# Form 2 Mathematics End of Term 3 Exam 2021

Class: Form 2

Subject: Mathematics

Level: High School

Exam Category: Form 2 End Term 3 Exams

Document Type: Pdf

Views: 586
Downloads: 113

## Exam Summary

1. Evaluate #(8 1/8 - 2 1/2)/(5 8/20 - 1 1/6 of 1 1/5)# (3mks)

2. A bus service number 4 leaves a terminus every 15 minutes. Services 8 and 3 leaves after every 20 and 30 minutes respectively. If all the three services leave together at 6.00 am, what is the earliest time the three buses will leave together again? (3mks)

3. A Line passes through A (1, 1) and B(x, y). The mid-point of AB is (3, 5). If line BC is perpendicular to AB, find the equation of line BC. (3mks)

4. Solve for the equation #(27/8)^(x+7) -(4/9)^(3x) = 0# (3mks)

5. Elvis exchanged Ksh.600,000 to Sterling pounds. After settling the bills worth £1200, he changed the balance to Euros. He then purchased goods worthy 200 Euros. Using the exchange rates below, calculate his balance in Kenyan shillings. (3mks)

6.Find the mass of a wooden beam 4m long, 25cm wide and 18cm deep if the density of the wood is 625kg/m3. (3mks)

7. Solve the inequality below hence represent the solution in a number line (3mks)

# 3 + 2x < 3x - 1 <= 2x + 7#

8. Each exterior angle of a regular polygon is a fifth of the interior angle.

a) Find the size of the exterior angle (2mks)

b) Find the number of sides of the polygon (2mk)

9. The figure below shows a solid prism:-

Sketch the net of the prism above and show with arrows the path ACDB and F via E (3mks)

10. The angle of elevation of the top of a flag post from a point x on level ground is 13°. The angle of elevation of the top of the flag post from another point y nearer the flag post and 120 metres from x is 30°. Y is between A and the bottom of the flag post and the three points are collinear. Find the height of the flag post. (3mks)

11. Use logarithm, correct to 4 decimal places to evaluate (4mks)

#root(3)(7.071/(456.3sin45°)#

12. In the figure below PQ is parallel to RS. PS and QR intersect at A. Given that PQ=9cm, RS=3cm and AS=4cm, calculate the length of PS. (3marks)

13. A two digit number is such that the product of its tens and ones is 56.When the digits are reversed the number formed exceeds the original number by 9. Find the number. (3marks)

14. Two boys and a girl shared some money. The elder got #4/9# of it, the younger boy got #2/5# of the remainder and the girl got the rest. Find the percentage share of the younger boy to the girls share. (3mks)

15. Annette has some money in two denominations only. Fifty shillings notes and twenty shilling coins. She has three times as many fifty shilling notes as twenty shilling coins. If altogether she has sh. 3,400, find the number of fifty shilling notes and 20 shilling coin. (3mks)

16. The mean of five numbers is 20. The mean of the first three numbers is 16. The fifth number is greater than the fourth by 8. Find the fifth number. (3mks)

SECTION 2 (50MARKS)

Attempt ALL the questions in this section

17. The intersecting circles centres S and R have radii 28 and 35 respectively. A common chord AB = 38cm.

a) Calculate

i) Angle ASB (2 marks)

ii) Angle ARB (2 marks)

b) Calculate the area of the shaded region. (6 marks)

18.(a) The members of a photography club decided to buy a camera worth Ksh 4000 by each one contributing the same amount of money. Fifteen members fail to pay their contribution and as a result each of the other members has to pay Ksh 60 more.

a).Find the number of members in the club. (8mks)

(b) What is the percentage increase in the contribution per member? (2mks)

19. Three business partners, Bela Joan and Trinity contributed Kshs 112,000, Ksh,128,000 and ksh,210,000 respectively to start a business. They agreed to share their profit as follows: 30% to be shared equally 30% to be shared in the ratio of their contributions 40% to be retained for running the business. If at the end of the year, the business realized a profit of ksh 1.35 Million. Calculate:

a) The amount of money retained for the running of the business at the end of the year. (1mk)

b) The difference between the amounts received by Trinity and Bela (6mks)

c) Express Joan’s share as a percentage of the total amount of money shared between the three partners. (3mks)

20.A surveyor recorded the following information in his field book after taking measurement in metres of a plot.

a) Sketch the layout of the plot. 4 mks.

b) Calculate the area of the plot in hectares. 6mks)

21. The diagram below represents a conical vessel which stands vertically. The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. #(Take pi= 22/7)#.

a) Calculate the volume of the water in the vessels in #cm^3# 3mks

b) When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm. Calculate:

