**GENERAL MATHEMATICS** **SS1 FIRST TER**M

This scheme of work contains week, topic , content , teacher’s and students activities as well as instructional resources which are very vital for your lesson planning. please be guided.

**1 NUMBER BASES (I)**

i. Decimal base (Base 10) and other bases e.g. base 2(binary)

base 7 (days of the week) etc.

ii. Conversion from Base 10 to other bases, conversion from

other bases to base 10.**Teacher**:

i. Guides students to realize other bases other than binary (base2) and denary (base 10)

ii. Guides students to convert the following:

one base to the other, are numbers with decimal fraction to base 10.**Students**:

Mention other base such as 4, base 5(quandary), base 8(octal) base 16 (Hexadecimal).

Convert decimal fractions to base 10 and one base to another base.**Instructional Resources:**

Charts showing the conversion from one

base (except base 2) to another base.

2 **NUMBER BASES (II)**

i. Problem solving, addition, subtraction, multiplication and

division of number in the various bases.

ii. Conversion of decimal fraction

in one base to base 10.

iii. Apply number base system to computer programming.**Teacher:**

Guides students to perform mathematical operations of: addition, subtraction, multiplication and division.**Students**:

Perform the mathematical operations.**Instructional Resources:**

As in week one above.

3 **. MODULAR ARITHMETIC**

i. Revision of addition, division, multiplication and subtraction of integers.

ii. Concept of modular arithmetic

iii. Addition, subtraction and**Teacher**:

Guides students to revise the mathematical

operations of integers

-to define modular arithmetic and uses

activities to develop the concept. To add, subtract, divide and multiply inmultiplication operations in modular arithmetic.

iv. Application to real life

situations.

modular arithmetic.

**Teacher** :To appreciate its application to shift duty,

menstrual chart, name of market days.**Students**:

-Define modular arithmetic

-Perform the mathematical operations in modular arithmetic

-Appreciate the concept of modular arithmetic and apply in daily life.**Instructional Resources:**

Modular arithmetic charts, samples of shift

duty chart, menstrual chart.

4 **INDICES**

i. Laws of indices and their applications e.g.

a. ax x ay = ax+y

b. ax /ay = ax-y

c. (ax)y = axy

ii. Application of indices, simple indicial/exponential equations.**Teacher**:

Guides students to represent numbers in indices and gives examples.

Explains laws of indices with examples, drill students on problem solving.**Students**:

-Study the laws of indices and solve related problems.

-Study the steps in indicial equation and solve exercises.**5 STANDARD FORM (AX10n)**

i. Writing numbers in index form

ii. Adding two numbers and writing the results in standard

form.

iii. Subtracting one number from the other in standard form.

iv. Multiplying numbers in standard form

v. Dividing numbers in standard form including square root of

such numbers.**Teacher**:

Guides students to convert numbers to standard form with emphasis on the values of ‘A’ and ‘n’.**Students**:

-Convert numbers to standard form

-Convert long hand to short hand notation. (i.e. ordinary form to standard form and standard form to ordinary form)**Instructional Resources:**

Charts of standard form and indices.**6. LOGARITHMS (I)**

i. Deducing logarithm from

indices and standard form i.e. if**Teacher**:

Guides students to learn logarithm as inverse

of indices with examples.y=10x, then x=logy10

ii. Definition of logarithm e.g. log101000=3

iii. Graph of y=10x using x=0.1, 0.2,………..

-Define logarithm and find the various values of expressions like logaN

plot the graph of y=10x and read the required values.

-to find logarithm of a number (characteristics, mantissa, differences and locate decimal points) and the antilogarithm.**Students**:

Deduce the relationship between indices and

logarithms.

Define logarithm and find the various values of expressions like logaN numbers plot the graph of y=10x

Find the logarithm and antilogarithm of numbers greater than 1.**Instructional Resources:**

Indices/logarithms chart, definition chart of logarithm, graph board with graph of y=10x, graph book etc.**7. LOGARITHM (II)**

Calculations involving multiplication and division.**Teacher**:

Guides students to read logarithm and antilogarithm table in calculation involving multiplication and division.**Students**:

Read the tables and solve problems involving multiplication and division.**Instructional Resources:**

Logarithm table chart and Antilogarithm table chart made of flex banner logarithm table booklet.**8 LOGARITHM (III)**

i. Calculations involving power and roots using the logarithm

tables.

ii. Solving practical problems using logarithm tables relating to capital market.

iii. Explain the concept of capital**Teacher**:

-Guides students to read logarithm and antilogarithm tables in calculations involving powers and roots.

-Explain meaning of capital market.

