Mathematics Paper 1 Questions and Answers - Maranda Pre-Mock Examinations 2022

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QUESTIONS
SECTION I (50 Marks)
Answer ALL the questions in this section in the spaces provided below each:

  1. Evaluate 1 (4 marks)
  2. Jane working as a Sales Executive earns a basic salary of Kshs. 20,000 and a commission of 8% for the sales in excess of Kshs. 100,000. Determine the amount of sales she made in the month of January if she earned a total of Ksh.48,000 in salaries and commissions for that month. (3 marks)
  3. Convert 1.065πc into degrees. (2 marks)
  4. After heating his oven to 87°C Masoudi allowed it to cool to 23°C, calculate the number of minutes it took to cool to the final temperature given that it cooled at a rate of 8'C per every 12 seconds. (3 marks)
  5. Peter cast 15 equal wax cubes from one litre of melted wax. Given that the volume of the cubes reduced by 4% on cooling, calculate the dimension of a cube in centimetres. (3 marks)
  6. Three casual workers: Alice, Benson and Charles working in a Juice Processing Factory earns in a way such that Benson eårns twice as much as Alice and Charles earns sh 70 more than Benson. If their total earning is sh1120 per day, express the ratio of their earnings, Alice:Benson:Charles, in its simplest form. (3 marks)
  7. A watch which looses a half-minute every hour was set to read the correct time at 0545h on Monday, Determine the time, in the 12 hour system, the watch will show on the following Friday at 1945h. (3 marks)
  8. Given that log Y=1.2534 and the product of X and Y, XY=427.2, calculate X leaving your answer in standard form.(3 marks)
  9. The figure is a circle in which AB, AC, DC and DB are chords. Angles ACE and CEB are 70° and 120° respectively.
    2
    Calculate the size of angle EDB labelled x°(3 marks)
  10. Solve for m in the equation -54 = 10 - (m-10)3/2 (3 marks)
  11. The image of P(2, 3) under an enlargement with a scale factor 3 is Pl(4,9). Determine the centre of enlargement (3 marks)
  12. Solve for x in the equation 4sin (x +20°) = 3 for 0 ≤ x ≤ 360 (3 marks)
  13. The figure below shows a triangular kitchen garden with lengths AC=17m, AD-8m and BC=21m
    3
    Calculate the length of the wire required to fence it round, (3 marks)
  14. The graph below is a plot for the function y = ax + bx + c where a, b and care constants.
    4
    Determine the function and its y intercept marked d. (4 marks)
  15. Find the equation of a line L1 whose slope is -3 and passes through the intersection of the curves y = 1/x and y = 1/2x-1 (3 marks)
  16. Evaluate, to 3 decimal places,2/12.56 + (0.12)½ - (0.25)3 using the Tables of Reciprocals, Square roots and Cubes. (4 marks)

SECTION II (50 Marks)
Answer ONLY FIVE questions in this section in the spaces provided below each:

