The committee formed by Education Cabinet Secretary George Magoha on Wednesday, May 13 has urged stakeholders and the public to submit written proposals to its secretariat on or before Friday, May 22.

“They have to do so in reference for the basic education sub-sector,” Ruto stated on Thursday, May 14.

Those submitting the proposals are required to identify ways of enforcing preventive measures when schools reopen.

The committee also expects submissions on how to reorganise the school calendar, discuss the fate of boarding schools and how the poor will access education and the health and safety measures for schools.

These are among the issues CS Magoha wants the committee to table solutions to him.

On Wednesday, May 13, the World Health Organisation warned that the virus may stay for long, shifting from a pandemic to an endemic and most countries are trying to hatch ways to live with the virus.

A feature by Citizen TV added that as the idea of school resumption takes shape, parents are concerned with how social distancing will be enforced.

Among questions raised are how many learners will be allowed in a class? Will the students learn in shifts?

The Dr Sarah Ruto led committee is looking at ways in which learning can be conducted in shifts, with students attending schools on alternative days.

For the students who use school buses, the Ministry of Health’s guideline on only allowing 60% passengers in the buses will be considered.

Another concern on the table is how teachers above 58 years and those with pre-existing conditions will be protected, as they are among the most vulnerable.

Countries that have reopened schools have taken drastic measures such as abolishing school assemblies, limiting sports participation, while some school meetings have been abolished.

Written proposals are to be submitted to the sSecretariat, National Covid-19 Education Response Committee. They can be forwarded to covid19erc@kicd.ac.ke or addressed to P.O. Box 30231-00100, Nairobi.

 

The Ministry of Education says it will require additional funding to the tune of Sh429 million to facilitate the testing and provision of protective kits for the trainers and students in the country’s Techinical and Vocational Training colleges in the post-COVID-19 period.

In documents presented before the Education Committee, the ministry said trainers, trainees and all staff will be required to be tested, have face masks, soaps, sanitizers and running water before they resume learning.

The Ministry of Health recently announced that testing for COVID-19 has been pegged at Sh1,000 at all public health facilities but it is estimated that the test cost between Sh4,000- Sh10,000 depending on where they are conducted. Private hospitals are more expensive.

The Government ordered all basic and tertiary colleges shut in March after the country reported its first case of the pandemic which has so far claimed 42 lives in the country and infected 758.

The move, among others, was introduced as the government moved to ban gatherings in public places which had been identified as one the avenues that can fuel infections.

The Ministry said it requires a further Sh3.8billion for the expected increase in enrolment of students.
According to the Ministry, the current allocation of Sh5.2 billion only caters for the 173,000 students against a projected enrollment of 300,000 students.

A teacher who is seeking for a transfer, for instance, must fill the Transfer form that is endorsed by the head and submitted to the TSC for action.

Other, many, types of TSC forms also exist. If you have been wondering where to get the forms, then worry not. Click on the links below to download the forms free of charge and in PDF form. Each form contains instructions on how to complete the parts. Remember to read these instructions correctly before completing the form. In case in doubt, do not hesitate to consult your head or TSC Subcounty office for clarification.

Here are the TSC forms:

TEACHER TRANSFER APPLICATION FORM

This form is filled by a teacher who wishes to change his/ her current work station. The form enables the commission to consider a teacher’s intra and inter county transfer request. The reason for seeking the transfer must be satisfactory enough to warrant the transfer. Such reasons as ‘on medical grounds’ with supportive evidence is presumably given much weight by TSC. Those with organized swaps also get an easy ride.  Click on this link to get the TSC Transfer Form

TSC EMPLOYMENT FORM

This form is filled by teachers after successful interview/ recruitment. Get the TSC Employment Form here

TSC PROMOTION FORM

The TSC promotion form is for common cadre promotions. It is filled by teachers who have successfully served the required number of years in a given job grade. The form is filled by the head of institution. It is good to get the form ready and sent to TSC three months prior the expiry of the required minimum number of years that a teacher is to serve in the job group. The TSC Job group promotion form can be found on this link.

The education sector was the first to suffer from the coronavirus pandemic when President Kenyatta ordered all learning institutions to close after the first case of the disease was confirmed in the country. Weeks later, schools that had adequate infrastructure resulted in teaching their learners online using different web conferencing facilities.

With the first term closed prematurely and now into the second term with schools still closed, administrators are uncertain about which direction to take. With disrupted academic calendars, lack of revenue, and staff to pay, administrators are devising mechanisms to ensure all systems run amidst the pandemic.

Last Friday, the University of Nairobi, Vice-Chancellor, Prof. Kiama, through an address to the students and staff, said the University Senate had approved for the examinations that were due in April to be administered online.

Notably, the University has been teaching students using Google platforms and late in April, through a partnership with Telkom Kenya, the University provided students and staff with Telkom lines to facilitate the online learning and teaching.

The announcement has caused a lot of unease among the students, with a lot of uncertainty surrounding how the examination will be administered. Concerns have also been raised on the quality of such examinations and degrees that will be awarded after a question that the University is yet to answer. At the time of this publication, the University had not issued any guidelines on how the examinations will be conducted, including the quality tests that it certifies.

Should the University of Nairobi succeed in this endeavor, it will be a game-changer on examinations administration in the country and the first of its own kind.

