Mathematics lesson note for JSS2 First Term is now available for free. The State and Federal Ministry of Education has recommended unified lesson notes for all secondary schools in Nigeria, in other words, all private secondary schools in Nigeria must operate with the same lesson notes based on the scheme of work for Mathematics.
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For prospective school owners, teachers, and assistant teachers, Mathematics lesson note is defined as a guideline that defines the contents and structure of Mathematics as a subject offered at SS level. The lesson note for Mathematics for SS stage maps out in clear terms, how the topics and subtopics for a particular subject, group works and practical, discussions and assessment strategies, tests, and homework ought to be structured in order to fit in perfectly, the approved academic activities for the session.
To further emphasize the importance of this document, the curriculum for Mathematics spells out the complete guide on all academic subjects in theory and practical. It is used to ensure that the learning purposes, aims, and objectives of the subject meant for that class are successfully achieved.
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The JSS2 Mathematics lesson note provided here is in line with the current scheme of work hence, would go a long way in not just helping the teachers in carefully breaking down the subject, topics, and subtopics but also, devising more practical ways of achieving the aim and objective of the subject.
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This post is quite a lengthy one as it provides in full detail, the Mathematics-approved lesson note for all topics and sub-topics in Mathematics as a subject offered in JSS2.
Please note that Mathematics lesson note for JSS2 provided here for First Term is approved by the Ministry of Education based on the scheme of work.
I made it free for tutors, parents, guardians, and students who want to read ahead of what is being taught in class.
JSS2 Mathematics Lesson Note (First Term) 2024
MATHEMATICS
SCHEME OF WORKS FOR FIRST TERM
WEEK 1 REVISION OF JSS 1 EXAMINATION QUESTION
WEEK 2 WHOLE NUMBER AND DECIMALS NUMBERS
WEEK 3 H C F AND L C M , SQUARE AND SQUARE ROOT
WEEK 4 FRACTIONS
WEEK 5 HOUSEHOLD ARITHMETIC
WEEK 6 APPROXIMATION OF NUMBER
WEEK 7 REVIEWS OF HALF LESSON AND PERIODIC TEST
WEEK 8 MULTIPLICATION AND DIVISION OF DIRECTED NUMBERS
WEEK 9 ALGEBRAIC EXPRESSION
WEEK 10 ALGEBRAIC FRACTION
WEEK11 REVISION AND EXAMINATION
WEEK 1 & 2 WHOLE NUMBER AND DECIMALS NUMBERS
COMMON MULTIPLES AND FACTOR
Factors: The factor of a number is the whole number that divides the number exactly. For example the factors of 18 may be found as follows;
18 = 1 x 18
= 2 x 9
= 3 x 6
Multiples: A multiple of a number is obtained by multiplying it by any whole number. Example the multiple of 4 are 4, 8, 12, 16, 20 , 24 etc.
A prime number is a number that can only divide itself. It has only two factor which is 1 and itself. Examples of prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19 etc.
Example: (a) find all the factors of 18
(b) State which of these factors are even
( c) state which of these factors are prime numbers
(d) Write the first three multiple of 18
Solution
- Factors of 18 are 1, 2, 3, 6, 9, and 18
- The even numbers are 2, 6, and 18
- The prime numbers are 2 and 3
Example 1: Find the factor of 56
Solution:
1 × 56
2 × 28
4 × 14
7 × 8
Therefore 56 = 1, 2, 4, 7, 8, 14, 28, and 56.
Product of Prime Factors.
Example 2: Express 56 and 108 as the product of prime factors in index notation.