  1. Given that A=(32 45) determine
    1. the inverse of matrix A. (2 marks)
    2. price of a skirt and a blouse using the inverse of matrix A if Jemima bought 3 skirts and 4 blouses and paid Kshs.1150 while Amina paid Kshs. 1000 for two skirts and 5 blouses from the same stall. (4 marks)
    3. how much less Sophie paid for 7 skirts and 3 blouses when she was given a 10% discount on each skirt and 10% increase in price of each blouse. (4 marks)
  2.    
    1. Construct triangle ABC in which angle ABC is 75 and lengths AB and BC are 10.1cm and 11.2cm respectively. (4 marks)
    2. Measure length AC and angle ACB. (2 marks)
    3. Construct the locus of a point P equidistant from the sides AB and AC. (2 marks)
    4. Shade the region Q such that Q is closer to AB than AC but not greater than 5.2cm from A.(2 marks) Act
  3. The figure below shows a drinking glass in the shape of a frustum.
    5
    Calculate to one decimal place:
    1. the height of the cone from which the glass was cut. (2 marks)
    2. the surface area, in cm2, of the glass in contact with liquid L. occupying the lower 15cm of the height. (3 marks)
    3. the surface area, in cm2, of a spherical ball which can be molded from the molten liquid L2 occupying the upper 20cm above liquid L1. (5 marks)
  4. Jenny may either walk to school along a route 5km or take a bus journey of 7km. The average speed of the bus is 24km/h faster than her average speed while walking. Taking the average walking speed to be x km/h:
    1. Write down expressions for time of the journey;(2 marks)
      1. when walking
      2. when using the bus
    2. The journey by bus takes 36 minutes less than the journey on foot, find her walking speed in km/h. (5 marks)
    3. Hence find total time she took while traveling to school when she walked for two days and boarded the bus for four days. (3 marks)
  5. The position vectors of A and B are (-46) and (-82) respectively. Point M is the midpoint of AB and N the midpoint of OA.
    1. Find:
      1. the vector AB(2 marks)
      2. the coordinates of points M and N. (2 marks)
      3. the modulus of NM. (3 marks)
    2. The coordinates of a point Cis (2,a). Vector CA is parallel to vector OB. Determine the (3 marks):
  6. A water vendor has a tank of capacity 18900 litres. The tank is being filled from two pipes A and B which are closed immediately the tank is full. Water flows at the rate of 150000cm per minute and 120000cm per minute from A and B respectively.
    1. Calculate the time it takes to fill the tank if both taps A and B are opened at the same time in hours. (4 marks)
    2. On a particular day the vendor started refilling the empty tank using taps A and B but was forced to start serving his customers after 25 minutes of filling. Given that the draining tap C supply 20 litres per minute to the customers determine the exact time of the day the tank was filled assuming that the customers supply was continuous from 1115hrs. (6 marks)
  7. A port B is on a bearings of 080° from a port A and at a distance of 95km. A submarine is stationed at a port D, which is on a bearing of 200° from A, and a distance of 124km from B. A ship leaves B and moves directly southwards to an island P, which is on a bearing of 140° from A. the submarine at D on realizing that the ship was heading for the island P, decides to head straight for the island to intercept the ship.
    1. Using a scale of lcm to represent 10km draw a diagram to show the positions of A, B,D and P.(4 marks)
    2. Hence determine:
      1. the distance from A to D. (2 marks)
      2. the bearing of the submarine from the ship when the ship was setting off from Port B.(1 mark)
      3. the bearing of the island P from D. (1 mark)
      4. the distance the submarine had to cover to reach the island P. (2 marks)
  8. The figure below shows a frequency polygon representing the scores of Form 4 Alpha students in a Kiswahili Test
    6
    1. Generate the Frequency Distribution of the data under the columns given below in the table below.(4 marks)
      Marks Frequency (f) Mid points(x) fx cf
               
    2. State the modal class.(1 mark)
    3. Estimate:
      1. The mean score.(2 marks)
      2. The median score. (3 marks)


