lOMoAR cPSD| 37664106
CEKENAS END OF TERM TWO
EVALUATION EXAM-2024 121/1
MATHEMATICS ALT. A
Paper 1
SECTION I: (50MKS)
ATTEMPT ALL THE QUESTIONS FROM THIS SECTION
1. Without using mathematical tables or calculator, evaluate (3mks)
3 1 1 3 1
of
8 2 3 4 10
2. Without using mathematical tables or calculator, evaluate (3mks)
3
729125
11,025
3. The currency exchange rates of a given bank in Kenya are as follows
Currency Buying Selling
1 Sterling pound 135.50 135.97
1 US dollar 72.23 72.65
A tourist arrived in Kenya with 5000 US dollars which he converted to Kenya shillings upon arrival. He spent
Kshs, 214,000 and converted the remaining to sterling pounds. How many pounds did he receive.
(3mks)
4. Without using mathematical tables or calculator evaluate 6Log2 64 10Log3 243
3 5
(3mks)
acces s free learning material by visiting www.freekcsepastpapers.com
9t 2 25a 2
5. Simplify (3mks)
6t 2 19at 15a 2
6. The base of a right pyramid is a rectangle of length 96cm and width 72cm. Each slant edge of the pyramid is
156cm. Calculate the volume of the pyramid. (3mks)
7. John bought two shirts and three pairs of trouser at Ksh 1750. IF he had bought three shirts and two pairs of
trousers, he would have saved Khs 250. Find the cost of a shirt and a trouser.
(3mks)
8. Three litres of water (density 1g/cm3) is added to twelve litres of alcohol. (density 0.8g/cm3). What is the density
of the mixture? (3mks)
9. List the integral values of x which satisfy the inequalities below. (3mks)
2x 21 15 2x x 6
10. Point B is 6 kilometers from A on a bearing of 1500. Point C is 5km from A on a bearing of 1200. Using a scale
drawing of 1cm to represent 1km, find the distance of C from B. (3mks)
11. Charles keeps goats and sheep. The number of goats exceeds the number of sheep by 4, during drought ¼ of the
goats and 1/6 of the of the sheep died. If he lost a total of 64 animals, how many animals did he have originally.
(4 mks)
2 5
12. Give that x is acute angle and cos x without using mathematical tables or calculator find Tan (90-x).
5
(2mks)
13. Without using mathematical tables or calculator evaluate . (3mks)
2 1
8 3 1002
1 13
2
0.5
64 36
3
27
1
, lOMoAR cPSD| 37664106
MATHEMATICS PAPER 1 & 2
14. The gradient of the tangent to the curve y=ax3 +bx at point (1,1) is -5. Calculate the value of a and b.
(4 mks)
15. The sum of interior angles of a regular polygon is 24 times the size of an exterior angle.
(a) Find the number of sides of the polygon (3mks)
(b) Name the polygon (1 mk)
16. A rally car travelled for 2hrs 40minutes at an average speed of 120km/h. The car consumes an average of a litres
for every 4 kilometers. A litre of fuel cost Ksh 60. Calculate the amount of money spent on fuel.
(3mks?)
SECTION II
ANSWER ANY FIVE QUESTIONS
17. Three business business partners Kamau, Tatwa and Makau contributed Kshs 100,000, Ksh 80,000 and Ksh
50,000respectively to start a business. After one year the business realized a profit in which they shared in the
ratio of their contributions.
(a) If Makau’s share of profit was Ksh. 20,000, how much was the total amount of profit? (3mks)
(b) At the beginning of the second year, Makau boosted his shares by Ksh. 10,000. If the
business profit increased by 20% at the end of the second year. Calculate
(i) Kamau’s share of the profit. (4mks)
(ii) The difference between Kamau’s and Tatwa’s share of the profit. (3mks)
18. The following data was obtained from masses of some pregnant women in maternity clinic.
Masses X 1.5 X 5.5 5.5 X 7.5 7.5 X 13.5 13.5 X 15.5 15.5 X 20.5
(Kg)
16 20 18 14 15
(a) Represent the information in the table above on a histogram on the graph paper provided.
access free learning material by visiting www.freekcsepastpapers.com
(6mks)
(b) Use the information in the table above to estimate
(i) The mean mass (2mks)
(ii) The median mass (2mks)
19. The figure below is a frustum of a solid cone of the base radius 24cm and top radius 8cm. The height of the
22
frustum is 10.5cm. (Take )
7
Calculate
(i) The height of the cone of the frustum was part of (2mks)
(ii) The slant height of the cone of the frustum was part of. (1mk)
(iii) The surface area of frustum (4 mks)
(iv) The volume of the frustum. (3mks)
2
, lOMoAR cPSD| 37664106
MATHEMATICS PAPER 1 & 2
20. The figure below shows two equal circles of radius 7cm, each with centres at X and Y. The two circles are in
Contact at Q.