Solution:
56 = 2 × 2 × 2 × 7 = 23 x 7
108 = 2 × 2 × 3 × 3 × 3 = 22 x 33
Note that the numbers must be a prime numbers
ASSIGNMENT
EXERCISE 1.1; NO 3, 5 & 9. PAGE 2
EXERCISE 1.2; NO 8, 9 & 12. PAGE 3
WEEK 3 HIGHEST COMMON FACTOR AND LOWEST COMMON FACTOR
EXAMPLE 1: Find the L C M of 18 and 24
Solution:
METHOD 1 METHOD 2
2 18 24 18 = 2 ×3 ×3
2 9 12 24 = 2 ×2 ×2 ×3
2 9 6 L C M = 2 ×2 ×2 ×3 ×3
3 9 3 = 72
3 3 1
1 1
L C M = 2 × 2 × 2 × 3 × 3 = 72
Example 2: Find the L C M of 72 and 90
Solution:
METHOD 1 METHOD 2
2 72 90 72 = 2 X 2X 2 X 3 X 3
2 36 45 90 = 2X 3 X3 X 5
2 18 45 L C M = 2 X 2 X 2 X 3 X 3 X 5
3 9 45 = 360
3 3 15
5 1 5
1 1
2 x 2 x 2 x3 x 3 x 5 = 360
Example 3: Find the H C F of 72 and 96
Solution: find the prime product of the number and pick the common ones
72 = 2 * 2 * 2 * 3 * 3
96 = 2 * 2 * 2 * 2 * 2 * 3
H C F = 2 * 2 * 2 * 3
= 24
SQUARE AND SQUARE ROOT
“Square” is the product of two equal terms example N * N = N²
Example 1: Find the square of 14 and 21
Solution:
14 * 14 = 196 (b) 21 * 21 = 441.
Square Root: A number that when multiply by itself equals a given number.
Example 2: find the square root of 144
Solution:
Using a prime factor method (method 1) Factor pairs method (method 2)
2 144 144 = 1 *144
2 72 = 2 * 72
2 36 = 3 * 48
2 18 = 4 * 36
3 9 = 6 * 24
3 3 = 8 * 18
1 = 9 * 16
Therefore (2 * 2) * (2 * 2) * (3 * 3) = 2* 2 * 3 = 12 = 12 x 12
ASSESEMENT
- Find the square of the following (a) 25, (b) 40 and (c) 132
- Find the square root of the following (a) 6400 (b) 16900 (c) 1296
Assignment: essential mathematics text book for J SS 2 PAGE 10 EXERCISE 1.6 NO 2 (e, f) , NO 6 (b, c)
WEEK 4 FRACTIONS (TYPES OF FRACTIONS), RATIO AND PERCENTAGES
Fraction is a small part or item forming a piece of a whole. It is the quotient of the rational numbers.
Types of Fractions
EQUIVALENT FRACTIONS: Examples are 2/5 = 4/10 = 8/20 = 16/40
IMPROPER FRACTIONS: Examples are 13/2, 100/7, 67/5,102/5
MIXED FRACTIONS: 72/3, 91/8, 1421/2 etc.
RATIOS, DECIMAL AND PERCENTAGE
RATIO is the relative magnitudes of two quantities (usually expressed as a quotient).
Example 1: In a bus station, the ratio of men to women is 2:5 (a) what fraction of the people are men (b) what fraction of the people
Solution:
2:5 = 2+5 = 7
The fraction of men = 2/7 (i.e. the fraction of men over the total fraction)
The fraction of women = 5/7 (i.e. the fraction of women over the total fraction)
Example 2: The population of a country is estimated to be 12 million people. The last survey reveals that 40% were boys, 30% were girls, 10% were men and 20% were women. Express the composition in ratio and evaluate the estimate number of people in each categories.
Solution:
40% (boys) 30% (girls) 20% (women) 10% (men)
Step 1: eliminate the percentage first = 40 30 20 10
Step 2: divide through by to to reduce the value = 4 3 2 1
Therefore we have 4:3:2:1 = 4 + 3 + 2 + 1 = 10
Step 3: find the people for each categories.
MEN = 1/10 * 12 000 000 = 1 200 000 (ZERO CANCEL ZERO)
WOMEN = 2/10 * 12 000 000 = 2 400 000 (ZERO CANCEL ZERO)
GIRLS = 3/10* 12 000 000 = 3 600 000 (ZERO CANCEL ZERO)
BOYS = 4/10 * 12 000 000 = 4 800 000 (ZERO CANCEL ZERO)
THEREFORE: 4 800 000 + 3 600 000 + 2 400 000 + 1 200 000 = 12 000 000.
FRACTION AND DECIMALS TO PERCENTAGES
Example 1: Express the following fraction to percentage (a) 5/12 (b) 120/500 (c) 0.009
Solution:
5/12 * 100 = 500/ 12 = 412/3
120/500 * 100 = 24%
0.009 = 9/1000 * 100 = 0.9%
ASSESSMENT
ESSENTIAL MATHEMATICS BOOK 2
EXERCISE 4.1 NO 1 (I, J, K, L), NO 4 (A, B, F, G) PAGE 44
EXERCISE 4.3 NO 6 AND 7. PAGE 47
WEEK 5 HOUSEHOLD ARITHMETIC (SIMPLE INTEREST, PROFIT AND LOSS, DISCOUNT AND COMMISSION)
PROFIT AND LOSS
When a trader buys or sells goods, the price at which he /she sells is called selling price while the price at which he/she buys is called cost price.
