GRADE 10- MATHS- ENGLISH MEDIUM

Day 1

UNIT 13 – Algebraic fraction

Do the review exercise

Do the exercise 13.1 – a) e) f) h) j) l)

Simplify

1) 𝑎

4+

5𝑎

12−

𝑎

3 4)

𝑥

𝑎𝑏+

𝑦

𝑏𝑐+

𝑧

𝑎𝑐

2) 3

𝑥−2−

2

𝑥+2

3) 3𝑥

(𝑥+1)2 −2

𝑥+1

Before simplify check whether denominator is in the factor form. Eg; if it is a

quadratic expression find the factors of it and then simplify.

Exercise 13.2

(A) a , h , d , k , f , l

(B) a , g , c , I , e , j

REVISION

1) 1/4TH of a certain sum of money is Rs 500. Find the value of 1/5th of it.

2) Find the value of 3𝑥 + 2𝑦 𝑖𝑓 x= -1 and y= 1/2

3) Factorize 𝑥2-9

4) Find the value 2−3

5) Make the subject u = v + ft

6) Find the gradient of the straight line passing through ( 0 ,3 ) and ( 2 , 5).

7) Find the value of x.

2x +65 x+25

8) Find factors 2𝑥2 + 9𝑥 + 4.

9) √10 lies between which whole numbers ?

10) Find the value using the complete square knowledge232.

GRADE 10 -MATHEMATICS – ENGLISH MEDIUM

Day 2

UNIT 14 – PERCENTAGES

Do the review exercise

14.1 – TAXES

Please go through the note in the text book related to different types of taxes.– rates ,

custom duty , income tax , value added tax (VAT)

RATES – a percentage of the assessed value charged annually or quarterly.

1 quarter has 3 months

There are 4 quarters for a year

Do Exercise 14.1 - 1, 2, 3, 4, 5 questions.

Do the Western province 2015 2nd term paper 2 , part A , question 1

REVISION

A man left ½ of his wealth to his wife. 1/8 of the remaining to his son and 2/7 of the remaining to his

daughter.

1) Find the fraction of land given to the son of the total.

2 ) Find the fraction of land given to the daughter.

3) If the value of remaining portion is Rs 222 000, find total amount of his wealth.

GRADE 10- MATHEMATICS –DAY 3

14.1-TAXES

CUSTOM DUTY –

a certain percentage of the value of an item which has to be paid to the government when

items are imported or exported.

Custom duty = value of the item × duty percentage

Do exercise 14.1 - 6 , 7 , 8 , 9 , 10

Do the Western province 2016, 2nd term , paper 2 ,1st question, part A

REVISION SET 3

1) The general term of a number pattern is; Tn = 7 - 3n

1) Write the first 3 terms.

2) Find the common difference.

3) Which term is -29 of this pattern?

4) Show that there is no term as 131.

GRADE 10 MATHEMATICS – DAY 4

Income Tax - The government imposes a tax on the annual income of an individual, which is

earned as salary, from property or through a business, and which exceeds a certain limit.

Such taxes are called income taxes.

Please refer the table in page 142.

According to the table whoever gets a salary less than Rs 500 000 needs not pay tax.

Those who receive more than Rs 500 000 needs to pay tax accordingly.

Please refer the example 1 and example 2.

Do exercise 14.1 – 11, 12, and 13.

Do Western Province 2015 Gampaha Zone – Term 2 – Paper 2 - 1st question.

Value added tax -

When a product or a service is bought, a percentage of its total value is charged as value

added tax.

Do exercise 14 .1 – 14 , 15 and 16 th

Revision

1. Find the LCM , 4xy , 10x( 5x + 2 )

2. Factorise. 2x2 – 11 xy + 15 y2

3. Convert it to a faction. 0.72

4. Expand. ( 3x – 5 ) 2

5. Find the median. 13 , 23 , 14 , 23 , 20

6. Simplify. 5

2𝑥 +

𝑎

5𝑥

7. Find the value of x.

3x - 20 2x + 45

8. Draw a Venn diagram and shade the given region. A 1 ∩ B

9. The value of an exterior angle of a regular polygon is 60. Find the number of sides.

10. Simplify. ( a + 7 ) ( a – 3 )

11. Find the first 3 terms of the number pattern, 10 – 7n

12. A:B = 2:3 and B:C = 5:7 . Find the ratio of A:B:C

13. Find the circumference of a circle with 3.5 cm radius.

14. Make x the subject. Ax + B= Cx

15. Solve. 𝑥

2 +

𝑥

3 = 10

DAY 5 – INTEREST

Interest

When an amount of money is given as a loan or taken as loan, an amount is payable above

the amount borrowed, such an amount is known as interest.

Annual interest rate

Interest payable on Rs. 100

Eg: A person who borrowed Rs. 1000 had to pay back Rs. 1100

(Extra amount he had to pay) Interest = 1100 – 1000

= 100

Annual simple interest

When the interest for each period is calculated on the initial amount (principal) only, then it is

known as annual simple interest.

