REVIEW OF FIRST TERM WORK, EXPANDING AND FACTORIZING ALGEBRAIC EXPRESSIONS, SOLVING OF QUADRATIC EQUATIONS.

Subject : Mathematics

Class : JSS 2

Term : Second Term

Week : Week 1

Topic : REVIEW OF FIRST TERM WORK, EXPANDING AND FACTORIZING ALGEBRAIC EXPRESSIONS, SOLVING OF QUADRATIC EQUATIONS.

Previous Lesson : Third Term JSS 1 EXAMS QUESTIONS MATHEMATICS

Behavioural Objectives : By the end of the lesson, pupils should be able to

• Recall topics that they have been taught in their previous lesion
• Solve simple questions on REVIEW OF FIRST TERM WORK, EXPANDING AND FACTORIZING ALGEBRAIC EXPRESSIONS, SOLVING OF QUADRATIC EQUATIONS.
• students will be able to expand and factorize algebraic expressions and solve quadratic equations using different methods.

Materials:

• Whiteboard or blackboard
• Markers or chalk
• Handout with practice problems
• Calculator (optional)

Content ;

1. Expanding Algebraic Expressions Expanding algebraic expressions involves simplifying expressions by removing parentheses and combining like terms. The process often involves applying the distributive property.

Examples: a) (2x + 3)(x – 4) = 2x(x) + 2x(-4) + 3(x) + 3(-4) = 2x^2 – 8x + 3x – 12 = 2x^2 – 5x – 12

b) 4(3y – 2) – 6y = 12y – 8 – 6y = 6y – 8

2. Factorizing Algebraic Expressions Factorizing algebraic expressions involves breaking down an expression into simpler factors, often by finding common factors or using specific techniques like grouping, difference of squares, or trinomial factorization.

Examples: a) 6x^2 + 15x = 3x(2x + 5)

b) x^2 – 9 = (x + 3)(x – 3) [difference of squares]

c) x^2 + 5x + 6 = (x + 2)(x + 3) [trinomial factorization]

3. Solving Quadratic Equations Quadratic equations are equations of the form ax^2 + bx + c = 0. There are several methods for solving them, including factoring, completing the square, and using the quadratic formula.

a) Factoring Solve by setting each factor equal to zero and solving for x.

Example: x^2 – 5x + 6 = 0 (x – 2)(x – 3) = 0 x – 2 = 0 or x – 3 = 0 x = 2 or x = 3

b) Completing the Square Manipulate the quadratic equation to create a perfect square trinomial and solve for x.

Example: x^2 – 4x + 3 = 0 (x^2 – 4x + 4) – 1 = 0 (x – 2)^2 = 1 x – 2 = ±√1 x = 2 ± 1 x = 1 or x = 3

c) Quadratic Formula Use the formula x = (-b ± √(b^2 – 4ac)) / 2a to find the roots of the equation.

Example: x^2 – 4x + 3 = 0 a = 1, b = -4, c = 3 x = (4 ± √((-4)^2 – 4(1)(3))) / (2 * 1) x = (4 ± √(16 – 12)) / 2 x = (4 ± √4) / 2 x = 1 or x = 3

Evaluation

1. Which of the following expressions is equivalent to (2x + 5)(x – 3)?

A) 2x^2 + x – 15 B) 2x^2 – x – 15 C) 2x^2 – 4x – 15 D) 2x^2 + 4x – 15

2. What is the factored form of x^2 – 4x + 4?

A) (x – 4)(x – 1) B) (x – 2)(x – 2) C) (x + 2)(x + 2) D) (x + 4)(x + 1)

3. Which method is used to solve the quadratic equation x^2 – 7x + 10 = 0?

A) Quadratic formula B) Factoring C) Completing the square D) Graphing

4. What is the discriminant of the quadratic equation 3x^2 – 6x + 2 = 0?

A) 0 B) 12 C) 36 D) -12

5. When solving a quadratic equation using the quadratic formula, the term under the square root is called:

A) The discriminant B) The constant term C) The linear coefficient D) The quadratic coefficient