When the good is sold at a price greater than the cost price, then the trader has made a gain or profit. On the other hand, when the good is sold at a price less than the cost price, then the trader has made a loss.
S.P means selling price, C.P means cost price.
Profit = SP – CP %P = P/CP * 100 LOSS = CP –SP %L = L/CP *100
Example 1: a man buys a pair of shoe for Ħ3000 and sold it for Ħ3300. Find the percentage profit.
Solution:
SP = Ħ3300, CP = Ħ3000,
P = SP – CP = Ħ3300 – Ħ3000 = 300
%P = P/CP * 100 = 300/3000 * 100 = 30000/3000
= 10%
Example 2: a market woman bought 50 oranges at a total cost of Ħ2000. She sold each one at Ħ45. Find the percentage profit?
Solution:
CP = Ħ2000, SP = Ħ 45* 500 = Ħ2250,
P = SP – CP = Ħ2250 – Ħ2000 = Ħ250
SP = P/CP * 100 = 250/2000 * 100 = 25000/2000 = 12.5%
Ezample 3: A dealer bought an item for Ħ6000 after three months he sold it at a price of Ħ55000. What is the percentage loss?
Solution:
CP = Ħ60000, SP = 55000,
LOSS = CP – SP = Ħ60000 – Ħ55000 = Ħ5000
%LOSS = L/CP * 100 = 5000/60000 * 100 = 500000/60000
= 8.3%
Example 3:A dealer bought an article for Ħ65000. Find the price he will sell it in order to make a profit of 20%
Solution :
CP = Ħ65000, SP = ?, %P =20%
STEP 1: Find the % of the cost price
P = 20/100 * 65000 = 130000/100 = 13000
P = SP – CP = Ħ 13 000 = SP – CP = SP = Ħ 65000 + Ħ 13000 = Ħ 78000
SIMPLE INTEREST
SI = P * R * T/100 where P principal, R = rate, T = time and SI = simple interest
Example 1: Mr Smith saves Ħ 70000 with a bank for 3 years at the rate of 5%.
(a). calculate the interest he will receive at the end of the years
(b). calculate the simple interest for 7 years
(c). what is the total amount he will save at the end of 5 years?
Solution:
P = Ħ 7000, R = 5%, T = 3
(a). S I = P * R * T/100 = 7000 * 5 * 3/100 – 700 * 15 = Ħ 10000
(b). S I = Ħ70000 * 5 * 7/100 = Ħ 700 * 35 = Ħ 24 500
(C). Ħ70000 * 5 * 5/100 = 700 * Ħ 17500
Amount = P + S I = Ħ 70000 + 17500 = Ħ 87500
COMMISSION AND DISCOUNT
Commission is simply a payment received for selling a good.
Example 1: An insurance company pays an agent a basis salary of Ħ5000 per month plus a commission of 15% of all the sales above Ħ100000. Calculate his gross earning in a month if he sells good to the value of Ħ1 200,000.
Solution:
Basis salary = Ħ15000, commission = 15% 0f Ħ100000
But he sold 1200000, therefore Ħ 1200000 – Ħ100000 = Ħ1100000
15% of 1100000 = Ħ165000
Basic salary + commission = Ħ5000 + Ħ165000 = Ħ180000
DISCOUNT is the amount of money taken of a price of a good in order to promote the sale.
Example: Mr adeoye, a regular customer is given a discount of 12% on an item that cost Ħ84500. How much does he pay?
Solution:
The item cost Ħ84500,12% of 584500
12% of 84500 – Ħ10140
He pays Ħ84500 – Ħ10140 = Ħ74360.
Example 2: A car company advertises a discount of 12.5% of all their vehicles. How much would it cost to purchase.
