Lesson+Notes

Scheme of work second term ss1 Week 1 Quadratic equation i. Factorizing quadratic expression ii. Solving quadratic equation by factorization iii. Forming quadratic equation with given roots Week 2 Quadratic equation: solution by graphical method. Week 3 Length of arc of circles, perimeter of sectors and segments. Week 4 Area of sectors and segments of circles. Week 5 Mensuration of solid shapes, the cone as related to sector of a circle. Week 6 Mensuration of solid shapes: surface areas and volumes of cube, cuboids, cylinder and cone. Week 7 Geometrical construction i. Line, line segment, line bisection ii. Construction of angles 600, 900 and angle bisector 300, 450 etc Week 8 construction of Shapes, triangles, quadrilaterals etc Week 9 Locus of moving pints i. Equidistant from two lines ii. Equidistant from two points iii. Equidistant from a fixed point. Week 10 Deduction proof:- a) Triangle – types and properties b) Angle sum of any triangle is 1800 c) Exterior angle of a triangle equal sum of opposite interior angles. Week 11 Revision Week 12 Examination

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **i.** **Identify a quadratic expression** **ii.** **Factorise a quadratic expression** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners** || **Y =2x + 3 and** **ax + bx = x(a + b)** || **__Solution__** **Coefficient is the numerical factor multiplying the variable, in this case X2** **Answer = 3** || **X2 + 5x + 6** **__Solution__** **First Multiply the first term by the last term** **X2 *6 = 6 X2** **Next, find two factors of 6 X2 such that when multiplied gives 6 X2 and when added gives the middle term i.e. 5 X** **2x and 3x** **Next, replace the middle term 5x by the sum of 2x and 3x** **X2 + 2x + 3x + 6** **Next group and factorise the expressions** **(X2 + 2x) + (3x + 6)** **X(x+2) +3(x+2)** **Re-factorising gives** **(X+3)(x+2)** || **Example 3: Factorise the Quadratic expression** **X2 - 2x -3** **First, two factors of -3X2, these are -3x and +1x** **Next replace -2x with +x-3x** **X2+ x -3x -3** **(X2+ x) + (-3x -3)** **Factorise** **X(x+1) -3(x+1)** **Factorising again** **(x-3)(x+1)** || **__Class Work.__** **Factorise the following** **a)** **X2 +2x +3** **b)** **3X2 -2x -1** **__Correction__** **a)** **X2 +2x -3** **X2 +3x-x -3**  **(X2 +3x)+(-x -3)**  **X(x+3) -1(x+3)**  **(x-1)(x+3)**
 * **DATE** ||  || **31st January 2011** ||
 * **CLASS** ||  || **SS 1 E** **&** **F** ||
 * **TIME** ||  || **10:20 – 11:55** ||
 * **DURATION** ||  || **35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Quadratic Expression** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners have been treated to linear equations with one and two variables like**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners what is a QUADRANT why is it called a Quadrant?** ||
 * **PRESENTATION** |||| **Teacher presents the lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: What is the coefficient of X2 in the expression 3X2 + 4x + 8**
 * ^  || **Step 2** || **Example 2: Factorise the quadratic expression**
 * ^  || **Step 3** || **Teacher gives another example**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**

**b)** **3X2 -2x -1** **3X2 -3x +x -1**  **(3X2 -3x) +(x -1)**  **3x(x-1) +1(x-1)**  **(3x+1)(x-1)** || **Assignment:**  **Factorise the following**  **1)** **X2 +7x +12** **2)** **3X2 -4x -7** || **2.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on Quadratic expression, it is identified and factorised as a prelude for factorising quadratic equations.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **REFRENCES** ||  || **1.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **iii.** **Solve complex quadratic expression** **iv.** **Factorise a quadratic expression** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners** || **1)** **X2 +7x +12**  **2)** **3X2 -4x -7** || **1)** **X2 +7x +12** **X2 +4x+3x +12**  **(X2 +4x)+(3x +12)**  **X(x+4)+3(x+4)**  **(x+3)(x+4)**
 * **DATE** ||  || **1st February. 2011** ||
 * **CLASS** ||  || **SS 1 E** **&** **F** ||
 * **TIME** ||  || **10:20 – 11:55** ||
 * **DURATION** ||  || **35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Quadratic Expression** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners have been treated to simple quadratic expressions**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by solving the take home assignments.**

**2)** **3X2 -4x -7** **3X2 -7x+3x -7**  **(3X2 -7x)+(3x-7)**  **X(3x-7)+1(3x-7)**  **(x+1)(3x-7)** || **__Solution__**  **x2 + 2ax + a2**  **x2 + ax+ax + a2**  **(x2 + ax)+(ax + a2)**  **x(x+a)+a(x+a)**  **(x+a)(x+a)** || **3m2 + 5mn + -2n2**  **__Solution__**  **3m2 + 5mn -2n2**  **3m2 + 6mn-mn + -2n2**  **(3m2 + 6mn)+(-mn -2n2)**  **3m(m+2n) -n(m+2n)**  **(3m-n)(m+2n)** || **a)** **X2 – 9 b) X2 - 2x**
 * **PRESENTATION** |||| **Teacher presents the days lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: Factorise the expression X2 + 2ax + a2**
 * ^  || **Step 2** || **Example 2: Factorise the quadratic expression**
 * ^  || **Step 3** || **Example 3: Factorise the expression**

**a)** **X2 – 9** **= X2 - 32**  **(x-3)(x+3)**

**b)** **X2 - 2x** **X(x-2)** || **Example 4: Factorise the Quadratic equation**  **X2 - 2x -3=0**  **First, two factors of -3X2, these are -3x and +1x**  **Next replace -2x with +x-3x**  **X2+ x -3x -3**  **(X2+ x) + (-3x -3)=0**  **Factorise**  **X(x+1) -3(x+1)=0**  **Factorising again**  **(x-3)(x+1)=0**  **(x-3)=0 or (x+1)=0**  **x-3=0 or x+1=0**  **x=3 or x=-1** || **__Class Work.__**  **Solve by Factorisation the following**  **a)** **X2 +2x +3 = 0** **b)** **3X2 -2x -1 = 0** **__Correction__**  **a)** **X2 +2x -3=0** **X2 +3x-x -3=0** **(X2 +3x)+(-x -3)=0** **X(x+3) -1(x+3)=0** **(x-1)(x+3)=0** **x-1=0 or x+3=0** **x=1 or x=-3**
 * ^  || **Step 4** || **Teacher gives another example**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**