-Solve related problems and other real life problems. market operation

iv. Use logarithm tables in multiplying the large numbers

involved in capital market operation.

**Students**

Read the tables and solve problems involving multiplication and division, and solve problems related to real life problems.**Instructional Resources:**

Logarithm tables chart, logarithm table booklet etc.**9 DEFINITION OF SETS**

i. Set notation – listing or roster method, rule method, set builder notation

ii. Types of sets: e.g. universal set, empty set, finite set and

infinite set, subset, disjoint set, power set etc.**Teacher**:

Guides students to:

-define set

-define types of sets

-write down set notations

-use the objects in the classroom, around the school and within home to illustrate sets.**Students**:

Define set, use set notations

Identify types of sets.**Instructional Resources:**

Objects in the classroom, sets of students,

set of chairs, mathematical sets, other

instrument etc.**10 SET OPERATIONS**

i. Union of sets and intersection of sets complement of sets.

ii. Venn diagram

iii. Venn diagram and application up to 3 set, problems**Teacher**:

Guides students to explain and carry out set operations:

-explains Venn diagram, draws, interprets and uses diagram.

-applies Venn diagram to real life problems.**Students**:

Carry out set operations, draw, interpret and use Venn diagrams.**Instructional Resources:**

As in week nine above.**11 SIMPLE EQUATIONS**

i. Change of subject of formulae

ii. Formula involving brackets, roots and powers.

iii. Subject of formula and substitution.**Teacher**:

Guides students in the process involved in changing the subject in a formula and carries out substitution.**Students**:

Follow the process involved in changing subject in a formula and substitute in the formula.**Instructional Resources:**

Charts displaying processes involved in change of subject in a formula.

Charts displaying the various types.**12 SIMPLE EQUATION AND VARIATIONS**

i. Revision of simultaneous linear equation in two (2)

unknown

ii. Types and application of variations.**Teacher**:

Revises solution of simultaneous equations in two unknowns.

Treats each type of variation with examples and solve problems in variation.**Students**:

Solve problems involving all types of variations.**Instructional Resources**

As in week 11 above.

13 **Revision/Examinations ****14 Examinations**

**GENERAL MATHEMATICS SS ONE SECOND TERM****WEEK TOPIC / CONTENT ACTIVITIES****1 FACTORISATION OF QUADRATIC EXPRESSION OF THE FORM ax2**+bx+c where a, b, c are constants

i. Factorising quadratic expression of the form ax2+bx+c

ii. Factorising quadratic expression of the form ax2-bx+c

iii. Factorising quadratic expressions of the form ax2+bx-c

iv. Factorising quadratic expressions of the form ax2-bx-c

v. Solving quadratic equation of the form ax2+bx+c = 0 using**Teacher**:

i. Illustrates the factorization of quadratic expressions using:

(a) Grouping (b). factor methods

ii. Teacher leads students to factorize quadratic expressions written in the different forms.**Students**:

-Factorize quadratic expressions using the methods.

-Factorize the different forms given.**Instructional Resources:**

Quadratic expressions and factors chart.

Sharing at least six expressions each of the factorization method. form ax2+bx+c, ax2-bx+c, ax2+bx-c and ax2bx-c (could be in flex banners).**2 APPROXIMATION**

i. Rounding up and rounding down of numbers to significant

figures, decimal places and nearest whole numbers.

ii. Application of approximation to everyday life

iii. Percentage error.**Teacher**:

Gives students two roots and leads them to form a quadratic equation.**Students**:

Use the roots given to construct quadratic equation.**Instructional Resources:**

Given values, in integer and fractions

incomplete table showing various numbers and approximation to various significant figures, decimal places etc. to be completed in class as illustration**3 QUADRATIC EQUATIONS(III)**

i. Plotting graph in which one is quadratic function and one is a linear function.

ii. Using an already plotted curve to find the solution of the various equations.

iii. Finding the gradient of a curve, the maximum value of y,

and minimum value of y and the corresponding values of x.

iv. Solving a comprehensive quadratic and linear equation

graphically.

v. Word problem leading to quadratic equations.**Teacher**: Leads students to construct tables of values, drawsthe x and y axis, chooses scale, graduates the axis and plot the points. Identifies the maximum and minimum

values.**Students**:Follow the teacher lead in plotting the graph, Follow the teacher leads and read the

roots . Also read the minimum and maximum values.**Instructional Resources:**

Graph boards, graph books are mandatory.**4 LOGICAL REASONING (I)**

i. Meaning of simple statement –open and close statements, true or false.

ii. Negation of simple statements

iii. Compound statements –conjunctions, disconjunctions,**Teacher**:

a. Uses examples to explain simple statements.

b. State the true value of a statement

c. States simple statements and writes not or “it is not true that” a negation of simple statements implication, bi-implication with examples.

d. Guides students to write examples of compound statements and distinguishes them from simple statements.

