts and 4 trousers for $100. The shirts cost $15 each, and the trousers cost $25 each. How much is the cost of each item?"
  2. olve: "A bank offers a savings account with 4% interest and a certificate of deposit with 6% interest. If a person invests $5000 in both accounts and the total interest earned is $240, how much is invested in each account?"
  3. Solve: "A company sells pens at $2 each and notebooks at $3 each. A customer buys 10 pens and 5 notebooks for $35. How many pens and notebooks did the customer buy?"
  4. Solve: "A car rental company charges $50 for a flat rate and $0.25 per mile. If the total cost is $75, how many miles were driven?"
  5. Solve: "A farmer plants crops that yield 5 tons per hectare for one crop and 3 tons per hectare for another. The total yield is 50 tons. How many hectares were planted of each crop?"