**b)** **3X2 -2x -1=0** **3X2 -3x +x -1=0**  **(3X2 -3x) +(x -1)=0**  **3x(x-1) +1(x-1)=0**  **(3x+1)(x-1)=0**  **3x+1=0 or x-1 = 0**  **3x =-1 0r x = 1**  **X =**  **or x= 1** || **Assignment:**  **Factorise the following**  **a)** **24p2 + pq – 23q2** **b)** **4X2 – 25** **Solve using factorisation method**  **c)** **X2 +7x +12 =0** **d)** **3X2 -4x -7 = 0** || **2.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on factorisation of quadratic expression with two powers of x, and solving quadratic equations by factorisation method.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **REFRENCES** ||  || **1.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **v.** **Solve complex quadratic expression** **vi.** **Factorise a quadratic expression** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners** || **3)** **X2 +7x +12**  **4)** **3X2 -4x -7** || **3)** **X2 +7x +12** **X2 +4x+3x +12**  **(X2 +4x)+(3x +12)**  **X(x+4)+3(x+4)**  **(x+3)(x+4)**
 * **DATE** ||  || **3rd February. 2011** ||
 * **CLASS** ||  || **SS 1 D B & F** ||
 * **TIME** ||  || **8:40 – 10:00/ 1055 -11:30** ||
 * **DURATION** ||  || **40/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Quadratic Expression** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners have been treated to simple quadratic expressions**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by solving the take home assignments.**

**4)** **3X2 -4x -7** **3X2 -7x+3x -7**  **(3X2 -7x)+(3x-7)**  **X(3x-7)+1(3x-7)**  **(x+1)(3x-7)** || **__Solution__**  **x2 + 2ax + a2**  **x2 + ax+ax + a2**  **(x2 + ax)+(ax + a2)**  **x(x+a)+a(x+a)**  **(x+a)(x+a)** || **3m2 + 5mn + -2n2**  **__Solution__**  **3m2 + 5mn -2n2**  **3m2 + 6mn-mn + -2n2**  **(3m2 + 6mn)+(-mn -2n2)**  **3m(m+2n) -n(m+2n)**  **(3m-n)(m+2n)** || **c)** **X2 – 9 b) X2 - 2x**
 * **PRESENTATION** |||| **Teacher presents the days lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: Factorise the expression X2 + 2ax + a2**
 * ^  || **Step 2** || **Example 2: Factorise the quadratic expression**
 * ^  || **Step 3** || **Example 3: Factorise the expression**

**b)** **X2 – 9** **= X2 - 32**  **(x-3)(x+3)**

**d)** **X2 - 2x** **X(x-2)** || **Example 4: Factorise the Quadratic equation**  **X2 - 2x -3=0**  **First, two factors of -3X2, these are -3x and +1x**  **Next replace -2x with +x-3x**  **X2+ x -3x -3**  **(X2+ x) + (-3x -3)=0**  **Factorise**  **X(x+1) -3(x+1)=0**  **Factorising again**  **(x-3)(x+1)=0**  **(x-3)=0 or (x+1)=0**  **x-3=0 or x+1=0**  **x=3 or x=-1** || **__Class Work.__**  **Solve by Factorisation the following**  **c)** **X2 +2x +3 = 0** **d)** **3X2 -2x -1 = 0** **__Correction__**  **c)** **X2 +2x -3=0** **X2 +3x-x -3=0** **(X2 +3x)+(-x -3)=0** **X(x+3) -1(x+3)=0** **(x-1)(x+3)=0** **x-1=0 or x+3=0** **x=1 or x=-3**
 * ^  || **Step 4** || **Teacher gives another example**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**

**d)** **3X2 -2x -1=0** **3X2 -3x +x -1=0**  **(3X2 -3x) +(x -1)=0**  **3x(x-1) +1(x-1)=0**  **(3x+1)(x-1)=0**  **3x+1=0 or x-1 = 0**  **3x =-1 0r x = 1**  **X =**  **or x= 1** || **Assignment:**  **Factorise the following**  **e)** **24p2 + pq – 23q2** **f)** **4X2 – 25** **Solve using factorisation method**  **g)** **X2 +7x +12 =0** **h)** **3X2 -4x -7 = 0** || **4.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on factorisation of quadratic expression with two powers of x, and solving quadratic equations by factorisation method.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **REFRENCES** ||  || **3.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **1.** **Form quadratic equation from given roots** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners** || **1.** **X2 + 2ax + a2** **2.** **3m2 + 5mn + -2n2 and solve for roots of quadratic equations like:** **X2 - 2x -3=0** || **a)** **24p2 + pq – 23q2** **b)** **4X2 – 25** **c)** **X2 +7x +12 =0** **d)** **3X2 -4x -7 = 0**
 * **DATE** ||  || **4th February. 2011** ||
 * **CLASS** ||  || **SS 1 D B & F** ||
 * **TIME** ||  || **9:20-10:00/11:50-12:25** ||
 * **DURATION** ||  || **40/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Solving Quadratic equation by factorisation** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners know how to factorise quadratic expressions of the type below.**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by solving the take home assignments.**

**a)** **24p2 + pq – 23q2** **24p2 + 24pq -23pq– 23q2**  **(24p2 + 24pq)+( -23pq– 23q2)**  **24p(p+q) – 23q(p+q)**  **(p+q)(24p-23q)**

**b)** **4X2 – 25** **22X2 – 52 Difference of two squares**  **(2x)2 - 52**  **(2x-5)(2x+5)**

**c)** **X2 +7x +12 =0** **X2 +3x+4x +12 =0**  **(X2 +3x)+(4x +12) =0**  **X(x+3)+4(x+3)=0**  **(X+4)(x+3)=0**  **X+4=0 or x+3 =0**  **X= -4 or x = -3**