(i) The radius of the new water surface in the vessel; (2mks)

(ii) The volume of the metal sphere in #cm^3# (3mks)

(iii) The radius of the sphere. (3mks)

2. A bus service number 4 leaves a terminus every 15 minutes. Services 8 and 3 leaves after every 20 and 30 minutes respectively. If all the three services leave together at 6.00 am, what is the earliest time the three buses will leave together again? (3mks)

3. A Line passes through A (1, 1) and B(x, y). The mid-point of AB is (3, 5). If line BC is perpendicular to AB, find the equation of line BC. (3mks)

4. Solve for the equation #(27/8)^(x+7) -(4/9)^(3x) = 0# (3mks)

5. Elvis exchanged Ksh.600,000 to Sterling pounds. After settling the bills worth £1200, he changed the balance to Euros. He then purchased goods worthy 200 Euros. Using the exchange rates below, calculate his balance in Kenyan shillings. (3mks)

6.Find the mass of a wooden beam 4m long, 25cm wide and 18cm deep if the density of the wood is 625kg/m3. (3mks)

7. Solve the inequality below hence represent the solution in a number line (3mks)

# 3 + 2x < 3x - 1 <= 2x + 7#

8. Each exterior angle of a regular polygon is a fifth of the interior angle.

a) Find the size of the exterior angle (2mks)

b) Find the number of sides of the polygon (2mk)

9. The figure below shows a solid prism:-

Sketch the net of the prism above and show with arrows the path ACDB and F via E (3mks)

10. The angle of elevation of the top of a flag post from a point x on level ground is 13°. The angle of elevation of the top of the flag post from another point y nearer the flag post and 120 metres from x is 30°. Y is between A and the bottom of the flag post and the three points are collinear. Find the height of the flag post. (3mks)

11. Use logarithm, correct to 4 decimal places to evaluate (4mks)

#root(3)(7.071/(456.3sin45°)#

12. In the figure below PQ is parallel to RS. PS and QR intersect at A. Given that PQ=9cm, RS=3cm and AS=4cm, calculate the length of PS. (3marks)

13. A two digit number is such that the product of its tens and ones is 56.When the digits are reversed the number formed exceeds the original number by 9. Find the number. (3marks)

14. Two boys and a girl shared some money. The elder got #4/9# of it, the younger boy got #2/5# of the remainder and the girl got the rest. Find the percentage share of the younger boy to the girls share. (3mks)

15. Annette has some money in two denominations only. Fifty shillings notes and twenty shilling coins. She has three times as many fifty shilling notes as twenty shilling coins. If altogether she has sh. 3,400, find the number of fifty shilling notes and 20 shilling coin. (3mks)

16. The mean of five numbers is 20. The mean of the first three numbers is 16. The fifth number is greater than the fourth by 8. Find the fifth number. (3mks)

SECTION 2 (50MARKS)

Attempt ALL the questions in this section

17. The intersecting circles centres S and R have radii 28 and 35 respectively. A common chord AB = 38cm.

a) Calculate

i) Angle ASB (2 marks)

ii) Angle ARB (2 marks)

b) Calculate the area of the shaded region. (6 marks)

18.(a) The members of a photography club decided to buy a camera worth Ksh 4000 by each one contributing the same amount of money. Fifteen members fail to pay their contribution and as a result each of the other members has to pay Ksh 60 more.

a).Find the number of members in the club. (8mks)

(b) What is the percentage increase in the contribution per member? (2mks)

19. Three business partners, Bela Joan and Trinity contributed Kshs 112,000, Ksh,128,000 and ksh,210,000 respectively to start a business. They agreed to share their profit as follows: 30% to be shared equally 30% to be shared in the ratio of their contributions 40% to be retained for running the business. If at the end of the year, the business realized a profit of ksh 1.35 Million. Calculate:

a) The amount of money retained for the running of the business at the end of the year. (1mk)

b) The difference between the amounts received by Trinity and Bela (6mks)

c) Express Joan’s share as a percentage of the total amount of money shared between the three partners. (3mks)

20.A surveyor recorded the following information in his field book after taking measurement in metres of a plot.

a) Sketch the layout of the plot. 4 mks.

b) Calculate the area of the plot in hectares. 6mks)

21. The diagram below represents a conical vessel which stands vertically. The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. #(Take pi= 22/7)#.

a) Calculate the volume of the water in the vessels in #cm^3# 3mks

b) When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm. Calculate:

(i) The radius of the new water surface in the vessel; (2mks)

(ii) The volume of the metal sphere in #cm^3# (3mks)

(iii) The radius of the sphere. (3mks)

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