Given that angle AXD = angle BYC= 1200 and lines AB, XQY and DC arc parallel. Calculate the area of:
22
(a) The minor sector XAQD (Take ) (2mks)
7
(b) The trapezium XABY. (5mks)
(c) The shaded region. (3mks)
21. A particle start from rest and moves in a straight line. Its velocity Vms-1 is given by V=t2 -3t+2 where t is the time
in seconds taken from point O.
(a) Find
(i) The velocity when t=3 (2mks)
(ii) The displacement from O when t=3 (3mks)
(iii) The acceleration of the particle when t= 3 (2mks)
(b) At what time is the particle momentarily at rest. (3mks)
access free learning material by visiting www.freekcsepastpapers.com
22. The distance between towns M and N is 280km. a car and a lorry travel from M to N. The average speed of the
lorry is N. The average speed of the lorry is 20km per hour less than that of the car. The lorry takes one hour
and ten minutes more than the car to travel from M to N.
(a) If the speed of the lorry is Xkm per hours find X. (6mks)
(b) The lorry left town M at 8.1 5am. The car left town M and overtook the lorry at 12.1 5p.m.
Calculate the time the car left town M. (4mks)
23. In the figure below, AB=16cm, AC=12cm, AD=14cm, CD=5.64cm and <CAB=500
3
, lOMoAR cPSD| 37664106
MATHEMATICS PAPER 1 & 2
Calculate to one decimal place.
(a) The length BC (2mks)
(b) The size of angle ABC (3mks)
(c) The size of angle CAD (3mks)
(d) The area of triangle ACD (2msk)
1 2 3
24. (a) Express in the form ax2 +bx+c= 0 where a, b and c are constants,
x 2 x 5 x 1
hence solve for x. (4 mks)
(b) Wamuyu did M test and scored a total of 240 marks. She did two more tests which she scored 28 and 26
respectively. The mean score of the first M test was 6 more than the mean score for all the test she did.
Find the total number of test that she did. (6mks)
CEKENAS END OF TERM TWO EXAM-2021
121/2
MATHEMATICS ALT. A
Paper 2
Nov-Dec-2021
SECTION I: (50MKS)
ATTEMPT ALL THE QUESTIONS FROM THIS SECTION
1. Find the percentage error in the volume of a cone whose radius is 7.0cm and has an exact vertical height of
16cm. access free learning material by visiting www.freekcsepastpapers.com (3mks)
2. Solve for x in Log3(2x+1)=2+Log3 (3x-11) (3mks)
3. Two brands of tea A and B cost Kshs 45 and 32 per kg respectively. They are mixed such that the selling price of
one kilogram of the mixture is Kshs 45. If a 25% profit is relised. find the ratio in which the two brands were
mixed. (3mks)
4. Make a the subject of the formula (3mks)
1 1 1
a b c
5. Given that sin (x+20)0 = -7660, find x to the nearest degree, for 0 x 3600 (3mks)
6. Expand (x-y)6 (1 mks)
(b) Use your expansion upto forth term to estimate the value of (1.98)6 giving your answer to 4
significant figures. (2mks)
7. Express the following in surd form and simplify by rationalizing the denominator without ' using a calculator
and leave your answer in the form a + b c (3 mks)
8. The points A and B have position vectors i + 7j + 2k and -5i + 5j + 6k respectively. The point C divides AB in the
ratio : 3: -1 . Find the position vector of C in terms of i, j and k. (3 mks)
9 Jamais invests Ksh 60000 in a bank that pays an interest at a rate of 1.5% p.a compound interest. He wants to
earn more than Ksh 10,000 interest. Determine the least time, in whole years that this will take(3 mks)
10. Line XY is the diameter of circle such that the coordinates are X (-1,1) and Y (5,1)
i) Determine the centre and radius of the circle (2mks)
4
CEKENAS END OF TERM TWO
EVALUATION EXAM-2024 121/1
MATHEMATICS ALT. A
Paper 1
SECTION I: (50MKS)
ATTEMPT ALL THE QUESTIONS FROM THIS SECTION
1. Without using mathematical tables or calculator, evaluate (3mks)
3 1 1 3 1
of
8 2 3 4 10
2. Without using mathematical tables or calculator, evaluate (3mks)
3
729125
11,025
3. The currency exchange rates of a given bank in Kenya are as follows
Currency Buying Selling
1 Sterling pound 135.50 135.97
1 US dollar 72.23 72.65
A tourist arrived in Kenya with 5000 US dollars which he converted to Kenya shillings upon arrival. He spent
Kshs, 214,000 and converted the remaining to sterling pounds. How many pounds did he receive.