**d)** **3X2 -4x -7 = 0** **3X2 -7x +3x-7 = 0**  **(3X2 -7x) +(3x-7) = 0**  **X(3x-7)+1(3x-7) = 0**  **(X+1)(3x-7) = 0**  **X+1 = 0 or 3x – 7 = 0**  **X = -1 or 3x = 7**  **X = -1 or x =**  **X = -1 or x =2** || **__ Solution __**  ** X=1 or x=2 **  ** x-1=0 or x-2=0 **  ** (x-1)(x-2) = 0 Expand **  ** X2 -2x –x ****+2 = 0**  **X2 -3x +2 = 0 QED** || **__Solution__**  **X=-3 or x=2**  **X+3=0 or x-2=0**  **(X+3)(x-2) = 0**  **X2 -2x +3x - 6 = 0**  **X2 +x -6 = 0** || **__Solution__**  **X=-** **or x= -2**  **X+** **= 0 or x+2=0**  **(X+****(x+2) =0** **X2+2x+** **+** **= 0** **X2+2** **+** **= 0** **X2+** **+** **= 0 Multiply through by 3** **3X2+8x** **+4 = 0** || **__Class Work.__** **Find the equation whose roots are** **a)** **X = -2 or x = 1** **b)** **X = 4 or x = 3** **__Correction__** **a)** **X= -2 or x=1** **X+2=0 or x-1=0**  **(X+2)(x-1) = 0**  **X2 -x +2x --2 = 0**  **X2 +x -2 = 0**
 * **PRESENTATION** |||| **Teacher presents the days lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: Find the equation whose roots are 1 and 2**
 * ^  || **Step 2** || **Example 2: Find the equation whose roots are -3 and 2**
 * ^  || **Step 3** || **Example 3: Find the equation whose roots are -** **and -2**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**

**b)** **X = 4 or x = 3**  **X-4=0 or x-3=0**  **(X-4)(x-3) = 0**  **X2 -3x -4x +12 = 0**  **X2 -7x +12 = 0** || **Assignment:**  **F ind the equation whose roots are**  **a)** **X=**  **or -****1** **c)** **X=5 or x=-3** **d)** || **3.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on finding quadratic equations of given roots** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **REFRENCES** ||  || **2.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **4.** **Form quadratic equation from given roots** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners** || **3.** **X2 + 2ax + a2** **4.** **3m2 + 5mn + -2n2 and solve for roots of quadratic equations like:** **X2 - 2x -3=0** || **e)** **24p2 + pq – 23q2** **f)** **4X2 – 25** **g)** **X2 +7x +12 =0** **h)** **3X2 -4x -7 = 0**
 * **DATE** ||  || **7th February. 2011** ||
 * **CLASS** ||  || **SS 1 D B & F** ||
 * **TIME** ||  || **8:00-8:40/9:20-10:00/10:55-11:30/2:50-3:30** ||
 * **DURATION** ||  || **40/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Solving Quadratic equation by factorisation** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners know how to factorise quadratic expressions of the type below.**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by solving the take home assignments.**

**e)** **24p2 + pq – 23q2** **24p2 + 24pq -23pq– 23q2**  **(24p2 + 24pq)+( -23pq– 23q2)**  **24p(p+q) – 23q(p+q)**  **(p+q)(24p-23q)**

**f)** **4X2 – 25** **22X2 – 52 Difference of two squares**  **(2x)2 - 52**  **(2x-5)(2x+5)**

**g)** **X2 +7x +12 =0** **X2 +3x+4x +12 =0**  **(X2 +3x)+(4x +12) =0**  **X(x+3)+4(x+3)=0**  **(X+4)(x+3)=0**  **X+4=0 or x+3 =0**  **X= -4 or x = -3**

**h)** **3X2 -4x -7 = 0** **3X2 -7x +3x-7 = 0**  **(3X2 -7x) +(3x-7) = 0**  **X(3x-7)+1(3x-7) = 0**  **(X+1)(3x-7) = 0**  **X+1 = 0 or 3x – 7 = 0**  **X = -1 or 3x = 7**  **X = -1 or x =**  **X = -1 or x =2** || **__ Solution __**  ** X=1 or x=2 **  ** x-1=0 or x-2=0 **  ** (x-1)(x-2) = 0 Expand **  ** X2 -2x –x ****+2 = 0**  **X2 -3x +2 = 0 QED** || **__Solution__**  **X=-3 or x=2**  **X+3=0 or x-2=0**  **(X+3)(x-2) = 0**  **X2 -2x +3x - 6 = 0**  **X2 +x -6 = 0** || **__Solution__**  **X=-** **or x= -2**  **X+** **= 0 or x+2=0**  **(X+****(x+2) =0** **X2+2x+** **+** **= 0** **X2+2** **+** **= 0** **X2+** **+** **= 0 Multiply through by 3** **3X2+8x** **+4 = 0** || **__Class Work.__** **Find the equation whose roots are** **c)** **X = -2 or x = 1** **d)** **X = 4 or x = 3** **__Correction__** **e)** **X= -2 or x=1** **X+2=0 or x-1=0**  **(X+2)(x-1) = 0**  **X2 -x +2x --2 = 0**  **X2 +x -2 = 0**
 * **PRESENTATION** |||| **Teacher presents the days lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: Find the equation whose roots are 1 and 2**
 * ^  || **Step 2** || **Example 2: Find the equation whose roots are -3 and 2**
 * ^  || **Step 3** || **Example 3: Find the equation whose roots are -** **and -2**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**

**f)** **X = 4 or x = 3**  **X-4=0 or x-3=0**  **(X-4)(x-3) = 0**  **X2 -3x -4x +12 = 0**  **X2 -7x +12 = 0** || **Assignment:**  **F ind the equation whose roots are**  **b)** **X=**  **or -****1** **g)** **X=5 or x=-3** **h)** || **6.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on finding quadratic equations of given roots** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **REFRENCES** ||  || **5.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **7.** **Form quadratic equation from given roots** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners** || **5.** **X2 + 2ax + a2** **6.** **3m2 + 5mn + -2n2 and solve for roots of quadratic equations like:** **X2 - 2x -3=0** || **i)** **24p2 + pq – 23q2** **j)** **4X2 – 25** **k)** **X2 +7x +12 =0** **l)** **3X2 -4x -7 = 0**
 * **DATE** ||  || **8th February. 2011** ||
 * **CLASS** ||  || **SS 1 D B & F** ||
 * **TIME** ||  || **8:00-8:40/10:55-12:05/12:15-12:50** ||
 * **DURATION** ||  || **40/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Solving Quadratic equation by factorisation** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners know how to factorise quadratic expressions of the type below.**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by solving the take home assignments.**

