MATHEMATICS PAPER 1 - KCSE 2019 NYANDARUA PRE MOCK EXAMINATION

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SECTION I   (50 Marks)

INSTRUCTIONS:Answer all questions in this section in the spaces provided

  1. Without using calculator, simplify (3 mks)
    math1yhuj
  1. Use table of reciprocals to evaluate     (3 mks)
    math2ujhy 
  1. Simplify (3 mks)
    math3ujhy
  1. Ouma had pigs, hens and ducks in his farm. The number of pigs was 32 and number of hens was twelve times the number of pigs. The number of ducks was 1344 more than the number of hens. If he sold 3/4 of the ducks, find the number of ducks that remained   (4 mks)
  1. The mass of a solid sphere of radius 0.14m is 7.89kg, find its density in g/cm3.   (3 mks)
    Take π=22
                7
  1. Simplify math6ujhy             (3 mks)                                
  1. A Kenyan bank buys and sells foreign currencies as shown below.
                                                                          Buying (ksh)             Selling (ksh)
    1 Stering pound (£)                                           129.24                           130.57
    1 South African Rand                                           9.15                             9.38
    A businessman on a trip to Kenya had £ 50,000 which he converted to Kenya shillings. While in Kenya, he spent 75% of the money and changed the balance to South African Rand. Calculate to the nearest a Rand the amount he obtained.                                                        (3 mks)
  1. Two students Paul and Omondi standing 10m apart on the same side of a tall building on a horizontalground. Paul who is closer to the building sees the roof top at an angle of 70 while Omondi at an angle of 46.8,If the building, Paul and Omondi lies on a straight line, Calculate the height of the building correct to 3 s.f. (4 mks)
  1. On the line AB, given below, divide it into 3 equal proportions.     (2 mks)
    math9ujhy
  1. The volume of two similar cans are 96cm3 and 1500cm3. If the surface area of a small can is 40cm2, find the surface area of a larger can.     (4 mks)
  1. The interior angles of a heptagon are math11ujhy, and  440 Find the size of the largest angle. (3 mks)
  1. The marks scored by a group of students in a test were recorded as shown below.

    Marks

    30-34

    35-44

    45-49

    50-64

    65-74

    No. of students

    10

    28

    5

    27

    4


    Draw a histogram.                                                                                                      (4 mks)
  1. A truck left Nakuru at 8.00am for Nairobi at an average speed of 60km/h. At 9.00am, a bus left Nairobi for Nakuru at a speed of 120km/h Find far from Nakuru did the vehicles meet if Nakuru is 160km for Nairobi.                           (4 mks)
  2. In the figure below, O is the center of the circle, The reflex angle AOD =256 and ACE =50
    math14ujhy
    Calculate angle BDC                                                                                                  (3 mks)
  1. Given that line 3x -2y =2 is drawn in a Cartesian plane, determine the acute angle the line makes with line y=1.     (2 mks)
  2. Below is a part of a solid cuboid ABCDEFGH.Complete the sketch. 
    math16ujhy

SECTION 2 (50 MARKS)
INSTRUCTIONS: Answer any FIVE questions

  1. The figure below is a solid which consists of a frustrum of a cone, a cylinder and a hemispherical top. The internal radii of a frustrum are 42cm and 21cm. The vertical height of an original cone was 40cm and the height of a cylinder is 30cm.   Take π=3.142
    math17ujhy
    Calculate:
    1. the volume of the frustrum part:          (5 mks)
    2. the volume of the cylindrical part:        (2 mks)
    3. the total volume of the solid.               (3 mks)
  1. Four posts A,B,C and D stand on a level horizontalground. Post Bis 240m on a bearing of 060 from A, Cis 210m to the south of B and D is 150m on a bearing of 140 from A.
    1. Using a scale of 1 cm to represent 30m, show the relative positions of the posts.   (4 mks)
    2. Use the scale drawing to:
      1. find the distance and the bearing of C from D.                                                     (2 mks)
      2. determine how far A is to the west of B.                                                              (2 mks)
      3. The height of post D is 18m. Calculate, correct to 2 decimal places, the angle of elevation of the top of post D from the foot of post A.                                                                    (2 mks)
  1. The vertices of a triangle are A(-2,2),   B(2,2) and C(2,8).
    1. On the grid provided, draw triangle ABC and its image A’B’C’ under a rotation of -90°about R (1,1). 
    2. The vertices of triangle A’’B’’C’’ are A’’(-1,-5), B’’(-1,-3) and C’’(-4,-3)
      1. Draw triangle A"B"C"’’.                                                                                                   (1 mk)
      2. Described fully the transformation X that maps A’B’C’and A’’B’’C’’.                   (1 mk)
    3. Triangle A’’’B’’’C’’’ is the image of triangle A’’B’’C’’ under a reflection in the line X=0.On the same grid draw triangle A’’’B’’’C’’’.
    4. State the type of congruence between:
      1. ABC and A’B’C’.
      2. A’’B’’C’’ and A’’’B’’’C’’’
  2.  The figure below shows triangle OPQ in which =p and OQ=q.Mand N are points on  and  respectively such that 3 =  and OM;OQ=2:3
    math20ujhy
    1. Express the following vectors in terms of P and q
      math20romans
    2. If lines pm and QN intersect at x such that  PX= hPM and QX = kQN. Find the values of h and k.          (6 mks)
    3. Line OX produced meets PQ at Y such that 5PY=3PQ. Find OY in terms of p and q.    (1 mk)
  1. The figurebelow shows two circles centers A and B and radii 8cm and 12cm respectively. The circles intersect at P and Q. If the centers re 15cm apart and taking  ∏= 3.142 
    MATH21UJHY
    Calculate
    1. the length of chord PQ                                                                                      (4 mk)
    2. the angle PAQ.                                                                                                                  (1 mk)
    3. the angle PBQ                                                                                                               (1 mk)
    4. the area of the shaded region.                                                                                        (4 mks)
  1. A line segment PQ is passing through P(-2,3) and Q (4,7).
    1. Find the equation of line PQ                                                                                                                   (3 mks)
    2. Perpendicular bisector of line PQ.                                                                             (4mks)
      1. If the perpendicular bisector meets the x axis at R, determine the co-ordinates of R. (2 mks)
      2. What would the y intercept of the perpendicular bisector in (ii) above.                  (1 mk)
  1. Three quantities R,S and T are such that R varies directly as S and inversely as the square of T.
    1. Given that R=480 when S= 150 and T=5, write an equation connecting R,S and T.       (3mks)
    2.  
      1. Find the value of R when S = 360 and T =1.5.                                                          (3mks)
      2. Find the percentage change in R if S increases by 5% and T decreases by 20%.             (4mks)
  1. Draw a graph of y=8-2x –x2 for -5≤ x ≤3               (5mks)

    X

    -5

    -4

    -3

    -2

    -1

    0

    1

    2

    3

     

    y

             

    8

           
    From the graph
    1. Determine the roots of 8-2x-x2 =0                                                                        (1 mk)                              
    2. Solve x2 + 4x =0                                                                                                    (4 mks)

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