solving problems kcse mathematics paper 1

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Solving Problems KCSE Mathematics Paper 1

KSh  1,155.00

Solving problem. — KCSE Mathematics Paper I contains a total of 672 questions in 28 KCSE model examination papers. It is divided into three parts

Part cam contains 10 solved KCSE model examination papers with a full marking scheme. In the marking scheme, alongside each solved question, the type of mark and the reason for awarding that mark is given at the stage where the mark matures. This is intended to instill the importance of ‘method’ in working out Mathematics questions. The Author has selected the simplest method of solving each question. Alternative methods of solving the same questions may exist. Finding these methods has been left out deliberately as a challenge to the reader.

Part two contains 18 unsolved KCSE model examination papers which are set in line with the solved KCSE model examination papers of part one. This is intended to provide the reader with ample practice exercises.

Part three contains answers to the unsolved KCSE model examination papers.

ISBN: 9966 49 653 X

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MATHEMATICS KCSE 2021 PAPER 1 MARKING SCHEME

6.In a race Kipsang maintained an average speed of \(5m/s\).When he was \(310 m\) to the finishing line, Mutunga was \(50 m\) behind him. However Mutunga finished the race \(10 m\) ahead of kipsang. Determine Mutunga's average speed

A table is sold at Kshs. 4500 and a chair at Kshs.2000 . A saleman earns a commission of 8\% on every table and 5\% on every chair sold. On a certain week he sold 3 more chairs than tables and his total earnings were Kshs. 3980. Determine the number chairs he sold that week. 3mks

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Mathematics Paper 1 Question Paper Sort by: Number   Topics

Section a (50 marks).

Oketch sells his car to Jane and makes a profit of 17%. Jane sells the same car to Issa at Sh.300, 000, making a loss of 10%. Determine the price at which Oketch bought the car.

Mr. Owino spends 1/4 of his salary on school fees. He spends 2/3 of the remainder on food and a fifth of what is left on transport. He saves the balance. In a certain month he saved Sh.3400.

What is his salary?

A straight line passes through points A (-2, 6) and B (4, 2). a) M is the midpoint of line AB. Find the co-ordinates of M.

In a book store, books packed in cartons are arranged in rows such that there are 50 cartons in the first row, 48 cartons in the next row, 46 in the next and so on. a) How many cartons will be there in the 8th row?

b) If there are 20 rows in total, find total number of cartons in the book store.

A rectangle whose area is 96m2 is such that its length is 4m longer than its width. Find a) Its dimensions

b) Its perimeter

In triangle ABC below, AC=BC, AB is parallel to DE, AB=15cm, DE=7.5cm and BE=6cm.

a) Length CE

b) Area of quadrilateral ABED.

A salesman gets a commission of 2.4% on sales up to sh.100, 000.He gets additional commission of 1.5% on sales above this. Calculate the commission he gets for sales worth sh.280, 000.

A bus and a car leave Nairobi at 7.30am and 9.30am respectively. If their speeds are 60km/h and 100km/h respectively, find the time when the car catches up with the bus.

The table below shows the number of children per house in a certain village.

(i) The mean number of children per house to the nearest whole number.

(ii) The median

. Solve the inequality below and state the integral values of your solution.

A measuring cylinder of radius 5cm contains water whose level reads 6cm high. A spherical object is immersed in the water and the new level reads 10cm. Calculate the radius of the spherical obj

Solve the equation

SECTION B (50 Marks)

The table below shows marks scored by a class in a math test.

a) Draw a histogram for the distribution above, on a graph paper.

b) i) State the group in which the median lies.

ii) A vertical line drawn through the median mark divides the total area of the Histogram into 2 equal parts. Using the information, estimate the median mark.

Karis owns a farm that is triangular in shape as shown below

a) Calculate the size of angle BAC.

b) Find the area of the farm in hectares.

c) Karis wishes to irrigate his farm using a sprinkler machine situated in the farm

such that it is equidistant from points A,B and C.

i) Calculate the distance of the sprinkler from point C.

ii) The sprinkler rotates in a circular motion so that the maximum point reached by

the water jets is the vertices A,B, and C. Calculate the area outside his farm that

will be irrigated.

The diagram below is a right pyramid on a rectangular base.

Given that the volume of the solid is 280m3 and its base area is 60cm2 and that AB:BC=3:5, determine

i) the height of the pyramid.

ii) the length and width of the base.

iii) the slant edge of the pyramid

Triangle ABC has vertices A(-5,-3),B(-3,-5) and C(-3,-1).

a) Plot triangle ABC and its image A1B1C1 under reflection in the line y=-x. (3mks)

PASTE GRAPH

b) A II B II C II is the image of AIBICI under rotation centre (0,0) through a positive quarter turn. Plot A 11 B 11 C 11 and state its co-ordinates.

c) A 3 B 3 C 3 with coordinates A 3 ( 7.5,-4.5),B3(4.5,-7.5) and C 3 (4.5,-1.5) is the image of A 11 B 11 C 11 under a certain transformation. Plot A 3 B 3 C 3 and describe this transformation. (2mks)

d) A 4 (5,-1.5) is the image of A 3 under translation. State the co-ordinates of B 4 and C 4.