**i)** **24p2 + pq – 23q2** **24p2 + 24pq -23pq– 23q2**  **(24p2 + 24pq)+( -23pq– 23q2)**  **24p(p+q) – 23q(p+q)**  **(p+q)(24p-23q)**

**j)** **4X2 – 25** **22X2 – 52 Difference of two squares**  **(2x)2 - 52**  **(2x-5)(2x+5)**

**k)** **X2 +7x +12 =0** **X2 +3x+4x +12 =0**  **(X2 +3x)+(4x +12) =0**  **X(x+3)+4(x+3)=0**  **(X+4)(x+3)=0**  **X+4=0 or x+3 =0**  **X= -4 or x = -3**

**l)** **3X2 -4x -7 = 0** **3X2 -7x +3x-7 = 0**  **(3X2 -7x) +(3x-7) = 0**  **X(3x-7)+1(3x-7) = 0**  **(X+1)(3x-7) = 0**  **X+1 = 0 or 3x – 7 = 0**  **X = -1 or 3x = 7**  **X = -1 or x =**  **X = -1 or x =2** || **__ Solution __**  ** X=1 or x=2 **  ** x-1=0 or x-2=0 **  ** (x-1)(x-2) = 0 Expand **  ** X2 -2x –x ****+2 = 0**  **X2 -3x +2 = 0 QED** || **__Solution__**  **X=-3 or x=2**  **X+3=0 or x-2=0**  **(X+3)(x-2) = 0**  **X2 -2x +3x - 6 = 0**  **X2 +x -6 = 0** || **__Solution__**  **X=-** **or x= -2**  **X+** **= 0 or x+2=0**  **(X+****(x+2) =0** **X2+2x+** **+** **= 0** **X2+2** **+** **= 0** **X2+** **+** **= 0 Multiply through by 3** **3X2+8x** **+4 = 0** || **__Class Work.__** **Find the equation whose roots are** **e)** **X = -2 or x = 1** **f)** **X = 4 or x = 3** **__Correction__** **i)** **X= -2 or x=1** **X+2=0 or x-1=0**  **(X+2)(x-1) = 0**  **X2 -x +2x --2 = 0**  **X2 +x -2 = 0**
 * **PRESENTATION** |||| **Teacher presents the days lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: Find the equation whose roots are 1 and 2**
 * ^  || **Step 2** || **Example 2: Find the equation whose roots are -3 and 2**
 * ^  || **Step 3** || **Example 3: Find the equation whose roots are -** **and -2**
 * **EVALUATION** || **Step 4** || **Teacher evaluates the learners by asking them to solve the questions below.**

**j)** **X = 4 or x = 3**  **X-4=0 or x-3=0**  **(X-4)(x-3) = 0**  **X2 -3x -4x +12 = 0**  **X2 -7x +12 = 0** || **Assignment:**  **F ind the equation whose roots are**  **c)** **X=**  **or -****1** **k)** **X=5 or x=-3** **l)** || **9.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on finding quadratic equations of given roots** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **REFRENCES** ||  || **8.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **vii.** **Tabulate values of y for a range of x values** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, graph board and graph book.** || || **x** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** || **5** || **6** || **7** ||
 * **DATE** ||  || **9th February 2011** ||
 * **CLASS** ||  || **SS 1 D** ||
 * **TIME** ||  || **10:20 – 10:55** ||
 * **DURATION** ||  || **35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Solving Quadratic Equation graphically** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners understand quadratic expression and equations and can factorise and deduce the equation from a given root.** ||
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners what is a PARABOLA?** ||
 * **PRESENTATION** |||| **Teacher presents the lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: Copy and complete the table of values of relation y=X2 -5x + 3**
 * **y** ||  || **9** ||   ||   || **-3** ||   || **-1** ||   ||   || **17** ||

**__Solution__** **y=X2 -5x + 3 When x = -2** **y = (-2)2 -5(-2)+3** **y = 4+10+3** **y = 17**

**y=X2 -5x + 3 When x = -1** **y = (-1)2 -5(-1)+3** **y = 1+5+3** **y = 9**

**y=X2 -5x + 3 When x = 0** **y = (0)2 -5(0)+3** **y = 0+0+3** **y = 3**

**y=X2 -5x + 3 When x = 1** **y = (1)2 -5(1)+3** **y = 1-5+3** **y = 1**

**y=X2 -5x + 3 When x =2** **y = (2)2 -5(2)+3** **y = 4-5+3** **y = 2**

**y=X2 -5x + 3 When x = 3** **y = (3)2 -5(3)+3** **y = 9-15+3** **y = -3**

**y=X2 -5x + 3 When x = 4** **y = (4)2 -5(4)+3** **y = 16-20+3** **y = -1**

**y=X2 -5x + 3 When x = 5** **y = (5)2 -5(5)+3** **y = 25-255+3** **y = 3**

**y=X2 -5x + 3 When x = 6** **y = (6)2 -5(6)+3** **y = 36-30+3** **y = 9**

**y=X2 -5x + 3 When x = 7** **y = (7)2 -5(7)+3** **y = 49-35+3** **y = 17** || **x** || **x** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **-2** || **-1** || **0** || **1** || **2** || **3** || **4** || **5** || **6** || **7** ||
 * **y** || **17** || **9** || **-1** || **-3** || **-3** || **-3** || **-1** || **3** || **9** || **17** ||
 * || **Step 2** || **Example 2: Copy and complete the table of values of relation y=5-2x-X2 for -4**
 * || **Step 2** || **Example 2: Copy and complete the table of values of relation y=5-2x-X2 for -4**
 * **y** ||  || **2** ||   ||   || **5** ||   ||   || **-10** ||

**__Solution__** **Eacher explores with leaners alternative method of using tables**


 * **X** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **5** || **5** || **5** || **5** || **5** || **5** || **5** || **5** || **5** ||
 * **-2x** || **8** || **6** || **4** || **2** || **0** || **-2** || **-4** || **-6** ||
 * **-x2** || **-16** || **-9** || **-4** || **-1** || **0** || **-1** || **-4** || **-9** ||
 * **y** || **-3** || **2** || **5** || **6** || **5** || **2** || **5** || **-10** ||
 * **EVALUATION** || **Step 3** || **Teacher evaluates the learners by asking them to solve the questions below.**
 * **EVALUATION** || **Step 3** || **Teacher evaluates the learners by asking them to solve the questions below.**
 * **EVALUATION** || **Step 3** || **Teacher evaluates the learners by asking them to solve the questions below.**

