MATHEMATICS PAPER 1 - 2019 MOKASA II MOCK EXAMINATIONS

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INSTRUCTIONS TO CANDIDATES

  • Write your name and Admission number in the spaces provided at the top of this page.
  • This paper consists of two sections: Section I and Section II
  • Answer ALL questions from section I and ANY FIVE from section II
  • Show all the steps in your calculation
  • Non – Programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.

SECTION I 50 MARKS

(Answer all the questions)

  1. Without using mathematical tables or calculator, evaluate:
    math p1 q1.PNG
    Leaving the answer as a fraction in its simplest form.                                (2 marks)
  2. Use prime factors to evaluate 
    math p1 q2.PNG                                               (3 marks)
  3. Solve for m in the equation:    (3 marks)
    math p1 q3.PNG
  4.  
    1. Find the greatest common divisor of the term.                                    (1 mark)
      math p1 q4a.PNG
    2. Hence factorize completely this expression
      math p1 q4b.PNG         (2 marks)
  5. Solve for x if
    math p1 q5(3 marks)
  6. A car dealer charges 10% commission for selling a car. He received a commission of Ksh. 27,500 for selling a car. How much did the owner received from the sale of his car if the dealer added an extra charges of 5 %.                                   (3 marks)
  7. Two similar cylinders have diameter of 7cm and 21cm. If the larger cylinder has a volume of 6237cm³. Find the heights of the two cylinders.                      (3 marks)
  8. A sector of radius 12 cm subtends and angle of 700 at the centre. If the sector is folded to form a cone, calculate ;
    1. The area of the curved part of the cone                                                  (2 marks)
    2. The radius of the cone formed.                                                                  (2 marks)
  9. Find all the integral values of x which satisfy the inequality              (3 marks)
    math p1 q9.PNG 
  10. The table below shows four principal crops produced in Kenya in the years 2000 and 2001. Use it to answer the questions below.
    1. Using a radius of 5 cm, draw a pie chart to represent crop production in the year 2000.                                                                                                                (3 marks)
    2. Calculate the percentage increase in wheat production between the years 2000 and 2001.                                                                                                            (1 mark)
                                         
      CROP  AMOUNT IN METRIC TONNES

      YEAR

      2000

      2001

      Wheat

      Maize

      Coffee

      Tea

      70,000

      200,000

      98,000

      240,000

      13,000

      370,000

      55,000

      295,000

  1. Construct line AB 12.2 cm. Use a line X which meets line AB at A such that angle XAB is YYY to divide line AB into 8 proportional parts.                    (3 marks)
  2. The cost of providing a commodity consists of transport, labour and raw material in the ratio 8:4:12 respectively. If the transport cost increases by 12% labour cost 18% and raw materials by 40%, find the percentage increase of producing the new commodity.                                                                                                      (3 marks)
  3. A line L1 passes through point (-1,1) and perpendicular to the line L2 which makes an angle of 18.434948820 with the x-axis. Find the equation of L1 giving your answer in the double intercept form.                                                            (4 marks)
  4. Given that math p1 q14a.PNGand  find math p1 q14c         (4 marks)
  5. The exterior angle of a regular polygon is equal to one-third of the interior angle. Calculate the number of sides of the polygon and give its name.    (3 marks)
  6. In the figure below, shows an irregular solid with a uniform cross-section. Complete the sketch, showing the edges clearly.                                          (2 marks)
    math p1 q16.PNG

SECTION II (50 MARKS)

(Answer ANY FIVE questions in the spaces provided)

  1. The figure below shows a frustrum container with base radius 8 cm and top radius 6 cm. The slant height of the frustrum is 30cm as shown below. The container 90 percent full of water.
    math p1 q17.PNG
    1. Calculate the surface area of the frustrum                                               (3 marks)
    2. Calculate the volume of water. (4 marks)
    3. All the water is poured into a cylindrical container of circular radius 7cm, if the cylinder has the height of 35cm; calculate the surface area of the cylinder which is not in contact with water. (3 marks)
  2. Complete the table below for the function
    math p1 q18a.PNG     (2 marks)   

    x

    -3

    -2

    -1

    0

    1

    2

    3

    4

    -x3

    27

    8

     