The Education Ministry has appointed a nine-member committee to take charge of the process of exploring the best possible strategies of restoring normalcy in the education sector.

This comes in awake of the effects of the Covid-19 pandemic that has hurt the basic education sector most and was threatening to wipe out the gains made to stabilize the academic calendar.

The Education Cabinet Secretary, Prof. George Magoha who launched the team on Tuesday at Kenya Institute for Curriculum Development (KICD) said the committee, who work starts immediate effect, would be chaired by KICD Chairperson, Dr. Sara Ruto.

The committee Terms of Reference would be to advise the CS on the reopening of the basic education institutions; pre-primary, primary and secondary schools, Teacher Training Colleges and Adult Education Institutions.

The committee should also review and reorganise the school calendar as part of the Covid-19 post-recovery strategy and advise the CS on ways of handling boarding students/pupils when the schools re-open.

Documentation of all Covid-19 related matters, lessons learnt and recommendations for future preparedness would also be looked at.

The CS said the committee would also look into the impact of the Covid-19 pandemic on the demand for education by poor households and suggest mitigation measures.

The committee, whose Secretariat will be located at the Kenya Institute of Curriculum Development, will further advise the CS on the Health and Safety measures to be put in place for the pupils/students, teachers and entire school community.

The committee is to also identify institutions that may have been adversely affected by Covid-19 and advice on mitigation and recovery measures as well as submit regular reports to the Cabinet Secretary on the implementation progress of Covid-19 related programmes.

The CS noted that although schools were expected to resume learning when the Second Term was scheduled to start on May 4th, 2020, the Government extended the reopening date for one month to given more room for the scaling up of the national efforts to fight the spread of Covid-19.

In the meantime, Prof. Magoha said the Ministry has come up with measures to mitigate the effects of Covid-19 in the education sector, including mounting of online learning and the drafting of a master-plan to guide the response to Covid-19 in the sector.

The Members of the committee are Indimuli Kahi Chairman, Kenya Secondary Schools Heads Association, Nicholas Gathemia Chairman, Kenya Primary Schools Heads Association Peter Ndoro CEO, Kenya Private Schools Association, Nicholas Maiyo Chairman, Kenya Parents Association and Augustine Muthigani from Kenya Conference of Catholic Bishops.

Others are Jane Mwangi, Kenya Association for Independent International Schools. Dr. Nelson Makanda of National Council of Churches of Kenya (NCCK), Sheikh Munawar Khan from Muslim Education Council and Peter Sitienei Chairman, Kenya Special Schools Heads Association.

Ruth Mugambi from KICD, Patrick Ochich of KNEC, Gabriel Mathenge (TSC), Paul Kibet Director, Secondary Education MoE, Ms. Anne Gachoya Directorate of Policy, Partnerships and EAC and Dr. Loice Ombajo Ministry of Health/University of Nairobi have been named as ex-Officio members.

Upon the outbreak of the Covid-19 in Kenya, President Uhuru Kenyatta ordered the closure of all schools and other learning institutions on March 15th as part of the measures to control the spread of the virus.

Kenya Nation Union of Teachers KNUT has now criticized the move by education cabinet secretary George Magoha to exclude teachers union in the education task force that was recently formed to ensure the school calendar is not affected following the effects of the COVID-19 pandemic.

In interview with Ghetto Radio News KNUT deputy secretary general Hesbon Otieno said the union was in the forefront in pushing for the formation of the same task force and by excluding them yet they represent thousands of teachers is uncalled for.

The  Machakos Kenya Union of Post Primary Education (KUPPET) Executive Secretary, Musembi Katuku has called upon the government go slow when rethinking of re-opening education institutions.

Speaking to the press in Machakos on Tuesday, Katuku said it was too early to mull the possibility of opening schools at a time when the number of Covid-19 cases are on the rise in the country.

The unionist warned that any talk of students going back to school soon is not tenable at this time and the best the government can do is ensure the deadly virus which has claimed 36 Kenyans is contained first.

“Let us first embrace the pandemic and also learn to stay with it just like Malaria. Once we are there, let us then start thinking about education and the opening of our schools after the disease has been brought under control,” said Musembi who is also a member of the Machakos County Education Board.

Drawing  examples from Spain, Italy and France that have borne the brunt of the pandemic after losing hundreds of their citizens to Covid-19, the unionist said the most ideal thing for Kenya to do for now, is ease restriction on other sectors like the hospitality industry to help keep the economy afloat, before thinking of allowing pupils and teachers to go back to class.

He said as a union, they are opposed to any idea of asking teachers to go back to school soon owing to the risk of being infected with the disease.

“We are not ready to allow teachers to go back to school when this thing (disease) is on. The teachers can also get it from students who are travelling from counties which have confirmed cases such as Mombasa, Wajir, Mandera and Nairobi. This is not the time to give ultimatums but to work together to end the pandemic,” he added.

He says the Ministry of Education should however first consider allowing class eight and form four students back to class owing to the fact that they are set to sit for their national exams towards the end of the year, adding that the current online learning platform may never achieve much due to logistical challenges.

The  Education Cabinet Secretary(CS), Prof. George Magoha recently issued a strong indication to the effect that schools may remain closed for much longer than expected saying the safety of pupils was of paramount importance.