(a). a Toyota car priced at Ħ650000
(b). a Volvo car priced at Ħ450000
(c). a Peugeot car priced at Ħ360000
Solution:
(a). Toyota car = 12.5% of Ħ650000 = Ħ81250
Therefore Ħ650000 – Ħ81250 = Ħ568750
(b). Volvo car = 12.5% of Ħ450000 = Ħ56250
Therefore Ħ450000 – Ħ56250 = Ħ393750
(c).Peugeot car = Ħ12.5% of Ħ360000 = Ħ313500
Ħ360000 – Ħ46500 = Ħ313500
ASSESEMENT: ESSENTIAL MATHEMATICS BOOK FOR JSS 2
EXERCISE 6.7 NO 2(A, B, C), 3, 8, 12 AND 14. PAGE 76
EXERCISE 6.8 NO 6, 14, 16 & 19. PAGE 75
EXERCISE 6.10 NO 3, 4 AND 5. PAGE 77
WEEK 6 APPROXIMATION AND ESTIMATION (SIGNIFCANT AND DECIMAL PLACES)
SIGNIFICANT: TO ROUNDOFF A NUMBER CHANGE 0,1,2,3,4 TO 0 WHILE 5,6,7,8,9 TO 1 AND ADD IT TO THE NEXT NUMBER
Example 1: round off 492.763 to (a) 3 s.f (b) 3 s.f (c) 2 d.p (d) 4 d.p
Solution:
(a). 492.763 = 49 (since the third number is 2 it has change to zero)
(b). 492.763 = 493 (the 2 as change to 3 because 7 as change to 1 and been added to 2 to become 3)
(c).492.763 = 492.76 (in decimal point we count after the point).
(d). 492.763 = 492.7630(since the number is not upto 4d.p we add zero to it.)
Example 2: calculate the following and round your answer to the given degree of a accuracy
(a). 576.175 + 20.82 (2 d.p)
(b). 8.52 x 0.0651 (3 s.f)
Solution:
(a). 576.173 + 20.82 = 596.99
596.99 = 596.99 (2 d.p)
(b). 8.52 * 0.0651 = 0.554652
0.554652 = 0.555(3s.f)
ASSESEMENT: ESSENTIAL MATHEMATICS BOOK FOR JSS 2
EXERCISE 7.1 NO 9 (A – K). PAGE 85
EXERCISE 7.3 NO 1 (A– R). PAGE 86
WEEK 7 MID TERM EXAMINATION
WEEK 8 MULTIPLICATION AND DIVISION OF DIRECTED NUMBERS
Revision on addition and subtraction of directed numbers
Note that:
(a). + + = + OR – – = + (Replacing the same signs that apprear together by a positive sign
(b). + – = – OR – + = – (Replacing two different signs that appear together by a negative sign
Example 1: Find the values of the following:
(a). + 7 + (+8) (b) +13 – (+6)
Solution:
(a). + 7 + (+8) = 7 + 8 = 15
(b). + 13 – (+6) = 13 – 6 = 7
Example 2 : Calculate the following (a) 25 – (+3) (b) 12 – (-9)
Solution
(a). 25 – (+3) = 25 – 3 = 22
(b). 12 – (-9) = 12 + 9 = 21
MULTIPLICATION OF DIRECTED NUMBERS
RULES:
- + * – = – OR – * + = – (If different signs are multiplied the answer is NEGATIVE).
- + * + = + OR – * – = + ( If the same signs are multiplied the answer is positive).
Example1: Simplify the following (a) (+12) * (+5) (b) (-3) * (-8)
Solution:
(a). 12 * 5 = 60
(b). -3 * -8 = + 24
Example 2: Find the values of the following (a) -4 * -2 * -2 * -2 * -2 (b) 7 * (-3) * (-1) * (-1) * 20
Solution:
( a). -4 * -2 * -2 * -2 * -2 = – 64 ( rules, we have equal signs to give positive while different sign gives negative)
(b). 7 * (-3) * (-1) * (-1) * 20 = 7-3 = -21 *-1 * -1 = -2120 = – 420
DIVISION OF DIRECTED NUMBERS
RULES:
- ÷ + = + OR – ÷ – = + ( If the sign are divided the answer is positive)
÷ + = – OR – ÷ + = =- (Ie the sign are different theanswer is negative).
Eample 1: work out the following (a) (+80) ÷ (-10) (b) (-25) ÷ (-5)
Solution:
- (+80) ÷ (-10) = – 8 (because the signs are different)
- (-25) ÷ (-5) = + 5(because the signs are the same)
DO THESE:
Simplify the following
(b) (-25) ÷ (-5)
(a). 3 x 5 x 2 x 15 (-9) (b). -8 x (-11) x 9 x (-5)
-5 x 25 x 3 2 x (-33) x (-3)
ASSESEMENT: ESSENTIAL BOOK FOR JSS 2
EXERCISE 10.3 N0 1, 2, 3 (ATO E). PAGE121 TO 123
WEEK 9 ALGEBRAIC EXPRESSION
To expand algebraic expression, those expression will have to be in bracket. When the bracket ever moved, then any factor outside the bracket must be multiplied by each term inside bracket.