**__Class Work.__** **Copy and complete the table of values of relation y=2+x-X2 for -3** || **x** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** ||
 * **y** || **-10** ||  ||   || **2** ||   ||   || **-4** ||   ||

**__Correction__** **Assignment:** **1.** **Copy and complete the table of values of relation y=X2 + 6x +13 for -4** || **x** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **x** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** ||
 * **2** || **2** || **2** || **2** || **2** || **2** || **2** || **2** || **2** ||
 * **X** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** ||
 * **-x2** || **-9** || **-4** || **-1** || **0** || **-1** || **-4** || **-9** || **-16** ||
 * **y** || **-10** || **-4** || **0** || **2** || **2** || **0** || **-4** || **-10** ||
 * **CONCLUSION** ||  || **The lesson of the day is on copying and completing tables for Quadratic relations.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **y** ||  ||   ||   ||   ||   ||   ||   ||   ||

**2.** **Copy and complete the table of values of relation y=7+5x-X2 for -4** || **x**
 * **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **y** ||  ||   ||   ||   ||   ||   ||   ||   ||

**3)** **4.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **REFRENCES** ||  || **3.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**
 * **REFRENCES** ||  || **3.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **viii.** **Tabulate values of y for a range of x values** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, graph board and graph book.** || || **x** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** || **5** || **6** || **7** ||
 * **DATE** ||  || **10th February 2011** ||
 * **CLASS** ||  || **SS 1 D, B** **&** **F** ||
 * **TIME** ||  || **8:40 – 10:00/11:30-12:05** ||
 * **DURATION** ||  || **35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Solving Quadratic Equation graphically** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners understand quadratic expression and equations and can factorise and deduce the equation from a given root.** ||
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners what is a PARABOLA?** ||
 * **PRESENTATION** |||| **Teacher presents the lesson in steps with examples.** ||
 * ^  || **Step 1** || **Example 1: Copy and complete the table of values of relation y=X2 -5x + 3**
 * **y** ||  || **9** ||   ||   || **-3** ||   || **-1** ||   ||   || **17** ||

**__Solution__** **y=X2 -5x + 3 When x = -2** **y = (-2)2 -5(-2)+3** **y = 4+10+3** **y = 17**

**y=X2 -5x + 3 When x = -1** **y = (-1)2 -5(-1)+3** **y = 1+5+3** **y = 9**

**y=X2 -5x + 3 When x = 0** **y = (0)2 -5(0)+3** **y = 0+0+3** **y = 3**

**y=X2 -5x + 3 When x = 1** **y = (1)2 -5(1)+3** **y = 1-5+3** **y = 1**

**y=X2 -5x + 3 When x =2** **y = (2)2 -5(2)+3** **y = 4-5+3** **y = 2**

**y=X2 -5x + 3 When x = 3** **y = (3)2 -5(3)+3** **y = 9-15+3** **y = -3**

**y=X2 -5x + 3 When x = 4** **y = (4)2 -5(4)+3** **y = 16-20+3** **y = -1**

**y=X2 -5x + 3 When x = 5** **y = (5)2 -5(5)+3** **y = 25-255+3** **y = 3**

**y=X2 -5x + 3 When x = 6** **y = (6)2 -5(6)+3** **y = 36-30+3** **y = 9**

**y=X2 -5x + 3 When x = 7** **y = (7)2 -5(7)+3** **y = 49-35+3** **y = 17** || **x** || **x** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **-2** || **-1** || **0** || **1** || **2** || **3** || **4** || **5** || **6** || **7** ||
 * **y** || **17** || **9** || **-1** || **-3** || **-3** || **-3** || **-1** || **3** || **9** || **17** ||
 * || **Step 2** || **Example 2: Copy and complete the table of values of relation y=5-2x-X2 for -4**
 * || **Step 2** || **Example 2: Copy and complete the table of values of relation y=5-2x-X2 for -4**
 * **y** ||  || **2** ||   ||   || **5** ||   ||   || **-10** ||

**__Solution__** **Eacher explores with leaners alternative method of using tables**


 * **X** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **5** || **5** || **5** || **5** || **5** || **5** || **5** || **5** || **5** ||
 * **-2x** || **8** || **6** || **4** || **2** || **0** || **-2** || **-4** || **-6** ||
 * **-x2** || **-16** || **-9** || **-4** || **-1** || **0** || **-1** || **-4** || **-9** ||
 * **y** || **-3** || **2** || **5** || **6** || **5** || **2** || **5** || **-10** ||
 * **EVALUATION** || **Step 3** || **Teacher evaluates the learners by asking them to solve the questions below.**
 * **EVALUATION** || **Step 3** || **Teacher evaluates the learners by asking them to solve the questions below.**
 * **EVALUATION** || **Step 3** || **Teacher evaluates the learners by asking them to solve the questions below.**

**__Class Work.__** **Copy and complete the table of values of relation y=2+x-X2 for -3** || **x** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** ||
 * **y** || **-10** ||  ||   || **2** ||   ||   || **-4** ||   ||

**__Correction__** **Assignment:** **3.** **Copy and complete the table of values of relation y=X2 + 6x +13 for -4** || **x** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **x** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** ||
 * **2** || **2** || **2** || **2** || **2** || **2** || **2** || **2** || **2** ||
 * **X** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** ||
 * **-x2** || **-9** || **-4** || **-1** || **0** || **-1** || **-4** || **-9** || **-16** ||
 * **y** || **-10** || **-4** || **0** || **2** || **2** || **0** || **-4** || **-10** ||
 * **CONCLUSION** ||  || **The lesson of the day is on copying and completing tables for Quadratic relations.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **ASSIGNMENT** ||  || **Teacher gives assignments to learners to do at home.**
 * **y** ||  ||   ||   ||   ||   ||   ||   ||   ||

**4.** **Copy and complete the table of values of relation y=7+5x-X2 for -4** || **x**
 * **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * **y** ||  ||   ||   ||   ||   ||   ||   ||   ||