Initially the government had floated the idea of reopening schools by June 4, but this was dispelled after Magoha said any decisions to do so would depend on the prevailing situation at the time.

The government closed schools among other sectors on March 15 this year after three Covid-19 cases were recorded in the country.

To date, Kenya has recorded a total of 715 infections, 259 recoveries and 36 deaths arising from the pandemic.

Globally, the disease has already claimed 286,353 people with 1.4 million recoveries as at May 12.

More than 4 million others have been infected with the coronavirus even as countries work round the clock to find a vaccine for the disease.

KCSE Past Papers Mathematics 2018 Paper 2

Mathematics Alt A – Paper 2 – November 2018 – 2.5 Hours

Kenya Certificate of Secondary Education

2018 Mathematics Paper 2

Section I (50 marks)

1. Given that 2 log x²+log = k log x, find the value of k. (2 marks)

2. A variable P varies directly as t³ and inversely as the square root of s. When t = 2 and s = 9, P = 16. Determine the equation connecting P, t and s, hence find P when s = 36 and t=3. (4 marks)

3. Asia invested some money in a financial institution. The financial institution offered 6% per annum compound interest in the first year and 7% per annum in the second year. At the end of the second year, Asia had Ksh 170 130 in the financial institution. Determine the amount of money Asia invested. (3 marks)

4. The figure below represents a wedge ABCDEF. EF 10 cm, angle FBE 45° and the angle between the planes ABFE and ABCD is 20°.

Calculate length BC, correct to l decimal place.(3 marks)

5. Simplify √ 54 + ∛ 3/ √ 3 (2 marks)

6. In the figure below, AB is a tangent to the circle, centre O and radius 6 cm. The arc AC subtends an angle of 60° at the centre of the circle.

Calculate the area of the shaded region, correct to 1 decimal place. (4 marks)

7. Use completing the square method to solve 3x² + Sx — 6 = 0, correct to 3 significant figures. (3 marks)

8. Three workers, working 8 hours per day can complete a task in 5 days. Each worker is paic Ksh 40 per hour. Calculate the cost of hiring 5 workers if they work for 6 hours per day tc complete the same task. (3 marks)

9. The table below represents a relationship between two variables x and y.

x	1	2	3	4	5	6
y	3.5	4.5	8.0	8.5	11	13

(a) On the grid provided draw the line of best fit.(3 marks)

(b) Use the graph to find the value off when x — 0.(1 marks)

10. State the amplitude and the phase angle of the curve y = 2sin x — 30° .(2 marks)

11. The mass, in kilograms, of 9 sheep in a pen were: 13, 8, 16, 17, 19, 20, 15, 14 and 11.

Determine the quartile deviation of the data. (3 marks)

12. The position of two points C and D on the earth’s surface are (8°N, l 0OE) and (8°N, 30°E) respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. (3 marks)

13. In the figure below OP — p, OR = r, PQ:QR = 1:2 and PS = 3PR.

Express QS in terms of p and r. (4 marks)

14. In a certain firm there are 6 men and 4 women employees. Two employees are chosen at random to attend a seminar. Determine the probability that a man and a woman are chosen. (3 marks)

15. Under a transformation T = (4 —3) (2 3)

, triangle OAB is mapped onto triangle OA’B’ with vertices O(0,0), A’(18,0) and B'(18, 6). Find the area of triangle OAB. (3 marks)

16. Find the value of k if

Section II

Answer any 5 questions from this section

17. The 5th and 10th terms of an arithmetic progression are 18 and —2 respectively. (a) Find the common difference and the first term. (4 marks)

(b) Determine the least number of terms which must be added together so that the sum of the progression is negative. Hence find the sum. (6 marks)

18.Complete the table below for the equation y=x²-4x+2

(2 marks)

x	0	1	2	3	4	5
y

(b) On the grid provided draw the graph y = x² — 4x + 2 for 0≤ x ≤ 5. Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis. (3 marks)

(c) Use the graph to solve the equation, x² — 4x + 2 = 0 (2 marks)

(d) By drawing a suitable line, use the graph in (b) to solve the equation A-2 — 5x + 3 = O. (3 marks)

19. (a) The table below shows the frequency distribution of heights of 40 plants in a tree nursery.

(a) State the modal class. (1 marks)

(b) Calculate:

(i) the mean height of the plants; (3 marks)

(ii) the standard deviation of the distribution. (4 marks)

(c) Determine the probability that a plant taken at random has a height greater than 40 cm. (2 marks)

20. (a) Using a ruler and a pair of compasses only, construct: (i) a parallelogram ABCD, with line AB below as part of it, such that AD = 7 cm and angle BAD = 600; (3 marks)

(ii) the locus of points equidistant from AB and AD; (1 mark)

(iii) the perpendicular bisector of BC. (1 mark) (b) (i) Mark the point P that lies on DC and is equidistant from AB and AD. (1 mark)

(ii) Measure BP. (1 mark)

(c) Describe the locus that the perpendicular bisector of BC represents. (1 mark)

(d) Calculate the area of trapezium ABCP. (2 marks)

21. The table below shows some values of the curves y = 2 cos x and y = 3 sin x.

(a) Complete the table for values of y = 2 cos x and y = 3 sin x, correct to 1 decimal place. (2 marks)

On the grid provided, draw the graphs of y = 2 cos x and y = 3 sin x for 0° x 360°, on the same axes. (5 marks)

(c) Use the graph to find the values of x when 2 cos x — 3 sin x = 0 (2 marks)

(d) Use the graph to find the values of y when 2 cos x = 3 sin x. (1 marks)

22. The figure below is a model of a watch tower with a square base of side 10 cm. Height PU is 15 cm and slanting edges UV = TV = SV = RV = 13 cm.