Students:

i. Gives examples of the non examples of simple statements writes the true value of a given statements.

ii. Negates some simple statement using ‘not’ or ‘it is not true that’.

iii. Write examples of compound statements.

Instructional Resources:

Charts showing examples of simple statement, true and false statements, negation of statements.**5 LOGICAL REASONING (II)**

i. Logical operations and symbols

– Truth value table – compound statement, Negation (NA),

conditional statement, bin-conditional statement.**Teacher**:

Leads students to list the five logical operations and their symbols.

-Leads students to construct truth value for

each operation.

Students:

List the five logical operations with symbols

and construct truth value chart for each.

Instructional Resources:

Truth table chart etc.

6 .**MENSURATION OF SOLID SHAPES (I)**

i. Length of arc of a circle with practical demonstration, using

formula

ii. Revision of plane shapes –perimeter of sector and segment

iii. Area of sector and segment.

Teacher:

Guides students to find the length of arcs of circle using cut card board practically, deduces the formula and apply it in solving problems.

-cuts out sectors and segment, solve exercises.

-guides students to cut a circle into sectors and measure the angles.

-cut out triangle from a sector.

Students:Practice the practical demonstration.

Participate in deducing the formula and applyit to solve problems carry out teacher

activities.

Follow the teacher instruction to carry out the

activities.

Instructional Resources:

Cardboard paper, rope, string, scissors,

drawings on cardboard showing various arcs

(minor and major arcs in a circle).

7 __MENSURATION OF SOLIDSHAPES (II)__

i. Relationship between the sector of a circle and the surface area of a cone.

ii. Surface area of solids – cube, cuboids, cylinder, cone, prism,

pyramids.

Teacher:

-Guides students to cut out a sector and folding sector into a cone.

-Leads students to determine the relationship between the sector of a circle and the surface area of a cone.

-Revise the areas of the plane shapes that formed the listed solids and lead students to find their surface areas.

Students:

-Follow the teacher in carrying out the activities and observe the relationships

-Participate in the revision of the areas of the solids.**Instructional Resources:**

Cut out papers, (sectors and segments) etc.

8 __MENSURATION OF SOLID SHAPES (III)__

i. Volume of solids – cube, cuboids, cylinder, cone, prism,

pyramids, frustum of cone and pyramids.

ii. Surface area and volume of compound shapes.

Teacher:

-Revise the area of the listed solids and lead students to find their volumes, show model of fraction of cones pyramids and solve problems.

-Lead students to solve problems on surface area and volume of compound shapes.

Students: Participate in the revision of the areas and volume of the solids.

-Solve problems on compound shapes.**Instructional Resources:**Shapes of cube, cuboids, cylinder, cone, prism, pyramids, lampshade and buckets asfrustum as cone etc.

9 ** CONSTRUCTION** (I)

i. Lines, line segments, bisection of a line segment e.g. horizontal,

vertical, inclined lines etc.

ii. Construction and bisection of angles e.g. 180°, 90°, 45°, 22° 60o, 30°, 150°, 75°, 135o, 105°, 165°etc.

iii. Construction of triangles

iv. Construction of quadrilaterals.

Teacher: -Lists out steps for drawing a line segment and how to bisect line segment.

-Leads students to construct special angles with the steps involved in bisection of angles.

Inspect them.

Students: List out triangle, draw a line and bisect, construct the given angles and bisect them.

Instructional Resources

Whiteboard, mathematical set, students

mathematical set. Teacher’s construction

instruments mandatory.

10 LOCUS OF MOVING POINTS

i. Equidistant from 2 intersecting

straight lines

ii. Equidistant from 2 points

iii. Equidistant from a fixed pointetc.

iv. Construction of locus

equidistant from a given straight

line.

Teacher:

Guides students to list and explain the steps

involved in constructing locus of moving

points equidistance from:

i. Two intersecting straight lines

ii. Two given points

iii. One point

iv. A given straight line on the

chalkboard using chalkboard

mathematical set .

Inspects students constructing.

Students:

-Attempts to list and explain the steps

involved, write down the steps listed and

explained by the teacher and ask questions.Students: Follow teacher’s demonstration on the

chalkboard by carrying out similar activities in

their exercise book with their mathematical

sets.Participate in the teacher’s re-

demonstration and take special notes of the

salient steps.