**4)** **6.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **REFRENCES** ||  || **5.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**
 * **REFRENCES** ||  || **5.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **1** **Plot a quadratic graph** **2** **Estimate roots of quadratic equation from the graph** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, graph board and graph book.** || **__Solution__** **Let y = X2 - 2x -3** || **X** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** || **5** ||
 * **DATE** ||  || **11th February 2011** ||
 * **CLASS** ||  || **SS 1 D, B** **&** **F** ||
 * **TIME** ||  || **10:20 – 10:55** ||
 * **DURATION** ||  || **35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Solving Quadratic Equation graphically** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners understand quadratic expression and equations and can factorise and deduce the equation from a given root.** ||
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners what is a PARABOLA?** ||
 * **PRESENTATION** |||| **Teacher presents the lesson in steps with examples.** ||
 * ^  || **Step 1** || **Solve the equation X2 - 2x -3 = 0 graphically for values of e ranging from x = -2 to 5.**
 * **X2** || **4** || **1** || **0** || **1** || **4** || **9** || **16** || **25** ||
 * **-2x** || **4** || **2** || **0** || **-2** || **-4** || **-6** || **-8** || **-10** ||
 * **-3** || **-3** || **-3** || **-3** || **-3** || **-3** || **-3** || **3-** || **-3** ||
 * **y** || **5** || **0** || **-3** || **-4** || **-3** || **0** || **5** || **12** ||

**X = 3 and x = -1** **Hence x2 - 2x -3 =0 x =3 or -1** || **Correction** **Table for 3x2 +x -7=y** || **X** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * ||  || **X2 - 2x -3 are the value of x where y = 0 on the x-axis .**
 * ||  || **X2 - 2x -3 are the value of x where y = 0 on the x-axis .**
 * **EVALUATION** || **Step 2** || **Teacher evaluates the lesson by asking learners to solve the equation 3x2 +x -7 = 0 graphically for values of e ranging from x = -3 to 3.**
 * **3x2** || **27** || **12** || **3** || **0** || **3** || **12** || **27** ||
 * **+x** || **-3** || **--2** || **-1** || **0** || **1** || **2** || **3** ||
 * **-7** || **-7** || **-7** || **-7** || **-7** || **-7** || **-7** || **-7** ||
 * **y** || **17** || **3** || **-5** || **-7** || **-3** || **7** || **2** ||

**Assignment** **1.** **Given that y=x2 + 3x – 2, copy and complete the table below** || **X** || **-5** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** ||
 * **CONCLUSION** ||  || **The lesson of the day is on plotting graph of quadratic equation.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **x2** || **25** || **16** || **9** || **4** ||  ||   ||   ||   ||
 * **+ 3x** || **-15** || **-12** || **-9** || **-6** ||  ||   ||   ||   ||
 * **– 2** || **-2** || **-2** || **-2** || **-2** ||  ||   ||   ||   ||
 * **y** || **8** || **2** || **-2** || **-4** ||  ||   ||   ||   ||

**(b) Hence draw a graph to find the roots of the equation x2-12x + 9 =0**

**2.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **REFRENCES** ||  || **1.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**
 * **REFRENCES** ||  || **1.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, the learners should be able to:** **3** **Plot a quadratic graph** **4** **Estimate roots of quadratic equation from the graph** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, graph board and graph book.** || **__Solution__** **Let y = X2 - 2x -3** || **X** || **-2** || **-1** || **0** || **1** || **2** || **3** || **4** || **5** ||
 * **DATE** ||  || **14th February 2011** ||
 * **CLASS** ||  || **SS 1 D,** **&** **G** ||
 * **TIME** ||  || **10:20 – 10:55** ||
 * **DURATION** ||  || **35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Quadratic Equation** ||
 * **SUB-TOPIC** ||  || **Solving Quadratic Equation graphically** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners understand quadratic expression and equations and can factorise and deduce the equation from a given root.** ||
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners what is a PARABOLA?** ||
 * **PRESENTATION** |||| **Teacher presents the lesson in steps with examples.** ||
 * ^  || **Step 1** || **Solve the equation X2 - 2x -3 = 0 graphically for values of e ranging from x = -2 to 5.**
 * **X2** || **4** || **1** || **0** || **1** || **4** || **9** || **16** || **25** ||
 * **-2x** || **4** || **2** || **0** || **-2** || **-4** || **-6** || **-8** || **-10** ||
 * **-3** || **-3** || **-3** || **-3** || **-3** || **-3** || **-3** || **3-** || **-3** ||
 * **y** || **5** || **0** || **-3** || **-4** || **-3** || **0** || **5** || **12** ||

**X = 3 and x = -1** **Hence x2 - 2x -3 =0 x =3 or -1** || **Correction** **Table for 3x2 +x -7=y** || **X** || **-3** || **-2** || **-1** || **0** || **1** || **2** || **3** ||
 * ||  || **X2 - 2x -3 are the value of x where y = 0 on the x-axis .**
 * ||  || **X2 - 2x -3 are the value of x where y = 0 on the x-axis .**
 * **EVALUATION** || **Step 2** || **Teacher evaluates the lesson by asking learners to solve the equation 3x2 +x -7 = 0 graphically for values of e ranging from x = -3 to 3.**
 * **3x2** || **27** || **12** || **3** || **0** || **3** || **12** || **27** ||
 * **+x** || **-3** || **--2** || **-1** || **0** || **1** || **2** || **3** ||
 * **-7** || **-7** || **-7** || **-7** || **-7** || **-7** || **-7** || **-7** ||
 * **y** || **17** || **3** || **-5** || **-7** || **-3** || **7** || **2** ||

**Assignment** **2.** **Given that y=x2 + 3x – 2, copy and complete the table below** || **X** || **-5** || **-4** || **-3** || **-2** || **-1** || **0** || **1** || **2** ||
 * **CONCLUSION** ||  || **The lesson of the day is on plotting graph of quadratic equation.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **x2** || **25** || **16** || **9** || **4** ||  ||   ||   ||   ||
 * **+ 3x** || **-15** || **-12** || **-9** || **-6** ||  ||   ||   ||   ||
 * **– 2** || **-2** || **-2** || **-2** || **-2** ||  ||   ||   ||   ||
 * **y** || **8** || **2** || **-2** || **-4** ||  ||   ||   ||   ||