Giving the answer correct to two decimal places, calculate:

(a) length MP; (2 marks)

(b) the angle between MU and plane MNPQ; (2 marks)

(c) Length of VO; (3 marks)

(d) The angle between planes VST and RSTU; (3 marks)

23. The table below shows monthly income tax rates for a certain year.

In that year a monthly personal tax relief of Ksh 1 280 was allowed. In a certain month of that year, Sila earned a monthly basic salary of Ksh 52 000, a house allowance of Ksh 7 800 and a commuter allowance of Ksh 5 000.

(a) Calculate:

(i) Sila’s taxable income;(3 marks)

(ii) the net tax payable by Sila in that month;(5 marks)

(b) In July that year, Sila’s basic salary was raised by 4%. Determine Sila’s net salary in July.(3 marks)

24 A hotel buys beef and mutton daily. The amount of beef bought must be at least 30kg and that of mutton at least 20 kg. The total mass of beef and mutton bought should not exceed 100 kg. The beef is bought at Ksh 360 per kg and the mutton at Ksh 480 per kg.

The amount of money spent on both beef and mutton should not exceed Ksh 43 200 per day. Let x represent the number of kilograms of beef and y the number of kilograms of mutton.

(a) Write the inequalities that represent the above information.(3 marks)

(b) On the grid provided, draw the inequalities in (a) above.(3 marks)

(c) The hotel makes a profit of ksh 50 on each kg of beef and ksh 60 on each kg of mutton.Determine the maximum profit the hotel can make(3 marks)

2018 Mathematics Paper 2

1. Given that 2 log x²+log = k log x, find the value of k. (2 marks)

2 log x²+log√x=klogx

log(x⁴x^1/2

=logx^k

k=1/2

2. A variable P varies directly as t³ and inversely as the square root of s. When t = 2 and s = 9, P = 16. Determine the equation connecting P, t and s, hence find P when s = 36 and t=3. (4 marks)

3. Asia invested some money in a financial institution. The financial institution offered 6% per annum compound interest in the first year and 7% per annum in the second year. At the end of the second year, Asia had Ksh 170 130 in the financial institution. Determine the amount of money Asia invested. (3 marks)

p²=170130

p²=170130/1.07

=Ksh 150000

4. The figure below represents a wedge ABCDEF. EF 10 cm, angle FBE 45° and the angle between the planes ABFE and ABCD is 20°.

Calculate length BC, correct to l decimal place.(3 marks)

BF = 10 B1

Cos 20‘ BC/10

BC=10 Cos 20º

=9.4 cm

5. Simplify √ 54 + ∛ 3/ √ 3 (2 marks)

6. In the figure below, AB is a tangent to the circle, centre O and radius 6 cm. The arc AC subtends an angle of 60° at the centre of the circle.

Calculate the area of the shaded region, correct to 1 decimal place. (4 marks)

AB=6tan 60º or OB = 6/cos69

Area of triangle OAB =1/2x60x 6tan 60º

Area of sector OAC=60/360 x π x 6²

Area of shaded part = 31.18 —18.85

— 12.3 cm²

7. Use completing the square method to solve 3x² + Sx — 6 = 0, correct to 3 significant figures.(3 marks)

8. Three workers, working 8 hours per day can complete a task in 5 days. Each worker is paic Ksh 40 per hour. Calculate the cost of hiring 5 workers if they work for 6 hours per day tc complete the same task. (3 marks)

W : H : D

3 : 5 😡

No. of Days = 5x 8/6×3/5

=4days

cost=5x6x4x40

=Ksh4800

9. The table below represents a relationship between two variables x and y.

x	1	2	3	4	5	6
y	3.5	4.5	8.0	8.5	11	13

(a) On the grid provided draw the line of best fit.(3 marks)

(b) Use the graph to find the value off when x — 0.(1 marks)

When = 0, y = 1

10. State the amplitude and the phase angle of the curve y = 2sin x — 30° .(2 marks)

Amplitude = 2

Phase angle = 30°

11. The mass, in kilograms, of 9 sheep in a pen were: 13, 8, 16, 17, 19, 20, 15, 14 and 11.

Determine the quartile deviation of the data. (3 marks)

12. The position of two points C and D on the earth’s surface are (8°N, l 0OE) and (8°N, 30°E) respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. (3 marks)

Longitude difference = 30 — 10 = 20°

600 — 20 x 60 Cos B

Cos 8 = 0.5

8 = 60°

Latitude = 60°N

13. In the figure below OP — p, OR = r, PQ:QR = 1:2 and PS = 3PR.

Express QS in terms of p and r. (4 marks)

14. In a certain firm there are 6 men and 4 women employees. Two employees are chosen at random to attend a seminar. Determine the probability that a man and a woman are chosen. (3 marks)