Instructional materials: As shown in week 9Revision/Examinations Revision/Examinations

12 Examinations Examinations

**GENERAL MATHEMATICS SS1 THIRD TERM**

**WEEK TOPIC / CONTENT ACTIVITIES**__)__

**1 DEDUCTIVE PROOFS (I**i. Types and properties of triangles

ii. Proofs of sum of angles in a

triangle is 180o

, the exterior angles

is equal to the sum of its two interior

opposite angles.

Teacher:

carrying out proofs in geometry, by

explaining the concepts of: given, required

to prove, construction, proof, conclusion.

Guides the students to prove the two

theorems on the board with necessary

diagrams.

Assists students to carryout practical

demonstrations, and to solve examples and

give students some task to solve and inspect

them.

Students:

Participate in discussing the format for

proving geometrical theorem, take special

note of the format, then write them down and

ask questions.

-Solve the task given.

Instructional Resources:

Cardboard paper, cutout of triangles,

protractor to verify and establish the truth

about the theorem.

2

**DEDUCTIVE PROOFS (II)**i. Similar and congruent triangles

ii. Isosceles and equilateral

triangles.

Teacher:

Demonstrates on the chalkboard how to

prove the followings:

Angles of parallel lines, angles in a polygon,

congruent triangles, properties of

parallelogram, deductive reasoning and

axioms using relevant models of plane

shapes.

Students:

Participate in the teacher’s demonstrations

by contributing in making some deductions

and write down essential points agreed upon,

on angles of a polygon, congruent triangles.

etc.

Instructional Resources:

Parallel lines, congruent triangles, polygons,

cut out paper, protractors.

3 __DEDUCTIVE PROOFS (III)__

i. Properties of parallelogram and

related quadrilaterals.

ii. Intercept theorem

iii. Parallelogram of the same

base and between the same

parallel lines are equal in area.

Teacher:

properties of the riders using paper cutouts,

protractors, models of parallelogram,

polygon, congruent triangle etc.

Guides students to solve problems and help

them to reproduce arguments based on the

reasons (theorem or axioms).

Students:

Carry out practical demonstration of the

properties of the rides along with the teacher

using paper cutouts, construct models of

plane shapes. Apply deductive reasoning to

solve the given practical problems.

Instructional Resources:

As in week 2

4

__POLYGON – TYPES__i. Sum of interior angles of any n-

sided polygon.

ii. Sum of exterior angles of any

polygon

iii. Problem solving on polygon.

Teacher:

As in week 2 and 3 above.

Students:

As in week 2 and 3 above

Instructional Resources:

As in week 2 and 3 above.

5

__TRIGONOMETRY (I)__i. Basic trigonometric ratios, sine,

cosine and tangent with respect

to right-angled triangles.

ii. Trigonometric ratio of special

angles 30o, 45o, 60o.

iii. Deriving trigonometric ratios of

Teacher:

Shows students a chart of right angled-

triangle with a clearly marked angle.

Guides students to identify ratios forming

sine, cosine and tangent of the marked

angles. (verify the position of the marked

angles) 30o, 45o, 60o.

– Lead students to construct right angled-

triangles of 30o, 45o, 60o.

Guides students to use the above shapesto derive trigonometric ratios of 30o, 45o, 60o.

Students:

Study the chart; identify ratios forming cosine

and tangent of marked angle on the chart.

Draw right-angled triangles and use it to

solve problem involving calculation of

lengths, construct right-angled triangles of30o, 45o

and 60o.

Derive trigonometric ratios of 30o, 45o and

60o

under teacher’s supervision.

Instructional Resources:

Charts showing trigonometric ratios of a right

angled triangle, pencil and ruler, protractor,

cutout shapes of right angled triangles

showing angles 45o, 30oand 60o

respectively.

6

__TRIGONOMETRY (II)__i. Solving problems involving use

of sine, cosine and tangent at

right-angled triangles.

ii. Application of trigonometric

ratios of 45o

, 30o

and 60o

to

solving problem without the use

of calculating aids.

Teacher:

i. Guides students to use sine, cosine and

tangents to solve problems involving

calculation of length, angles, angles of

elevation and depression etc.

ii. Leads students to draw right-angled

triangle of side 1 unit on the equal sides.

iii. Guides students on how to derive

trigonometric of ratio.

iv. Leads students to measure the two other

angles in the right angled triangle.

v. Lead students to obtain sine and cosines

of various angles using measured lengths.

Students:

Solve problems on practical application of

trigonometric ratios under guidance of

teacher.

Obtain sine and cosine of various angles.

Identify the relationship between the

trigonometric ratios and the measured 30o, 45o, 60o

– Lead students to construct right angled- triangles of 30o, 45o, 60o.