. Maru Secondary School consumes 40 bags of maize and 25 bags of beans per term. Kadu Secondary School consumes 35 bags of maize and 18 bags of beans per term. The schools purchase the grains from the same grain store. Maru pays sh.380,000 while Kadu pays sh.301,500 for the grains.

a) Write down two equations representing the cost of grains in the two schools.

b) Using matrix method , calculate the cost of each bag of maize and beans.

c) The following term the price of each bag of maize increased by 20% while that of beans decreased by 15%.

i) How much did Maru pay for the grains?

ii) If the school enrolment increased by 10% and the food ration also increased proportionally, how much would the school spend on the grains?

A ship leaves port M and sails on a bearing of 0500 heading towards Island L. Two navy destroyers sail from a noval base N to intercept the ship. Destroyer A sails such that it covers the shortest distance possible. Destroyer B sails on a bearing of 200 to L. If the bearing of N from M is 1000 and distance NM=300Km, Using a scale of 1cm to represent 50Km, determine

i) the positions of M,N and L.

ii) the distance travelled by destroyer A.

iii) the distance travelled by destroyer B.

iv) the bearing of N from L.

The table below shows values for the function

a) Complete the table above.

PASTE A GRAPH

c) Use your graph to solve the equation. i) 5+8x-2x 2 =0

ii) -2x 2 +5x+3=0

d) State the equation of the line of symmetry of the curve y=5+8x-2x 2

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Mathematics Paper 1 Questions and Answers - KCSE 2022 Past Papers

Next Topic » Mathematics Paper 2 Questions and Answers - KCSE 2022 Past Papers

SECTION I (50 marks)

Answer all the questions in this section in the spaces provided.

• Solve for n 6n / n-1 = 25 / n (3 marks)
• A family used two-fifths of its monthly income on school fees. Three-quarters of the remaining amount was used on family upkeep while the rest was invested. The family invested Ksh 13 500 monthly.Calculate the amount of money the family used on school fees every month. (4 marks)
• Solve for x in the equation. 5 2x-1 -25 x = 500 (3 marks)
• Determine the number of laps that Tanui had to run to complete the race after they were together. (3 marks)
• Simplify 18ax-(3a-4x)(3a+4x)    (3mrks)            3a-8x 

• A watch loses 8 seconds every hour. It was set to read the correct time at 1100 h on Sunday. Determine the time, in a 12-hour system, the watch will show on the following Thursday when the correct time is 0500 h. (3 marks)
• A lorry left town A for town B and maintained an average speed of 50 km/h. A car left town A for town B 42 minutes later and maintained an average speed of 80 km/h. At the time the car arrived in town B, the lorry had 25 km to cover to town B. Determine the distance between town A and B. (3 marks)
• Port L is 120 km on a bearing of $30°W from port K. A ship left port K at 1000 h and sailed at a speed of 40 km/h along the bearing of S60°E. Using scale drawing, determine the bearing of the ship from port L at 1400 h. (4 marks)
• The image of P(-2, 5) under a translation T is P'(2, 2). Q'(9, -5) is the image of Q under the same translation T. Determine the coordinates of Q. (3 marks)
• An electric post erected vertically is 20m from point P on the same level ground. The angle of elevation of the top, T, of the post from P is 30°. Given that S is the mid point of the post, calculate, correct to I decimal place, the angle of elevation of S from P. (3 marks)

• The capacities of two similar containers are 54 ml and 250 ml respectively. The difference in the heights of the two containers is 4 cm. Calculate the height of the larger container. (3 marks)
• The base, ABCDEF, of a right pyramid is a regular hexagon of side 2.5 cm. Point V is the vertex of the pyramid and the length of the slanting edges is 4 cm.Draw a labelled net of the pyramid. (3 marks)

SECTION 11 (50 marks)

Answer only five questions in this section in the spaces provided.