P(MW or WM) =6/10 + 4/9 + 4/10 + 6/9

24/90+24/90

=8/15

15. Triangle OAB is mapped onto triangle OA’B’ with vertices O(0,0), A’(18,0) and B'(18, 6). Find the area of triangle OAB. (3 marks)

16. Find the value of k if

Section II

Answer any 5 questions from this section

17. The 5th and 10th terms of an arithmetic progression are 18 and —2 respectively. (a) Find the common difference and the first term. (4 marks)

a + 4d= 18

a + 9d= — 2

5d = —20

a = 34

(b) Determine the least number of terms which must be added together so that the sum of the progression is negative. Hence find the sum. (6 marks)

18.Complete the table below for the equation y=x²-4x+2

(2 marks)

x	0	1	2	3	4	5
y

(b) On the grid provided draw the graph y = x² — 4x + 2 for 0≤ x ≤ 5. Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis. (3 marks)

(c) Use the graph to solve the equation, x² — 4x + 2 = 0 (2 marks)

x=0.6± 0.05

x=3.4 ± 0.05

(d) By drawing a suitable line, use the graph in (b) to solve the equation A-2 — 5x + 3 = O. (3 marks)

19. (a) The table below shows the frequency distribution of heights of 40 plants in a tree nursery.

(a) State the modal class. (1 marks)

Model Class 30 – 40

(b) Calculate:

(i) The mean height of the plants; (3 marks)

(ii) the standard deviation of the distribution. (4 marks)

(c) Determine the probability that a plant taken at random has a height greater than 40 cm. (2 marks)

No. of plants whose height>40 = 4+2=6

p(height>40cm)=6/40=0.15

20. (a) Using a ruler and a pair of compasses only, construct:

(i) a parallelogram ABCD, with line AB below as part of it, such that AD = 7 cm and angle BAD = 600; (3 marks)

(ii) the locus of points equidistant from AB and AD; (1 mark)

Angle bisector of (iii) the perpendicular bisector of BC. (1 mark)

bisector of BC ✓ drawn

(b) (i) Mark the point P that lies on DC and is equidistant from AB and AD. (1 mark)

Point P identified and ✓ marked on line DC

(ii) Measure BP. (1 mark)

BP = 7 ± O. 1 cm

(c) Describe the locus that the perpendicular bisector of BC represents. (1 mark)

Locus of Points equidistant from B and C

(d) Calculate the area of trapezium ABCP. (2 marks)

21. The table below shows some values of the curves y = 2 cos x and y = 3 sin x.

(a) Complete the table for values of y = 2 cos x and y = 3 sin x, correct to 1 decimal place. (2 marks)

On the grid provided, draw the graphs of y = 2 cos x and y = 3 sin x for 0° x 360°, on the same axes. (5 marks)

(c) Use the graph to find the values of x when 2 cos x — 3 sin x = 0 (2 marks)

2cosx-3sinx=0

=2cosx=3sinx

x=34° and x=214°

(d) Use the graph to find the values of y when 2 cos x = 3 sin x. (1 marks)

y=1.6 and y = -1.6

22. The figure below is a model of a watch tower with a square base of side 10 cm. Height PU is 15 cm and slanting edges UV = TV = SV = RV = 13 cm.

Giving the answer correct to two decimal places, calculate:

(a) length MP; (2 marks)

MP²=10²+10²

MP=√ 200 =14.14

(b) the angle between MU and plane MNPQ; (2 marks)

(c) Length of VO; (3 marks)

(d) The angle between planes VST and RSTU; (3 marks)

23. The table below shows monthly income tax rates for a certain year.

In that year a monthly personal tax relief of Ksh 1 280 was allowed. In a certain month of that year, Sila earned a monthly basic salary of Ksh 52 000, a house allowance of Ksh 7 800 and a commuter allowance of Ksh 5 000.

(a) Calculate:

Taxable income = 52000 + 7800 + 5000 = Ksh 64800

(i) Sila’s taxable income;(3 marks)

Tax payable 11180×0.1=1118

10534x 0.15 =1580.10

10534 x0.2 = 2106.80

10534x 0.25 = 2633.50

22018x 0.3 = 6605.4

Total tax = 14043.8

(ii) the net tax payable by Sila in that month;(5 marks)

Net tax = 14043.8 —1280 = 12763.8

(b) In July that year, Sila’s basic salary was raised by 4%. Determine Sila’s net salary in July.(3 marks)

Additional tax = 4/100 x 52000 x 0.3 100 = Ksh 624

40 Net salary = 64800 — 12763.8 — 624 + (4/100 x 52 000)

= Ksh 53492.20

24 A hotel buys beef and mutton daily. The amount of beef bought must be at least 30kg and that of mutton at least 20 kg. The total mass of beef and mutton bought should not exceed 100 kg. The beef is bought at Ksh 360 per kg and the mutton at Ksh 480 per kg.

The amount of money spent on both beef and mutton should not exceed Ksh 43 200 per day. Let x represent the number of kilograms of beef and y the number of kilograms of mutton.