(3mks)
4. Without using mathematical tables or calculator evaluate 6Log2 64 10Log3 243
3 5
(3mks)
acces s free learning material by visiting www.freekcsepastpapers.com
9t 2 25a 2
5. Simplify (3mks)
6t 2 19at 15a 2
6. The base of a right pyramid is a rectangle of length 96cm and width 72cm. Each slant edge of the pyramid is
156cm. Calculate the volume of the pyramid. (3mks)
7. John bought two shirts and three pairs of trouser at Ksh 1750. IF he had bought three shirts and two pairs of
trousers, he would have saved Khs 250. Find the cost of a shirt and a trouser.
(3mks)
8. Three litres of water (density 1g/cm3) is added to twelve litres of alcohol. (density 0.8g/cm3). What is the density
of the mixture? (3mks)
9. List the integral values of x which satisfy the inequalities below. (3mks)
2x 21 15 2x x 6
10. Point B is 6 kilometers from A on a bearing of 1500. Point C is 5km from A on a bearing of 1200. Using a scale
drawing of 1cm to represent 1km, find the distance of C from B. (3mks)
11. Charles keeps goats and sheep. The number of goats exceeds the number of sheep by 4, during drought ¼ of the
goats and 1/6 of the of the sheep died. If he lost a total of 64 animals, how many animals did he have originally.
(4 mks)
2 5
12. Give that x is acute angle and cos x without using mathematical tables or calculator find Tan (90-x).
5
(2mks)
13. Without using mathematical tables or calculator evaluate . (3mks)
2 1
8 3 1002
1 13
2
0.5
64 36
3
27
1
, lOMoAR cPSD| 37664106
MATHEMATICS PAPER 1 & 2
14. The gradient of the tangent to the curve y=ax3 +bx at point (1,1) is -5. Calculate the value of a and b.
(4 mks)
15. The sum of interior angles of a regular polygon is 24 times the size of an exterior angle.
(a) Find the number of sides of the polygon (3mks)
(b) Name the polygon (1 mk)
16. A rally car travelled for 2hrs 40minutes at an average speed of 120km/h. The car consumes an average of a litres
for every 4 kilometers. A litre of fuel cost Ksh 60. Calculate the amount of money spent on fuel.
(3mks?)
SECTION II
ANSWER ANY FIVE QUESTIONS
17. Three business business partners Kamau, Tatwa and Makau contributed Kshs 100,000, Ksh 80,000 and Ksh
50,000respectively to start a business. After one year the business realized a profit in which they shared in the
ratio of their contributions.
(a) If Makau’s share of profit was Ksh. 20,000, how much was the total amount of profit? (3mks)
(b) At the beginning of the second year, Makau boosted his shares by Ksh. 10,000. If the
business profit increased by 20% at the end of the second year. Calculate
(i) Kamau’s share of the profit. (4mks)
(ii) The difference between Kamau’s and Tatwa’s share of the profit. (3mks)
18. The following data was obtained from masses of some pregnant women in maternity clinic.
Masses X 1.5 X 5.5 5.5 X 7.5 7.5 X 13.5 13.5 X 15.5 15.5 X 20.5
(Kg)
16 20 18 14 15
(a) Represent the information in the table above on a histogram on the graph paper provided.
access free learning material by visiting www.freekcsepastpapers.com
(6mks)
(b) Use the information in the table above to estimate
(i) The mean mass (2mks)
(ii) The median mass (2mks)
19. The figure below is a frustum of a solid cone of the base radius 24cm and top radius 8cm. The height of the
22
frustum is 10.5cm. (Take )
7
Calculate
(i) The height of the cone of the frustum was part of (2mks)
(ii) The slant height of the cone of the frustum was part of. (1mk)
(iii) The surface area of frustum (4 mks)
(iv) The volume of the frustum. (3mks)
2
, lOMoAR cPSD| 37664106
MATHEMATICS PAPER 1 & 2
20. The figure below shows two equal circles of radius 7cm, each with centres at X and Y. The two circles are in
Contact at Q.