Guides students to use the above shapesto derive trigonometric ratios of 30o

, 45o, 60o.

Students:

Study the chart; identify ratios forming cosine

and tangent of marked angle on the chart.

Draw right-angled triangles and use it to

solve problem involving calculation of

lengths, construct right-angled triangles of

30o, 45oand 60o.

Derive trigonometric ratios of 30o,

, 45oand 60o

under teacher’s supervision.

Instructional Resources:

Charts showing trigonometric ratios of a right

angled triangle, pencil and ruler, protractor,

cutout shapes of right angled triangles

showing angles 45o, 30o and 60o

respectively.

6 TRIGONOMETRY (II)

i. Solving problems involving use

of sine, cosine and tangent at

right-angled triangles.

ii. Application of trigonometric

ratios of 45o, 30o and 60o to

solving problem without the use

of calculating aids.

Teacher:

i. Guides students to use sine, cosine and

tangents to solve problems involving

calculation of length, angles, angles of

elevation and depression etc.

ii. Leads students to draw right-angled

triangle of side 1 unit on the equal sides.

iii. Guides students on how to derive

trigonometric of ratio.

iv. Leads students to measure the two other

angles in the right angled triangle.

v. Lead students to obtain sine and cosines

of various angles using measured lengths.

Students:

Solve problems on practical application of

trigonometric ratios under guidance of

teacher.

Obtain sine and cosine of various angles.

Identify the relationship between the

trigonometric ratios and the measured values.

Instructional Resources:

Chart showing unit circle etc.

7 __TRIGONOMETRY (III)__

Trigonometric ratios related to

the unit circle

i. Draw graphs of sine from 0o≤ ө ≤ 360o

ii. Draw graphs of cosine from 0o ≤ ө ≤ 360o

Teacher:

Guides them to see the relationship between

calculated sine and cosine of trigonometric

ratios and the angles measured with

protractor in the unit circles.

Constructs table of values for 0o

≤ ө ≤ 360o

fie both sine and cosine, plots the points on

the graph board and draw the graphs.

Guides them on the activities to obtain

accurate values.

Leads them to obtain solution from graph

drawn.

Students:

Participates in the construction of table of

value for y and plotting of the points and

drawing of the graph.

Instructional Resources:

Graph board, graph book, pencils, and

mathematical sets. Mandatory.

8 STATISTICS

i. Revision on collection,

tabulation and presentation of

data.

ii. Construction of frequency

tables

iii. Bar charts and histogram

differentiate between bar chat

and histogram.

Teacher:

Guides students to:

-information on their age, number of children

in the families and other areas of life.

-tabulates data collected

-lists various forms of presentation of data

e.g. bar chart, pie chart.

-leads students to construct table from given

data; draw bar chart and histogram.

Students:

Submit objects like corks brought to class.

Tabulate into specific categories, list various

of presentation of dates, table from given

data.

Draw bar chart and histogram.

Instructional Resources:

Ages of students recorded on cardboard,

prices of goods, objects of different kinds.

Corks of soft drinks, posters containing real

life data.

Graph board, graph book.

9 __STATISTICS (II)__

i. Calculating the sectoral

component of pie chart.

ii. Drawing pie chart correctly.

iii. Interpreting the pie chart and

bar chart.

Teacher:

Leads students to calculate the angular

equivalent of the different frequency in a

given distribution using the idea of ratio and

proportion.

Guides students to draw pie chart using their

compass, and protractor.

Interpret the pie chart in terms of sectoral

angles.

Students:

Calculate sectoral angles, draw pie charts,

correctly to interpret data using the pie chart.

Instructional Resources:

Graph board, graph papers, a pair of

compass and protractor etc.

10 **STATISTICS (III) GROUPED DATA**

i. Drawing histogram

ii. Estimation of mode from

histogram.

Teacher:

Guides students to use frequency table to

draw histogram.

Leads students to construct table from given

data, construct group frequency table.

Guides students to use class boundaries to

draw histogram and how to read or estimate

mode from the histogram.

Students:

Participate in the activities with the teacher,

perform the instructions given by the teacher.

Draw histogram and estimate mode from the

histogram.

Construct frequency table of a grouped data.

Instructional Resources:

Graph board, graph papers etc.

11 **STATISTICS (III)**

Construction of frequency

polygon of a given distribution.

Teacher:

Guide the students to construct frequency

polygon of a given distribution.

Students:

Construct frequency polygon from a grouped

data.

Instructional Resources:

Graph board, graph papers etc.

12 **Revision Revision****13 Examinations Examinations**

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