**(b) Hence draw a graph to find the roots of the equation x2-12x + 9 =0**

**2.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **REFRENCES** ||  || **1.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**
 * **REFRENCES** ||  || **1.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, learners should be able to** **1.** **identify a circle and its part** **2.** **Calculate the length of arc of circles** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, Card Board diagrams of circles.** || **Answer Area of circle =** **r2** **r** || **__Solution__** **A** **Arc AB =** **2**  **O 1050** **=** **2x****x6 6cm**
 * **DATE** ||  || **18th February 2011** ||
 * **CLASS** ||  || **SS 1 D,** **&** **G** ||
 * **TIME** ||  || **8:00 – 10:00/11:30-12:05** ||
 * **DURATION** ||  || **80/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Length of Arc of circles, Perimeter of sectors and segments.** ||
 * **SUB-TOPIC** ||  || **Length of Arc of circles** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  ||  **Learners have worked with circles and can calculate the area of circle. Teacher asks learners what is the formula for calculating the area of a circle?**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners to identify circular objects in their environment.** ||
 * **PRESENTATION** |||| **Teacher presents the lesson in steps to calculate length of an arc** ||
 * ^  || **Step 1** ||  **Example.1. Calculate the length of an arc of a circle of radius 6cm which subtends at an angle of 1050. Take**  **as**

**= 11cm B** ||  **Solution** **Perimeter of Sector** **= 2r +** **2** **1080** **= 2****7 +****2**
 * ^  || **Step 2** || **Calculate the perimeter of a sector of a circle of radius 7cm, the angle of the sector being 1080 if** **.**

**= 14 + 13.2** **= 27.2cm** ||  **Solution** **Arc XY =** **2**
 * **EVALUATION** || **Step 3** || **What angle does an arc 6.6cm in length subtend at the centre of a circle of radius 14cm? Use** **as**

**6.6 =** **2** **6.6cm**

**= 270** || **Assignment** **Assignment** **Exercise 12 C page 135, New General Mathematics for SS 1.** **No. 1 a,b, & c** || **2.** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on plotting graph of quadratic equation.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **REFRENCES** ||  || **1.** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, learners should be able to** **1.** **identify a chord.** **2.** **Calculate the perimeter of segment.** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, and Card Board diagrams of segment.** ||  **Answer** **Perimeter of sector = 2r +****0****2****r** **r**
 * **DATE** ||  || **21st February 2011** ||
 * **CLASS** ||  || **SS 1 D,** **&** **G** ||
 * **TIME** ||  || **9:20-10:00/10:55-11:30** ||
 * **DURATION** ||  || **40/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Length of Arc of circles, Perimeter of sectors and segments.** ||
 * **SUB-TOPIC** ||  || **Perimeter of segments** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners have worked with circles and can calculate the area of circle. Teacher asks learners what is the formula for calculating the perimeter of a sector**

**r** || **What is a chord?** || ** Chord ** ||
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners the question.**
 * Arc**

 **__Solution__** **A** Perimeter of Segment = Chord AB + Arc AB o  Chord AB O
 * **PRESENTATION** |||| **Teacher presents the lesson in steps** ||
 * ^  || **Step 1** || **Example.1. Calculate the perimeter of the segment of a circle of radius 7cm, subtended at an angle of 900 at the centre O. Take**  **as**
 * ^  || **Step 1** || **Example.1. Calculate the perimeter of the segment of a circle of radius 7cm, subtended at an angle of 900 at the centre O. Take**  **as**

7cm 450 B

A B **D** **AB = AD + BD** **And AD = BD** **From**

**Sin** **=**

**Sin 450 =** **=** **AD =** **Thus AB = 2AD** **AB = 2 X** **By rationalisation** **AB =** **cm

Length AB = 02r

= 27

= **11**cm

Perimeter of Segment = Chord AB + Arc AB = cm + 11cm = 9.9cm +11cm = 20.9cm || Step 2 **||** Calculate the perimeter of a segment of a circle of radius 14cm, the angle of the sector being 1080 if.
 * ^  ||   || EVALUATION ||

__Solution__ A
 * Perimeter of Segment **
 * = Chord AB + Arc AB **
 *  Chord AB O o 1080 **

D AB = AD + BD And AD = BD From
 * 14cm 540 **
 * B **
 * A B **

Sin =

Sin 540 = = AD = Thus AB = 2AD AB = 2 X By rationalisation AB = cm = 9.9cm

Length AB = 02r

= 2

= 26.4cm Perimeter of Segment = Chord AB + Arc AB = 26.4cm+ 9.9cm = 36.3 cm** **__Assignment__** **Calculate the perimeter of a segment of a circle of radius 10cm, the angle subtended at the centre is 780. Take****..** || **2** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on the calculation of perimeter of a segment of a circle.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **REFRENCES** ||  || **1** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, learners should be able to** **1.** **Calculate the area of a sector.** **2.** **Calculate the area of segment.** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, and Card Board diagrams of sector and segment.** ||  **Answer** **Perimeter of sector = 2r +****0****2****r** **r**
 * **DATE** ||  || **22ND February 2011** ||
 * **CLASS** ||  || **SS 1 D,** **&** **G** ||
 * **TIME** ||  || **8:40-9:20/12:15-12:50** ||
 * **DURATION** ||  || **40 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Area of sectors and segments.** ||
 * **SUB-TOPIC** ||  || **Area of sectors and segments.** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners have worked with circles and can calculate the area of circle. Teacher asks learners what is the formula for calculating the perimeter of a sector**

**r** || **What is proportion? Why is a sector a proportion of circle?** || **__Solution__** **Area of Sector =** **0****r2** **r = 7cm and** **= 1200** **Area of sector =** **0****72** **=** **0** **= 51.33cm2** ||
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners the question.**
 * **PRESENTATION** |||| **Teacher presents the lesson in steps** ||
 * ^  || **Step 1** || **Example.1. Calculate the area of the sector of a circle of radius 7cm, subtended at an angle of 1200 at the centre O. Take**  **as**
 * ^  ||   || **EVALUATION** ||
 * Step 2** || **Calculate the Area of a segment of a circle of radius 14cm, the angle of the sector being 1080 if****.**