Eg: Mala borrowed Rs. 2000 from a local money lender at an annual simple interest rate of

20%.

Q1 What is the interest payable for Rs. 100 at the end of 1 year? Rs.20

Q2 What is the interest payable for Rs. 2000 at the end of one year?

20

100× 2000 = 400

Q3 What is the interest payable for Rs. 2000 at the end of two years?

400 × 2 = 800

Q4 What is the total amount payable at the end of two years?

Principal + Interest = Total amount

2000 + 800 = 2800

Answer the following questions

An annual interest of 8% is paid for fixed deposits

The above is a notice displayed in a bank. Accordingly,

(i) How much is the interest that is received at the end of the year, by a person

who deposits Rs. 100 in this bank?

(ii) How much is the interest that is received per annum, by Saman who deposits

Rs. 30000 in this bank?

(iii) How much more money should be deposited by Saman to obtain an interest of

Rs. 4000 at the end of the year?

(iv) If a person who deposits Rs. X receives a total amount of Rs. P at the end of

the year, show that P = 1.08 X

How much interest is received in three years when a loan of Rs. 5000 is given at an

annual simple interest rate of 12%?

If a person who gave a loan of Rs. 6000 at an annual simple interest rate, received Rs.

3600 as interest for 4 years, what is the annual simple interest rate that was charged?

A person takes a loan on annual simple interest, promising to settle the loan in two

years by paying Rs. 5000. However he was only able to settle the loan in five years, at

which time he had to pay Rs. 6500

(i) Calculate the interest he has paid for a year.

(ii) What was the amount he borrowed?

(iii) What was the annual simple interest rate that was charged?

Piyal borrowed Rs. 80000 from a certain financial institution at 24% annual simple

interest rate

(i) Find the monthly simple interest rate if the institution calculates the interest

monthly.

(ii) Calculate the interest that should be paid for the loan for a month.

(iii) If Piyal expects to settle the loan after 10 months calculate the total amount, he

has to pay at the end of 10 months.

If a person took a loan of Rs. P for a period of T years at an annual simple interest rate

of R

(i) Write down an expression for the interest he must pay for a month

(ii) Write down an expression for the total interest (I) that he must pay for a period

of T years.

DAY 6 – EQUATIONS

Solve the following equations.

(a) 2( 𝑋 − 3) = 4

(b) 𝑋

2+ 1 = 3

(c) 5𝑋−2

4= 2

(d) 𝑥

3+

𝑥

4= 7

(e) 4 − 5(3 − 𝑝) = 2(𝑝 − 1)

(f) 3

𝑥+2=

3

7

(g) 1

𝑎+1+

3

𝑎+1=

2

3

(h) 15

2(𝑝+1)−

3

𝑝+1= 2

(i) 1

𝑎−1+

3

4=

4

𝑎−1

(j) 𝑥+1

𝑥+3=

4

5

(k) 10

𝑎−3=

5

8

(l) 4

𝑥+1=

3

𝑥−2

(m) 2𝑥

𝑥+1+

2

3= 2

(n) 4

5𝑥−

1

3𝑥=

7

30

DAY 7 – SIMULTANEOUS EQUATIONS

I) Solve the following simultaneous equations.

(a) 2𝑥 + 5𝑦 = 9 3𝑥 + 2𝑦 = 8

(b) 6𝑥 + 5𝑦 = 5

9𝑥 − 4𝑦 = 19

(c) 3𝑥 + 𝑦 = 14 2𝑥 + 3𝑦 = 21

(d) 2𝑚 + 𝑛 = 5 𝑚 + 2𝑛 = 4

(e) 4𝑚 − 3𝑛 = 7 7𝑚 − 2𝑛 = 22

II)

(a) Nimal has twice the amount of money that Kamal has. The amounts of money

both have become equal, if Nimal gives Rs. 10 to Kamal.

(i) Obtain two simultaneous equations, by taking the amounts of money

Nimal and Kamal have as Rs. X and Y respectively.

(ii) Find the amount of money each has separately by solving these

equations.

(b) The cost of 8 pens and 5 erasers is 348. The cost of 4 pens is equal to the cost of

12 erasers.

(i) Obtain two simultaneous equations, by taking the price of a pen and

price of an eraser as Rs. X and Y respectively.

(ii) Find the price of a pen and price of an eraser by solving these

equations.

(c) The price of a can of pineapple is Rs. 5 more than three times the price of an apple.

A can of pineapple and 5 apples can be bought for Rs. 165

Construct two simultaneous equations and find the price of a can of pineapple and

the

price of an apple.

(d) The price of a book is Rs. 3 more than the price of a pen. 5 pens can be bought

from the amounts spent on 4 books.

(i) If the price of the book is x and the price of a pen is y, construct two

simultaneous equations.

(ii) Solve the two simultaneous equations and find the solutions for x and

y

(e) Ramu bought cows and hens. The total number bought was 35. The total number

of their legs is 84. By taking x as the number of cows and y as the number of hens, write

two simultaneous equations and find the number of cows and hens by solving them.