Example 1: Expand d(a + c)
Solution: d * a + d * c = da + dc
Example 2: Expand (y + 3)( y + 4)
Solution:
= Y * Y + Y * 4 + 3 * Y + 3 * 4
= Y2 + 4y + 3y + 12
FACTORIZATION OF SIMPLE ALGEBRAIC EXPRESSION
Factorization is the reverse of expanding brackets. The first step in factorization is to take any commom factor which the term are:
Example 1 :Factorise 3X2 + X
Solution:
X is common to the expression
Therefore = X(3X + 1)
Example 2: Factorize 6y3 – 4y2 – 4y
Solution:
2y is common in the expression
Therefore 2y(3y2 -2y -2
ALGERAIC EXPRESSION WITH FRACTIONS
Example 1: Solve X/3 + X- 2/5 = 6
Solution:
Find the L C M = 15
5x + 3X – 6 /15 = 6
Cross multiply
= 5X + 3X – 6 = 6*15
8X – 6 = 90
Add 6 to both sides = 8X – 6 + 6 = 90 + 6
8X = 96 (Divide both sides by 8)
X = 12.
FINDING LOWEST COMMON FACTOR AND HIGHEST COMMON FACTOR IN ALGEBRAIC FORM
Example 1: Find the L C M of 4xy,8xv and 10x2y
Solution:
2 4xy 8xy 10x2y
2 2xy 4xy 5x2y
2 xy 2xy 5x2y
5 xy xy x2y
X xy x y x2y
X y y xy
Y y y y
1 1 1
L C M = 2 * 2 * 2 * 2 * 5 * X * X * Y = 40X2Y
Example 2: find the H C F of 4xy, 8xy and 10x2y
Solution;
4xy = 2 * 2 * x * y
8xy = 2 * 2 * 2 * x * y
10x2y = 2 * 5 * x * x * y
H C F = 2 * X * Y = 2XY
ASSESEMENT: ESSENTIAL BOOK FOR JSS 2
EXERCISE 11.4 NO 25 – 35. PAGE 138.
EXERCISE 11.8 NO 2 (F, G & H), NO 4(E&F), NO 11(A, B, C & D). PAGE 143
WEEK10 ALGERAIC FRACTIONS
To add or subtract fractions with different denominators, first change them to equivalent fractions. This is done by finding the L C M of the denominators
Example1: Simplify 2a/5 + 4a/3
Solution:
The L C M is 15
6a + 20a/ 15 = 26a/15
Example 2: Simplify 3/5x + 1/2x – 1/4x
Solution:
Find the L C M of the expression = 20X
12 + 10 – 5 = 17/20X
SIMPLIFYING FRACTION
Example 1: Reduce 25X4Y3/35X3y3
solution
Divide through by 5X3Y3(the common factor )
= 5x/7
Example 2: Reduce 8X3Y2/6X3Z
Solution:
Divide through by 2X 3(the common factor)
4Y2/3Z
MULTIPLICATION AND DIVISION OF ALGEBRAIC FRACTION
Example 1: Simplfy (X-2)/7 * 4/(X-2)
Solution : X – 2/7 * 4/ X -2 (X-2) divides themselves
= 4/7
Example 2: Simplify 6X2/11y ÷ 18X/33Y2
Solution
6X2/11y * 33Y2/18X (division sign change to multiplication)
= XY
FRACTIONS WITH BRACKETS
Example1: simplify the following (a) 2x + 5/4 + 2X – 3 /4 (b) 7X – 2 /4 + X – 4 /6
Solution:
(a). The L C M is 4
(2X + 5) + ( 2X – 3)/4
4x + 2/4 = 2(2X + 1)/4
= 2X + 1/2
(b). 7X – 2 /4 + X – 4 /6
Solution:
The L C M = 12
21x – 6 + 2X – 6 – 8 / 12
= 23X – 14/ 12
ASSESEMENT: ESSENTIAL BOOK FOR JSS 2
EXERCISE 12.4 NO 7, 13, 19 & 20. PAGE 149
EXERCISE 12.6 NO 1, 2, 3 & 4. PAGE 151
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