MARKING SCHEME

  1. Numerator: 9/÷ 2/3 of 9/4 - 3/10
    9/52/33/10
    = 6/53/109/10
    Denominator: 5/6 + 22/39 x 13/11
    = 5/62/3
    = 3/2
    9/102/3
    3/
  2. commission earned = 48,000 - 20,000
    = 28,000
    If 8% = 28,000
    100% = 100% x 28000
    8%
    = 350,000
    sales = 100,000 + 350,000
    = 450,000
  3. if 2πc = 360°
    1.065πc = 1.065πc x 360°
                             2πc
    =191.7°
  4. change in temperature = 87°C - 23°C
    = 64°C
    time taken to cool in seconds = 64°C x 12
                                                       8°C
    = 96 seconds
    time taken in minutes = 96 ÷ 60 = 1.6minutes
  5. volume of each cube = 1000/15
    volume of each cube after cooling = 1000/15 x 96/100 
    dimension of the cube = 3√64
    = 4cm
  6. Alice Benson Charles
    x          2x       2x+70
    x + 2x + 2x +70 = 1120
    x = 210
    Alice:Benson:Charles
    = 210:420:490
    = 3:6:7
  7. total timebetween monda 0545h to friday 1945h
    = 4 x 24 + 14
    = 110hrs
    number of minutes lost = 110 ÷ 2 = 55mins
    time = 1945 - 55mins
    = 1850h
  8. log x + log y = log 427.2
    log x + 1.2534 = 2.6306
    log x = 1.3772
    x = 2.3834 x 101
  9. <EBD = 70º
    xº + 70º = 120º
    xº = 50º
  10. -64 = -(m - 10)3/2
    64 = (m - 10)3/2
    (43)2/3 = m-10
    m = 26
  11. let the centre of enlargement be (x,y)
    x - 4 = 3
    x - 2
    x = 1
    y - 9 = 3
    y - 3
    y = 0
  12. sin(x + 20)º = ¾
    (x + 20)º = 48.59º, 131.41º 
    x = 28.59º, 101.41º 
  13. DC = √172 - 82
    = 15
    AB =√62 + 82
    = 10
    L = 10 + 21 + 17 = 48m
  14. x = -2 or 3
    (x + 2)(x - 3) = 0
    x2 - 3x + 2x - 6 = 0
    x2 + x - 6 = 0
    y = x2 - x - 6
    d = -6
  15. at intersection 1/x = 1/2x-1
    2x - 1 = x
    x = 1
    y = 1
    point of intersection (1,1)
    y - 1 = -3
    x - 1
    y - 1 = -3x + 3 
    y = -3x + 4
  16.     2   =         2       
    12.56  1.256 x 101
    = 2recip1.256
              10
    = 0.2 x 0.7961
    = 0.15922
    (0.12)½ = (12 x 10-2)½
    = 3.4651 x 10-1
    = 0.34641
    (0.25)3 = (2.5 x 10-1)3
    = (2.5)3 x 10-3
    = 15.625 x 10-3
    = 0.015625
    0.15922 + 0.34641 - 0.015624
    = 0.490005
  17.      
    1. Det A = 3 x 5 - 4 x 2 
      = 7
      7
    2. 3s + 4b = 1150
      2s + 5b = 1000
      8
    3. new price of skirt = 90/100 x 250 = 225
      new price of blouse = 110/100 x 100 = 110
      cost before change in orice = 250 x 7 + 3 x 100
      = 2050
      cost after change in price = 225 x 7 + 3 x 110 
      = 1905
      amount paid = 2050 - 1905 = 145/-
  18.      
    1.    
      9
    2. AC = 13 ± 0.1cm
      <ACB = 50±1º
    3. B1 angle bisector locus
      labelling of locus of P
    4. dotted arc (<5.2 cm from A)
      region Q shaded
  19.    
    1. 21/14 = 35 + h
                     h 
      h = 70
      H = 70 + 35
      = 105.0cm2
    2. 21/R15 = 105/85
      R15 = 17cm
      area of the covered surface 
      = π x 17√172 + 852 - π x 14√142 + 702
      = 1489.770929
      total surface area = 1489.770929 + 615.7521601
      = 2105.5cm2
    3. volume of liquid = 1/3 x π (212 x 105 - 172 x 85)
      = 22766.07476
      4/3πr3 = 22766.07476
      = 5435
      = 17.58192877
      surface area = 4 (17.58192877)2
      = 3884.6cm2
  20.    
    1.      
      1. 5/x
      2. 7/x+24
    2. 5/x7/x+24 = 6/10
      50x + 1200 - 70x = 6x2 + 144x
      6x2 + 164x - 1200 = 0
      x = -164 ± 236
                 12
      x = 6 or 331/3
      x = 6km/h
    3. 2(5/6) + 4(7/30)
      = 23/5hrs
  21.      
    1.      
      1. AB = (-82) + - (-46)
        =(-4-4)
      2. m(-4 + -8 , 6+2) = m(-6,4)
                2         2 
        N(-2,3)
      3. NM = (-64) - (-23)
        = (-41)
        INMI = √(-4)2 + (1)2
        = 4.123

    2. 10
      k = ