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GENERAL MATHEMATICS

FIRST TERM SS TWO


WEEK

TOPIC / CONTENT

ACTIVITIES

1

LOGARITHMS

i. Revision of logarithm of numbers greater than one.

ii. Characteristics of logarithm of numbers greater than one and less than one and standard form of numbers.

iii. Logarithm of numbers less than one, multiplication, division, power and roots.

iv. Solution of simple logarithmic equations

v. Accuracy of results of logarithm table and calculator.



Teacher:

Guides students to:-

-Revises laws of logarithm

-Reads logarithm table and does calculation involving multiplication, division, power and roots of numbers greater than 1.

-Shows the relationship between the characteristics of logarithms and standard form of numbers.

-Calculation involving multiplication, roots of number less than 1 and less than 1.



Students:

Study the solution chart of logarithm.

State laws of logarithm, read logarithm table and use logarithm table in calculation involving multiplication, division powers and roots of numbers greater than 1.

Given a set of number, write them in standard forms and compare the characteristics of such numbers with the standard forms.

Solve simple equations involving logarithms.

Instructional Resources:

Logarithm table, booklet, solution chart of logarithm etc flex banner showing logarithms and antilogarithm of numbers).




2

APPROXIMATION

i. Rounding up and down of numbers to significant figures, decimal places and nearest whole numbers.

ii. Application of approximation to everyday life.

iii. Percentage error.



Teacher:

Guides the students to

-approximate given data to hundred, thousand, billion and trillions.

-solution using logarithm tables and calculator

-make comparison between results obtained from solution with logarithm table and calculator.

-calculate percentage error.

-solve examples of approximation in schools, health sector and social environment etc.

Students:

Approximate to hundred, thousand, million, billion and trillion.

Solve problems in approximation solve problems using logarithm table and calculators.

-compare the result obtained from the two calculations. Calculate percentage error of a given instrument.



Instructional Resources:

Financial reports and budget population figures logarithm table, calculators data from school records, health sector, economy etc.




3

ALGEBRAIC FRACTIONS (I)

i. Simplification of fractions

ii. Addition, subtraction, multiplication and division of algebraic fractions.


Teacher:

Guides students to:

-determining the L.C.M. of the denominators of the fraction and simplify the fractions.

-perform addition, subtraction, division and multiplication on the fractions.



Students:

Simplify a given algebraic fraction using the LCM

Perform addition, subtraction, division and multiplication on algebraic fractions.

Instructional Resources:

Chart showing LCM, addition, subtraction, multiplication and division etc.




4

ALGEBRAIC FRACTIONS (II)

i. Equation involving fractions

ii. Substitution in fractions

iii. Simultaneous equations involving fractions.

iv. Finding the value of unknown to make a fraction undefined.


Teacher:

Guides students to:

-solve equation involving fraction

-substitute for a given value in a fraction.

-solve simultaneous equation involving fractions

-guides students to determine undefined value of a fractions.



Students:

Follow the procedures for solving equations involving fraction.

Perform substitution in a given fraction.

Solve simultaneous equation, involving fraction.

Determine undefined value of a fraction.

Instructional Resources:

Oranges, apple, rule, sticks etc.



5

SEQUENCE AND SERIES 1 Arithmetic Progression (AP)

i. Meaning of sequences indicating first term (a) common difference (d) and the nth term of an Arithmetic Progression (A.P) and calculating the nth term of an A.P.

ii. Arithmetic mean and sum of an A.P.

iii. Practical problem solving involving real life situation on arithmetic mean of an A.P.

iv. Practical problem solving involving real life situation on sum of A.P.`


Teacher:

Guides students to:

-discover the meaning and types of sequences.

-identify examples of Arithmetic Progression (A.P.)

-derive the formula for the nth term of an A.P.

-define and use the formula for the sum of an A.P.

Gives exercises on A.P.

Students:

State the rule that gives a sequence.

Define and give an arithmetic progression.

Participate in deriving the formula for the nth term.

Calculate the nth term and sum of an A.P.

Solve problems on arithmetic progression.



Instructional Resources:

Ages of students, poles and pillars of different height, other objects of different sizes, numbers, etc.




6

SEQUENCE AND SERIES (II) Geometrical Progression (G.P)

i. Meaning of Geometry Progression (G.P.) indicating first term (a), common ratio (r) and nth term of a G.P and calculation of nth term of G.P.

ii. Geometric mean and sum of terms of G.P.

iii. Sum of infinity of G.P.

iv. Practical problem involving real life situation on G.P.


Teacher:

Guides students to:



-define and give examples of geometric progression.

-leads students to derive and use the formula for the nth term of a G.P, calculate the sum of G.P.



Students:
Define and give examples of geometric progression, participate in deriving the formula for the nth term.

Calculate the sum of G.P when n>1and n<1

Solve problems on geometric progression, including practical problems.

Instructional Resources:

As in week 5 above.




7

QUADRATIC EQUATION (I)

i. Revision of factorization

ii. Finding what should be added to an algebraic expression to make it a perfect square.

iii. Quadratic equation using completing the square method.

iv. Deducing the quadratic formula from completing the square and its application to solving problems.


Teacher:

Revise factorization of perfect squares i.e. x2+2ax+a2 as (x+a)(x+a)

Leads students to realize that all perfect squares are factorizeable.

Guides students in the steps involved in solving quadratic equation using completing the square method.

Leads students’ to deduce the completing the square method and solve some problems.

Students:

Expands and factorize perfect squares such as (x+3)2.

Use quadratic box to expand quadratic equations.

Follow the teacher’s examples to find constant k that makes quadratic expression a perfect square.

Participate in solving quadratic equations by completing the square.

Deduce quadratic formula from the method of completing squares.



Instructional Resources:

Quadratic equation box, completing the squares sheet..




8

QUADRATIC EQUATION (II)

1. Word problem leading to quadratic equation

2. Application of quadratic equation to real life situation.


Teacher:

Guide students in steps involved in the formation of quadratic equation using sum and product of roots.

Transforms a word problem into quadratic equation.

Obtains quadratic equation given roots of the equation using sum and product of the given roots.

Transform a word problem into quadratic equation.

Solve students’ activities; quadratic equation formed from word problem. Attempt the exercises given with the roots supplied.



Instructional Resources:

As in week 7 above.




9

SIMULTANEOUS LINEAR AND QUADRATIC EQUATION (I)

i. Revision of simultaneous linear equations

ii. Simultaneous linear and quadratic equation by elimination method.

iii. Simultaneous linear and quadratic equations by substitution method.

iv. Graphical method

v. Word problem leading to simultaneous linear and quadratic equation.



Teacher:

Guides students to solve simultaneous linear equations using elimination, substitution, graphical methods.

-Solves linear and quadratic equation using substitution method, to construct tables of values of y given the values of x.

-finds the solution of other related equation.



Students:

Solve problem in simultaneous linear equation using elimination, substitution and graphical method.

Solve simultaneous linear and quadratic equation.

Construct tables of value.



Instructional Resources:
Graph, chart showing how to find roots of graph y=ax2+bx+c.

Graph board, graph book, mathematical sets.




10

SIMULTANEOUS LINEAR AND QUADRATIC EQUATION (II)

1. Revision of linear and quadratic graph

2. Simultaneous linear and quadratic equations by graphical method.


Teacher:

As in week 9 above



Students:

As in week 9 above



Instructional Resources:

As in week 9 above.



11

GRADIENT OF A CURVE

1. Revision of a straight line graph

2. Gradient of a straight line.

3. Drawing tangent to curve

4. Determination of gradient of a curve.


Teacher:

Identifies x- intercept and y- intercept of linear graph.

Draw the graph

Guides students to:

- discover the meaning of gradient of a line

- find the gradient of a straight line.

- form straight line equation

-draw tangents to a curve at a given point.



Students:

Draw a straight graph of a given function, determine the gradient, determine gradient of a straight line give -2points on the line

– A point and the gradient of the line.

-draw tangents to a curve at a given point.



Instructional Resources:

Graph board, graph book, ruler. (Mandatory)




12

Revisions

Revisions

13

Examinations

Examinations

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