• Calculate the amount of money that was paid to Wema.(2 marks)
• For every 8 tonnes of stones Wema transported to site A, he spent Ksh 3000.Calculate the profit Wema made. (3 marks)
• Tatu transported the remaining 48 tonnes of stones to site B, a distance of 84 km. If Tatu made 44% profit, calculate the amount of money Tatu spent to transport the stones. (3 marks)
• Determine the ratio of the profit made by Wema to that made by Tatu. (2 marks)
• Determine the radius of the shot put, correct to I decimal place. (3 marks)
• Find the volume of the water in the bucket.(3 marks)
• The shot put ball is completely submerged in the water in the bucket. Calculate the new height of the water in the bucket.(4 marks)
• the equation of line AC in the form ar+by+c=0, where a, b and c are integers.(4 marks)
• the coordinates of point C.(3 marks)
• line passes through point A and is parallel to line BC. Determine the x-intercept of the line.(3 marks)

• locate point D on line AX such that AD: DX=3:1. (3 marks)
• complete trapezium ABCD such that line DC is parallel to line AB and angle ABC = 67.5°. (3 marks)
• draw a perpendicular line from D to meet AB at E. Measure DE. (2 marks)
• Calculate the area of the trapezium ABCD. (2 marks)

• the mediam amount of money spent on airtime bye 30 peope.  (3marks)
• the number of people who spent  more than Ksh 41.50 on airtime over that period . (2marks)

MARKING SCHEME 

SECTION  1 (50mark )

answer all the  queastions in the spaces provided 

• Solve  for 6n / n-1 = 25 / n n(6n)=25(n-1) 6n²-25n+25=0    m1 6n²-15n-10n+25=0 (3n-5)(2n-5)=0 3n-5=0 ⇒n= 5 / 3  = 1 2 / 3 or 2n-5=0⇒ n= 5 / 2 =2 1 / 2
• Afamily used two-fifths of its monthly income on school fees. Three-quaters of the remaining  amount was used on family upkeep while the rest was  invested . The family invested Ksh13500 monthly . calculate the amount of money the family used on school fees every month .     (4marks) Fees=  2 / 5 ,  rem= 5 / 5 - 2 / 5 = 3 / 5 upkeep= 3 / 4 × 3 / 5 = 9 / 20 ,  rem= 3 / 5 - 9 / 20 = 3 / 20 invest. = 3 / 20 =13500             = 2 / 5 ×13500× 20 / 3                =ksh36,000
• Solve for x in the equation  5 2x - 1  - 25 x =500 5 2x-1 -5 2x =500 5 2x ,5 1 - 5 2x  =500 let 5 2x be k ∴ 1 / 5  k - k =500 -4 / 5 k = 500 k =500× 5 / 4 = -62 5 2x = −625 5 2x = −5 x is indeterminate
• Kipkoech and Tanui began a 5000m race together at the starting line .kipkoech and Tanui took 72 seconds and 80seconds respectively to to run a 400m lap .The two athletes were together againat the starting line after some time. Determine the number of laps thatTanui had to run to complete the race after they were together.  Time taken to be together again ; L.C.M =2 4 ×3²×5=720sec No. of laps made  by Tanui= 720 / 80 =9 Remaining laps = 5000 / 400  =9 =3 1 / 2 
• Simplify 18ax−(3a−4a)(3a+4x)                        3a−8x (3a−4x)(3a+4x) =9a² −16² 18ax−(9a−16x²) = 16x²+18ax −9a²         3a−8x                 3a−8x = 16x² +24ax -6ax -9a²               3a-8x = (2x+3a)(8x-3a)             -1(8x-3a) = -2x-3a

• A watch loses 8 seconds  every hour . it was set to read the correct time at 1100h on sunday . Determine the time  12-hours system , the watch will show on the following thusday when the correct time is 0500     (3marks) 1100h sun →1100h wed =24×3 = 72hrs 1100h wed →0500hthus =18h Total =18+72=90h time lost = 90×8 =12mins                    60 Time on thur=5:00a.m −12min                      =4:48a.m
• A lorry left town A for town B and maintained an average speed of 50 km/h. A car left town A for town B 42 minutes later and maintained an average speed of 80 km/h. At the time the car arrived in town B, the lorry had 25 km to cover to town B. Determine the distance between town A and B. (3 marks) A←–——————→B Time taken by car = x / 80 h Distance by lory =50× 42 / 60 +50×( x / 80 ) =(x−25)                              0.625x+35=x−25                             (1−0.625)x =35+20                               x=160km

• An electric post erected vertically is 20m from point P on the same level ground. The angle of elevation of the top, T, of the post from P is 30°. Given that S is the mid point of the post, calculate, correct to I decimal place, the angle of elevation of S from P. (3 marks)                  Rt=20tan30° or  11.55m                     Rs 1 / 2  ×20tan30°                      =10tan30° or o.5774m                     θ = tan -1  ( 10tan30° / 20  ) or tan -1  ( 5.774 / 20  )                        16.1°

• The capacities of two similar containers are 54 ml and 250 ml respectively. The difference in the heights of the two containers is 4 cm. Calculate the height of the larger container. (3 marks)     VSF = 250 / 54 = 125 / 27      LSF =( 125 / 27 ) 1/ 3 =( 5 / 3 ) = 5 / 3        ∴ 5 / 3 = X+4 / X       5X =3X+12 ⇒X=6  H. of the container = 6+4 =10 cm