Given that angle AXD = angle BYC= 1200 and lines AB, XQY and DC arc parallel. Calculate the area of:
22
(a) The minor sector XAQD (Take ) (2mks)
7
(b) The trapezium XABY. (5mks)
(c) The shaded region. (3mks)
21. A particle start from rest and moves in a straight line. Its velocity Vms-1 is given by V=t2 -3t+2 where t is the time
in seconds taken from point O.
(a) Find
(i) The velocity when t=3 (2mks)
(ii) The displacement from O when t=3 (3mks)
(iii) The acceleration of the particle when t= 3 (2mks)
(b) At what time is the particle momentarily at rest. (3mks)
access free learning material by visiting www.freekcsepastpapers.com
22. The distance between towns M and N is 280km. a car and a lorry travel from M to N. The average speed of the
lorry is N. The average speed of the lorry is 20km per hour less than that of the car. The lorry takes one hour
and ten minutes more than the car to travel from M to N.
(a) If the speed of the lorry is Xkm per hours find X. (6mks)
(b) The lorry left town M at 8.1 5am. The car left town M and overtook the lorry at 12.1 5p.m.
Calculate the time the car left town M. (4mks)
23. In the figure below, AB=16cm, AC=12cm, AD=14cm, CD=5.64cm and <CAB=500
3
, lOMoAR cPSD| 37664106
MATHEMATICS PAPER 1 & 2
Calculate to one decimal place.
(a) The length BC (2mks)
(b) The size of angle ABC (3mks)
(c) The size of angle CAD (3mks)
(d) The area of triangle ACD (2msk)
1 2 3
24. (a) Express in the form ax2 +bx+c= 0 where a, b and c are constants,
x 2 x 5 x 1
hence solve for x. (4 mks)
(b) Wamuyu did M test and scored a total of 240 marks. She did two more tests which she scored 28 and 26
respectively. The mean score of the first M test was 6 more than the mean score for all the test she did.
Find the total number of test that she did. (6mks)
CEKENAS END OF TERM TWO EXAM-2021
121/2
MATHEMATICS ALT. A
Paper 2
Nov-Dec-2021
SECTION I: (50MKS)
ATTEMPT ALL THE QUESTIONS FROM THIS SECTION
1. Find the percentage error in the volume of a cone whose radius is 7.0cm and has an exact vertical height of
16cm. access free learning material by visiting www.freekcsepastpapers.com (3mks)
2. Solve for x in Log3(2x+1)=2+Log3 (3x-11) (3mks)
3. Two brands of tea A and B cost Kshs 45 and 32 per kg respectively. They are mixed such that the selling price of
one kilogram of the mixture is Kshs 45. If a 25% profit is relised. find the ratio in which the two brands were
mixed. (3mks)
4. Make a the subject of the formula (3mks)
1 1 1
a b c
5. Given that sin (x+20)0 = -7660, find x to the nearest degree, for 0 x 3600 (3mks)
6. Expand (x-y)6 (1 mks)
(b) Use your expansion upto forth term to estimate the value of (1.98)6 giving your answer to 4
significant figures. (2mks)
7. Express the following in surd form and simplify by rationalizing the denominator without ' using a calculator
and leave your answer in the form a + b c (3 mks)
8. The points A and B have position vectors i + 7j + 2k and -5i + 5j + 6k respectively. The point C divides AB in the
ratio : 3: -1 . Find the position vector of C in terms of i, j and k. (3 mks)
9 Jamais invests Ksh 60000 in a bank that pays an interest at a rate of 1.5% p.a compound interest. He wants to
earn more than Ksh 10,000 interest. Determine the least time, in whole years that this will take(3 mks)
10. Line XY is the diameter of circle such that the coordinates are X (-1,1) and Y (5,1)
i) Determine the centre and radius of the circle (2mks)
4