(a) Write the inequalities that represent the above information.(3 marks)

x≥30; y≥20

x+y=≤100

360x+480≤43200 0r 3x+4y≤360

(b) On the grid provided, draw the inequalities in (a) above.(3 marks)

(c) The hotel makes a profit of ksh 50 on each kg of beef and ksh 60 on each kg of mutton. Determine the maximum profit the hotel can make (3 marks)

objective function = 50x+60y

profit=50×60+60×60

=5600

KCSE Past Papers Mathematics 2018 (121/1)

kcse Mathematics Alt A – Paper 1 – November 2018 – 2.5 Hours

Kenya Certificate of Secondary Education

2018 Mathematics Paper 1

Section I (50 marks)

Answer all the questions in this section.

1. Without using a calculator, evaluate:(3 marks)

2. Given that 6 ^2n-3= 7776, find the value of n. (3 marks)

3. The base of a right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 130 cm. Calculate the volume of the pyramid. (3 marks)

4. In the figure below ABCDEF is a uniform cross section of a solid. Given that FG is one of the visible edges of the solid, complete the sketch showing the hidden edges with broken lines.

5. The lengths of three wires were 30m, 36 m and 84m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained. (4 marks)

6. A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number. (4 marks)

7. (a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle. (2 marks)

(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres. (2 marks)

8. Given that OA = 3 and OB = . Find the mid point M of AB.

9. Two towns R and S are 245 km apart. A bus travelling at an average speed of 60 km/h left tow: R for town S at 8.00 a.m. A truck left town S for town R at 9.00 a.m and met with the bus c 11.00a.m. Determine the average speed of the truck. (4 marks)

10. In the parallelogram WXYZ below, WX = 10 cm, XY = 5 cm and WXY = 150°.

Calculate the area of the parallelogram. (3 marks)

11. Without using mathematical tables or a calculator, evaluate sin 30°-sin60 °/tan60°(3 marks)

12. Use matrix method to solve: 5x + 3J = 35

3x — 4y — —8

(3 marks)

13. Expand and simplify.

(2x + 1)² + (x — 1)(x — 3).(2 marks)

14. Use mathematical tables to find the reciprocal of 0.0247, hence evaluate

𢆳.025/0.1247 correct to 2 decimal places.(3 marks)

15. A Kenyan businessman intended to buy goods worth US dollar 20 000 from South Africa Calculate the value of the goods to the nearest South Africa (S.A) Rand given that 1 US dollar = Ksh 101.9378 and 1 S.A Rand = Ksh 7.6326. (3 marks)

16. A photograph print measuring 24cm by 15 cm is enclosed in a frame.

A uniform space of width x cm is left in between the edges of the photograph and the frame. If the area of the space i‹ 270cm’, find the value ofx. (3 marks)

Section II (50 marks)

Answer any five questions from this section.

17. A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.

(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (4 marks)

(b) Find the capacity of the tank, in litres, correct to the nearest litre. (3 marks)

(c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water. (3 marks)

18. Two vertices of a triangle ABC are A (3,6) and B (7,12).

(a) Find the equation of line AB.(3 marks)

(b) Find the equation of the perpendicular bisector of line AB.(4 marks)

(c) Given that AC is perpendicular to AB and the equation of line BC is y = -5x + 47, find the co-ordinates of C. (3 marks)

19. The distance covered by a moving particle through point O is given by the equation, s = t³ – 15t² + 63f — 10.

Find:

(a) distance covered when f = (2 marks)

(b) the distance covered during the 3rd second;(3 marks)

(c) the time when the particle is momentarily at rest;(3 marks)

(d) the acceleration when t — 5.(2 marks>

20. The diagram below shows triangle ABC with vertices A(— 1, —3), B(1, — 1) and C(0,0), and line M.

(a) Draw triangle A’B’C’ the image of triangle ABC under a reflection in the line M. (2 marks)

(b) Triangle A“B“C“ is the image of triangle A’B’C’ under a transformation represented by the matrix T = (1 2) (0 1)

(i) Draw triangle A”B”C“ (3 marks)

(ii) Describe fully the transformation represented by matrix T. (3 marks)

(iii) Find the area of triangle A’B’C’ hence find area of triangle A“B“C”. (2 marks)

21. The figure below shows two triangles, ABC and BCD with a common base BC = 3.4 cm. AC = 7.2 cm, CD = 7.5 cm and ABC = 90°.

The area of triangle ABC = Area of triangle ∠BCD.

Calculate, correct to one decimal place:

(a) the area of triangle ABC;(3 marks)

(b) the size of ∠BCD; (3 marks)

(c) the length of BD;(2 marks)

(d) the size of ∠BDC.(2 marks)

22. (a) On the grid provided, draw the graph of y = 4-1/4x²for -4 ≤ x ≤ (2 marks)

(b) Using trapezium rule, with 8 strips, estimate the area bounded by the curve and the z-axis. (3 marks)

(c) Find the area estimated in part (b) above by integration. (3 marks)

(d) Calculate the percentage error in estimating the area using trapezium rule. (2 marks)

23. Three business partners Abila, Bwire and Chirchir contributed Ksh 120 000, Ksh 180 000 and Ksh 240 000 respectively, to boost their business.

They agreed to put 20% of the profit accrued back into the business and to use 35% of the profits for running the business (official operations).

The remainder was to be shared among the business partners in the ratio of their contribution. At the end of the year, a gross profit of Ksh 225 000 was realised.