6. What is the expanded form of (x + 2)^2?

A) x^2 + 4x + 4 B) x^2 + 4x – 4 C) x^2 + 2x + 4 D) x^2 – 4x + 4

7. What is the factored form of x^2 – 81?

A) (x – 9)(x + 9) B) (x – 3)(x + 3) C) (x – 9)^2 D) (x + 9)^2

8. Which method can be used to solve the quadratic equation x^2 – 4x + 4 = 0?

A) Quadratic formula B) Factoring C) Completing the square D) Both B and C

9. What are the roots of the quadratic equation x^2 – 5x + 6 = 0?

A) x = 2 and x = 3 B) x = -2 and x = -3 C) x = 1 and x = 6 D) x = -1 and x = -6

10. When does a quadratic equation have exactly one real solution?

A) When the discriminant is positive B) When the discriminant is negative C) When the discriminant is zero D) When the quadratic coefficient is zero

Lesson Presentation

Introduction (5 minutes)

1. Begin by briefly introducing the topic and its relevance in algebra and real-life applications.
2. Explain that the lesson will cover expanding and factorizing algebraic expressions, as well as solving quadratic equations using various methods.

Expanding Algebraic Expressions (15 minutes)

1. Define and explain the process of expanding algebraic expressions, emphasizing the distributive property.
2. Write a few examples on the board, and work through them step by step, explaining each step as you go.
3. Ask students to try expanding a few expressions on their own or in pairs and share their solutions.
4. Discuss common mistakes and address any questions or misconceptions.

Factorizing Algebraic Expressions (15 minutes)

1. Define and explain the process of factorizing algebraic expressions, highlighting different techniques (common factors, grouping, difference of squares, and trinomial factorization).
2. Write a few examples on the board for each technique, and work through them step by step, explaining each step as you go.
3. Ask students to try factorizing a few expressions on their own or in pairs and share their solutions.
4. Discuss common mistakes and address any questions or misconceptions.

Solving Quadratic Equations (20 minutes)

1. Define and explain quadratic equations, including the standard form ax^2 + bx + c = 0.
2. Present the three methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula.
3. Write examples on the board for each method, and work through them step by step, explaining each step as you go.
4. Discuss the discriminant and its role in determining the number of real solutions a quadratic equation has.
5. Ask students to solve a few quadratic equations using different methods on their own or in pairs and share their solutions.
6. Discuss common mistakes and address any questions or misconceptions.

Practice and Assessment (10 minutes)

1. Distribute a handout with practice problems, covering expanding and factorizing algebraic expressions and solving quadratic equations using various methods.
2. Allow students to work individually or in pairs to complete the problems.
3. Circulate around the room to monitor progress and provide guidance as needed.
4. Review the solutions as a class, discussing any difficulties or misconceptions.

Conclusion (5 minutes)

1. Summarize the key concepts covered in the lesson: expanding and factorizing algebraic expressions and solving quadratic equations using different methods.
2. Encourage students to practice these skills outside of class and apply them in future algebra problems.
3. Remind students of any upcoming assignments or assessments related to the topic.
4. Thank students for their participation and close the lesson

Weekly Assessment /Test

1. When expanding the expression (3x – 2)(x + 4), the result is _____.
2. To factorize the quadratic expression x^2 – 5x + 6, we can rewrite it as (x – _____)(x – _____).
3. The process of breaking an algebraic expression into simpler factors is called _____.
4. A quadratic equation is an equation of the form _____x^2 + _____x + _____ = 0.
5. When solving the quadratic equation x^2 – 6x + 9 = 0 using the method of completing the square, the perfect square trinomial is (x – _____)^2.
6. The quadratic formula is x = (-b ± √(_____ – 4ac)) / 2a.
7. In the expression 4x^2 – 20x, the greatest common factor is _____, and the factored form is _____(x^2 – 5x).
8. The expanded form of the expression (2x – 3)^2 is _____x^2 – _____x + _____.
9. When the discriminant of a quadratic equation is greater than zero, the equation has _____ real solutions.
10. To factorize the difference of squares expression x^2 – 16, we can rewrite it as (x + _____)(x – _____).