    0

     

    -8

       

    2x2

    18

    8

    2

    0

           

    -4x

     

    8

     

    0

         

    -16

    2

    2

    2

    2

    2

    2

    2

    2

    2

    y

     

    26

     

    2

     

    -6

     

    -46

           
  1. On the grid provided below draw the graph of math p1 q18b for math p1 q18c.PNG                  (3 marks) 
    math p1 graph
    1. Use the graph to estimate the roots ofp1 q183. (2 marks)
    2. By drawing a suitable line on the graph solve the equation math p1 q18d.PNG   (3 marks)
  2. A lorry left Malaba for Nairobi, 500 km away at 6.00 am and travelled at an average speed of 60km/h. After travelling for 1hour it stopped for 30 minutes to unload some luggage then proceeded with its average speed. A coast bus left Nairobi for Malaba at 8.00 am and travelled at an average speed of 90km/h. Calculate
    1. The distance travelled by the lorry before the bus started its journey. (2 marks) 
    2. The time of the day the two vehicles met                                                (4 marks)        
    3. How far from Malaba when they met.                                                      (3 marks)        
    4. The time the bus reached Malaba if it travelled continuously without stopping.        (1 mark)                            
  3. The table below shows measurements in metres made by a surveyor in her field book. (Distance are given in metres)

    F 50

    C 120

    B

    280

    250

    200

    150

    100

    40

    A

    E 40

    D 100

    B 50

    1. Using the representative fraction scale of a map is math p1 q19.PNG, Draw the accurate measurements of the field   (3 marks)
    2. Calculate the area of the field in hectares    (5 marks)
      Using the above scale:
    3. Calculate actual circumference of the circular maize farm of radius 2.1cm on the map in kilometres.  (2 marks) 
  1. The table below shows the marks of 100 candidates in an examination:
    1. Draw a cumulative frequency curve to represent above data                (3 marks)

      Marks

      1-10

      11-20

      21-30

      31-40

      41-50

      51-60

      61-70

      71-80

      81-90

      91-100

      No of students

      4

      9

      16

      24

      18

      12

      8

      5

      3

      1


      math p1 graph
    2. Using the graph determine:
    3. the upper quartile                                                                                    (1 mark)
    4. estimate how many students passed, if 55 marks is the pass mark.    (2 marks)
    5. find the pass mark if 70% of the students are to pass                    (2 marks)
    6. the range of marks obtained by the middle 80% of the students   (2 marks)
  2. A ball is thrown upwards with a velocity of 40 m/s.
    ( Take acceleration due to gravity to be 10m/s)
    1. Determine the expression of its height above the point of projection    (3 marks)
    2. Find the velocity and height after 2 seconds and 3 seconds                  (2 marks)
    3. Find the distance moved by the ball between t=1s and t=2s            (2 marks)
    4. Find the maximum height attained by the ball.                                     (3 marks)
  3. A transformation represented by the matrix math p1 q23.PNGmaps P(0,0), Q(2,0), R(2,3) and S(0,3) onto P’, Q’, R’, S’
    1. On the grid provided draw the quadrilateral PQRS and P’Q’R’S’    (3 marks)
      math p1 graph                    
    2. Determine the area of PQRS , Hence or otherwise find the area of P’Q’R’S’  (2 marks)
    3. A transformation represented by the matrixmath p1 q23cmaps P’Q’R’S’ onto P’’Q’’R’’S’’. On the same Cartesian plane draw and state the coordinates of P’’Q’’R’’S’’                                                                                                         (3 marks)
    4. Determine the matrix of transformation that would map P’’Q’’R’’S’’ onto PQRS (2 marks) 
  4. In the figure below, OB = b and OA = a. If Y divides line OA in the ratio 11:-3 and OX:XB=2:-1,
    math p1 q24
    1. Find in terms of a and b the vectors:
    2. XA   (1 mark)
    3. BY (1 mark)
    4. If XD=hXA and BD=kBY, express OD in terms of
      1. a, b and h (1 marks)
      2. a, b and k   (1 mark)
    5. using the results in (b) above, find the values of k and h hence find XD:DA and BD:DY.  (6 marks)   


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