(a) Calculate the amount:

(i) put back into the business;(2 marks)

(ii) used for official operations.(1 marks)

(b) Calculate the amount of profit each partner got.(4 marks)

(c) If the amount put back into the business was added to individuals’s shares proportionately to their initial contribution, find the amount of Chirchir’s new shares. (3 marks)

24. The equation of a curve is given as y=1/3x³-4x+5 Determine:

(a) The value of y when x = 3; (2 marks)

(b) The gradient of the curve at x = 3; (3 marks)

(c) The turning points of the curve and their nature. (5 marks)

 

Questions and Answers

2018 Mathematics Paper 1

1. Without using a calculator, evaluate:(3 marks)

2. Given that 6 ^2n-3= 7776, find the value of n. (3 marks)

7776 = 6⁵

66^2n-3 = 6⁵

2n —3 = 5

n = 4

3. The base of a right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 130 cm. Calculate the volume of the pyramid. (3 marks)

Height h = √ 130² – 50²

= l20cm

Volume=1/3 x80x 60 x 120

192000cm²

4. In the figure below ABCDEF is a uniform cross section of a solid. Given that FG is one of the visible edges of the solid, complete the sketch showing the hidden edges with broken lines.

5. The lengths of three wires were 30m, 36 m and 84m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained. (4 marks)

30 = 3x 2 x 5

36 = 2 x 2 x 3 x 3

84 = 2 x 2 x 3 x 7

G.C.D. —— 2 x 3 M1

= 6 AI

No of pieces obtained

30/6 + 36/6 + 84/6

= 25

6. A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number. (4 marks)

x+y=13

(l0y + x) – (l0x + y) = 9 or — x+ y = 1

x+y=13

y-x=1/2y=14

y=7

x=6

7. (a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle. (2 marks)

(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres. (2 marks)

RS= (7.8 ± 0.1) cm

Actua x 40m

= 312 ± 4m

8. Given that OA = (2/3) and OB = (-4/5)

Find the mid point M of AB.

9. Two towns R and S are 245 km apart. A bus travelling at an average speed of 60 km/h left tow: R for town S at 8.00 a.m. A truck left town S for town R at 9.00 a.m and met with the bus c 11.00a.m. Determine the average speed of the truck. (4 marks)

Distance covered by truck = 245 — 60 x 3

=65km

Time taken by the track = 11-9 = 2h

Average speed of truck

65/2

35.5km/hr

10. In the parallelogram WXYZ below, WX = 10 cm, XY = 5 cm and WXY = 150°.

Calculate the area of the parallelogram. (3 marks)

h = 5 sin 30°

= 2.5cm

Area = 2.5 x 10

=25cm³ 11. Without using mathematical tables or a calculator, evaluate sin 30°-sin60 °/tan60°(3 marks)

12. Use matrix method to solve: 5x + 3J = 35

3x — 4y — —8

(3 marks)

x=4

y=5

13. Expand and simplify.

(2x + 1)² + (x — 1)(x — 3).(2 marks)

(2x+1)’ +(x—1)(x—3) = 4x² + 4x + 1+ x² -4x + 3

= 5² + 4

14. Use mathematical tables to find the reciprocal of 0.0247, hence evaluate

𢆳.025/0.1247 correct to 2 decimal places.(3 marks)

15. A Kenyan businessman intended to buy goods worth US dollar 20 000 from South Africa Calculate the value of the goods to the nearest South Africa (S.A) Rand given that 1 US dollar = Ksh 101.9378 and 1 S.A Rand = Ksh 7.6326. (3 marks)

20000 dollars = 20000 x 101.9378

= Ksh. 2038756

In S.A. rand 20000 x 101.93.78/7.6326

=267112 rands

16. A photograph print measuring 24cm by 15 cm is enclosed in a frame.

A uniform space of width x cm is left in between the edges of the photograph and the frame. If the area of the space is 270cm², find the value ofx. (3 marks)

Area of space = 2x(15 +2x)z + 2×24 x

30a + 4x² + 48x — 270

4x² + 78x — 270 = 0

4x² — 12 + 90 — 270 = 0

4x(x — 3) + 90(z — 3) — 0

4x(x — 3) + 90(x — 3 = 0

(4x + 90)(z — 3) = 0

x =- 22.5 or x = 3

Section II (50 marks)

Answer any five questions from this section.

17. A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively.

(a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (4 marks)

(b) Find the capacity of the tank, in litres, correct to the nearest litre. (3 marks)

Volume = 1/3πR²H – 1/3πr²h

1/3xπx12²x14.4-1/3πx6²x7.2

= 1900.0 m³

Capacity = 1900 x 1000 litres

= 1900000 litres

(c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water. (3 marks)

Amount used by students per day. =40 x 500

=20000 litres

=No. of days = 1900000

=20000

= 95 days

18. Two vertices of a triangle ABC are A (3,6) and B (7,12).

(a) Find the equation of line AB.(3 marks)

(b) Find the equation of the perpendicular bisector of line AB.(4 marks)

(c) Given that AC is perpendicular to AB and the equation of line BC is y = -5x + 47, find the co-ordinates of C. (3 marks)