 **__Solution__** Area of Segment = Area of sector – Area of Trangle o 1080


 * ** Triangle ** ||

 || Sector  || = __
 * **Segment** ||

**0****r2 -- ½ r2Sin**

**Area of Segment =** **0****r2 -- ½ r2Sin** **=** **0****2** **-- ½X 142Sin1080** **= 184.8 - 93-2** **= 91.6**  **Assignment** **1.** **Calculate the Area of a Sector of a circle of radius 21cm, the angle of the sector being 720 .Take** **.** **2.** **Calculate the Area of a segment of a circle of radius 10cm, the angle subtended at the centre being 1440. Take** **.** || **2** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is on the calculation area of a segment of a circle.** ||
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **ASSIGNMENT** ||  || **Teacher gives assignment to learners to do at home.**
 * **REFRENCES** ||  || **1** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, learners should be able to** **1.** **Answer questions on the board.** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners,** ||
 * **DATE** ||  || **25th February 2011** ||
 * **CLASS** ||  || **SS 1 D,** **&** **G** ||
 * **TIME** ||  || **8:00-10:00/11:30-12:05** ||
 * **DURATION** ||  || **80/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Test.** ||
 * **SUB-TOPIC** ||  || **Test** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners have length to calculate the perimeter and areas of circles, sector and segments, given their areas and subtended angles.** ||
 * **INTRODUCTION** ||  || **Teacher prepares the learners with instructions and guides on how to take the tests.** ||
 * **PRESENTATION** ||  ||

 **Calculate the area of the sector of a circle of radius 7cm, subtended at an angle of 1200 at the centre O. Take** **as**  || **Step 2** **Teacher collects the scripts or answer sheets and gives correction to the learners.**  **__Correction__** **1.** **Area of Sector =****0****r2** **=****0** **=** **0**
 * **Teacher presents the test.** ||
 * **Step 1** || **1.**
 * || **2.** **Calculate the Area of a segment of a circle of radius 14cm, the angle of the sector being 1080 if****.**

**= 51.33cm2** **2.** **Area of Segment = Area of Sector – Area of Triangle** **=** **0****r2 -** **r2 Sin** **=** **0****x142 -** **142 Sin108 0** = 184.8 - 98X0.9511

= 184.8 - 93.20 = 91.6 cm2 || **2** **New School Mathematics for SS 1.MF Macrae et al.** ||
 * **CONCLUSION** ||  || **The lesson of the day is a test on the area of sector and segments** ||
 * **ASSIGNMENT** ||  || **Teacher gives the learners the assignment of finding out the similarities and differences between cones and cylinders.** ||
 * **REFRENCES** ||  || **1** **Multipurpose Mathematics for Secondary School, J. Olowofeso.**

**OBJECTIVES** ||  || **At the end of the lesson, learners should be able to** **1.** **Identify a cylinder** **2.** **Calculate the curved surface area of a cylinder** **3.** **Calculate the total surface area of a cylinder** || **RESOURCES** ||  || **Lesson Note, Chalk Board, Learners, Card Board diagrams of Cylinder and physical objects.** || **Answer Area of circle =** **r2** **Area of Sector =****0****r2** **Area of Segment = Area of Sector – Area of Triangle** **=** **0****r2 -** **r2 Sin** ||
 * **DATE** ||  || **28th February 2011** ||
 * **CLASS** ||  || **SS 1 D,** **&** **G** ||
 * **TIME** ||  || **9:20 – 10:00/10:55 -11:30** ||
 * **DURATION** ||  || **80/35 Minutes** ||
 * **SUBJECT** ||  || **Mathematics** ||
 * **TOPIC** ||  || **Area of Cones and Cylinders** ||
 * **SUB-TOPIC** ||  || **Area of cylinders** ||
 * **SPECIFIC**
 * **INSRTUCTIONAL**
 * **PREVIOUS KNOWLEDGE** ||  || **Learners have worked with circles and can calculate the area of circle Segments and sectors. Teacher asks learners what is the formula for calculating the area of a circle?**
 * **INTRODUCTION** ||  || **Teacher introduces the lesson by asking learners to identify Cylinders and cylindrical objects around the environment.** ||
 * **PRESENTATION** |||| **Teacher presents the lesson in steps to calculate length of an arc** ||
 * ^  || **Step 1** || <span style="height: 2160px; left: 4680px; line-height: normal; margin-bottom: 0.0001pt; margin-left: 16.5pt; margin-top: 0.05pt; position: absolute; top: 8639px; width: 1260px; z-index: -8;">  **r**

<span style="height: 9pt; line-height: normal; margin-bottom: 0.0001pt; margin-left: 304.5pt; margin-top: 12.85pt; position: absolute; width: 0.05pt; z-index: 28;"> **r** <span style="height: 9pt; line-height: normal; margin-bottom: 0.0001pt; margin-left: 304.5pt; margin-top: 14.55pt; position: absolute; width: 0pt; z-index: 27;"> **h h** || **Example 1. Calculate the Curved Surface Area of A cylinder of radius 7cm and height 20cm.** **Solution** **Curved Surface Area (CSA) = 2****rh** **= 2 X 22/7 X 7X 20** **= 880cm2** || **Total surface Area (TSA)= CSA + 2 x Area of Circle** **=** **2****rh + 2****r2** **=** **2****r(h + r)** **TSA = 2****X7(20 +7)** ** =44 (27)= __1188cm2__ || Clas work 1. Calculate the a) Curved Surface Area (CSA) b) Total Surface Area (TSA) of a cylinder of radius 21cm and height of 15cm. ( || Construct a cylinder of radius 15cm and height 20cm.Using any suitable material like a cardboard. || 2. New School Mathematics for SS 1.MF Macrae et al. ** ||
 * ^  || **Step 2** || **Teacher gives learners examples**
 * || **Step 3** || **Example 2. Calculate the Total Surface Area (TSA) of a cylinder of radius 7cm and height of 20cm.**
 * EVALUATION ||  || Teacher evaluates the learners by giving them class work to do
 * CONCLUSION ||  || The lesson of the day is on calculation of cylinders curved surface area and Total surface area. ||
 * ASSIGNMENT ||  || Teacher gives assignment to learners to do at home.
 * REFRENCES ||  || 1. Multipurpose Mathematics for Secondary School, J. Olowofeso.