SECTION  2(50marks)

Answer only five questions in this section in the spaces provided 

• Calculate  the amount of money that was paid to wema . 49 / 28  × 96 / 48  ×2400 ksh. 8400
• For every 8stonnes Wema transported to site A ,he spent ksh3000.calculate the profit Wema made.      (3marks) Expenses = 96 / 8  ×3000 =3600 profit =8400 -36000  =ksh48000
• Tatu transported the remaining 48 tonnes of stones to site B, a distance of 84 km. If Tatu made 44% profit, calculate the amount of money Tatu spent to transport the stones. (3 marks) Paid ; 84 / 28  × 48 / 48  ×24000 =ksh.72000 Expenses = 100-44 / 100  ×72000 = ksh.40,320
• Determine the ratio of the profit made by wema to that made by tatu. 44 / 100  ×72,000 =ksh 31,68 W:T =48,000:31680       =50:33
• Determine the radius of the shot put, correct to I decimal place. (3 marks) Vol; = 4 / 3  × 22 / 7  ×r³ =77.26× 1000 / 6.93  r³ = 7.26×1000×21 / 6.93×4×22  =250 r =3√250  =6.3cm
• Find the volume of the water in the bucket.(3 marks) 10.5 / 7  = h+15 / h  ⇒h =30cm                        H=45cm v = 1 / 3  × 22 / 7  (10.5²×45 -7²×30)     =3657.5cm³
•  The shot put ball is completely submerged in the water in the bucket. Calculate the new height of the water in the bucket.(4 marks)   New vol, =3657.5+7.26× 1000 / 6.93             = 197615 / 42  cm³ or 4705.1190476cm³  Vsf =( 45+x / 45 ) = 4705.1190476 / 3657.5  x =3.941 New weight = 15+3.441      =18.941cm
• the equation of line AC in the form ar+by+c=0, where a, b and c are integers.(4 marks) 5y= x+15⇒y = 1 / 5  x+3 Grad of AB = 4-(-2) / 5-1  = 6 / 4  = 3 / 2  Grad of AC = - 1 / 3 = − 2 / 3  y−(−2) / x−1  =  −2 / 3  ⇒-2x-3y-4=0 or 2x+3y+4=0

• A line passes through poin A and is parallel to line BC.Determine thr x-intercept of the line  BC ; y = 1 / 5  x+3 ⇒m 1  = 1 / 5  m 1  =m 2  = 1 / 5  y-(-2) / x-1  = 1 / 5  y=2 = 1 / 5 x - 1 / 5  y= 1 / 5  x -2 1 / 5  =0            x=11  x intercept=11

• draw a perpendicular line from D to meet AB at E. Measure DE. (2 marks)     DE =4.0cm 
• Calculate the area of the trapezium ABCD. A = 1 / 2  ×DE (AB+CD)   = 1 / 2  ×4 (10+4)   = 28cm²

• the medium amount of money spent on airtime by the 30 people . A=5×1.0 +5×1.4 +1.8x = 1 / 2 ×30  18x =15-12 =3 x=1 2 / 3  or 1.667 median =29.5+1.667                     =31.167                       =31.17
• the number of people who spent more than ksh 31.50 on airtime over the period       (2marks) 5×1.0+5×1.4+5×1.8+7×0.6 = 25.2 =26 people

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2021 KCSE Past Papers with Marking Schemes

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On this page, you can download all the 2021 K.C.S.E Past Papers by KNEC, the Kenya National Examination Council. 

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The 2021 KCSE Examination was conducted in March 2022 as a result of interference of the normal Kenyan school calendar due to the Covid-19 pandemic.

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The list containing the preview of the 2021 kcse examinations papers, includes the following subjects; English, Kiswahili, Mathematics, Biology, Chemistry, Physics, History, Christian Religious Education CRE, Geography, IRE, Agriculture, Business Studies, Computer Studies, Home Science, Woodwork, Art and Design, music, etc.

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Solving Problems KCSE Mathematics Paper 2

by C. Muturi

KCSE Mathematics Paper 2 contains a total of 672 questions in 28 KCSE model examination papers. It is divided into three parts:

Part one contains 10 solved KCSE model examination papers with a full marking scheme. In the marking scheme, alongside each solved question, the type of mark and the reason for awarding that mark is given at the stage where the mark matures. This is intended to instil the importance of 'method' in working out Mathematics questions.

The Author has selected the simplest method of solving each question. Alternative methods of solving the same questions may exist. Finding these methods has been left out deliberately as a challenge to the reader.

Part two contains 18 unsolved KCSE model examination papers which are set in line with the solved KCSE model examination papers of part one. This is intended to provide the reader with ample practice exercises.

Part three contains answers to the unsolved KCSE model examination papers.

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A Greate book

Very content-rich. This is all what my little sister needed and i got it for her.

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