19. The distance covered by a moving particle through point O is given by the equation, s = t³ – 15t² + 63f — 10.

Find:

(a) distance covered when f = (2 marks)

S⁽²⁾= 2 ³ – 15(2)² + 63(2) —10

— 8 — 60 +126 —10

= 64

(b) the distance covered during the 3rd second;(3 marks)

S_(s) = 3³ —15(3)² + 63(3) — 10

= 27 — 135 + 189 — 10

= 71

Distance in 3rd second

S₍₃₎ — S₍₂₎ = 71 – 64

= 7

(c) the time when the particle is momentarily at rest;(3 marks)

V=ds/dt = 3t<sup2< sup=””> — 30t + 63 = 0</sup2<>

t² -10t + 21 = 0

(t —3)(t—7) = 0

t = 3 or t = 7

(d) the acceleration when t = 5 (2 marks>

Acceleration = dv/dt = 6t — 30 = 6(5) — 30

= 0

20. The diagram below shows triangle ABC with vertices A(— 1, —3), B(1, — 1) and C(0,0), and line M.

(a) Draw triangle A’B’C’ the image of triangle ABC under a reflection in the line M. (2 marks)

(b) Triangle A“B“C“ is the image of triangle A’B’C’ under a transformation represented by the matrix T = (1 2) (0 1)

(i) Draw triangle A”B”C“ (3 marks)

(ii) Describe fully the transformation represented by matrix T.(3 marks)

• It’s a shear,
• The x axls invariant
• point B’(—2, 2) is mapped onto B”(2, 2)(iii) Find the area of triangle A’B’C’ hence find area of triangle A“B“C”. (2 marks)

  Area of triangle A’B’C’= 1/2 (3 + I) x 2 — 1.5 — 0.5

  = 4 — 2

  = 2 sq units

  Area of A’B’C’ = Area of A’B’C’

  = 2 square units

  21. The figure below shows two triangles, ABC and BCD with a common base BC = 3.4 cm. AC = 7.2 cm, CD = 7.5 cm and ABC = 90°.

  The area of triangle ABC = Area of triangle ∠BCD.

  

  Calculate, correct to one decimal place:(a) the area of triangle ABC;(3 marks)

  AB =√ 7.2² – 3.4² = 6.3cm Area of ∆ ABC 1/2x 6.3 x 3.4

  = 10.7 cm²

  (b) the size of ∠BCD; (3 marks)

  Area of ∆ ABC = Area of � 1/2 x 3.4 x 7.5 x sinθ = 10.7

  Sin θ =10.7 x 2 /3.4 x 7.5

  θ = 57. 1

  Obtuse Angle BCD = 180 – 57.1

  = 122.9

  (c) the length of BD;(2 marks)

  BD² = 7.5² + 3.4² — 2 x 3.4 x 7.5cos 122.9

  = 95.51

  BD = 9.8cm

  (d) the size of ∠BDC.(2 marks)

  Angle BDC: 3.4/Sin 8 = 9.8/Sin 122.9

  Sin 0 = 3.4sin122.9/9.8

  0 = 16.9°

  22. (a) On the grid provided, draw the graph of y = 4-1/4x²for -4 ≤ x ≤ (2 marks)

  
  

  (b) Using trapezium rule, with 8 strips, estimate the area bounded by the curve and the z-axis. (3 marks)Area — =1/2 x1(0 + 0 + 2(1.75 + 3 + 3.75 + 4 + 3.75 + 3 +1.75)

  =1/2x1x2x21

  = 21 sq units

  (c) Find the area estimated in part (b) above by integration. (3 marks)

  

  (d) Calculate the percentage error in estimating the area using trapezium rule. (2 marks)

  

  23. Three business partners Abila, Bwire and Chirchir contributed Ksh 120 000, Ksh 180 000 and Ksh 240 000 respectively, to boost their business.They agreed to put 20% of the profit accrued back into the business and to use 35% of the profits for running the business (official operations).

  The remainder was to be shared among the business partners in the ratio of their contribution. At the end of the year, a gross profit of Ksh 225 000 was realised.

  (a) Calculate the amount:

  (i) put back into the business;(2 marks)

  20/100 x 225000

  = 45000

  (ii) used for official operations.(1 marks)

  35 /100 x 225000

  =78750

  (b) Calculate the amount of profit each partner got.(4 marks)

  Amount for each contribution ratio contributions: Abiro: Bwire: Chirchir

  120000:180000:240000

  = 2 : 3 : 4

  (c) If the amount put back into the business was added to individuals’s shares proportionately to their initial contribution, find the amount of Chirchir’s new shares. (3 marks)

  Abila 2/9 x 45/100 x 225 000

  = 22500

  Bwire 3/9 x 45/100 x 225000

  33750

  Chirchir = 4/9 x 45/100 x 225000

  45000

  24. The equation of a curve is given as y=1/3x³-4x+5 Determine:

  (a) The value of y when x = 3; (2 marks)

  y = 1/3x³4x+5

  When x-3

  y = 1/3(3)³4(2)+5

  =2

  Gradient at x = 3

  (b) The gradient of the curve at x = 3; (3 marks)

  dy/dx=x²-4

  at x = 3

  dy/dx=(3)²-4

  =5

  (c) The turning points of the curve and their nature. (5 marks)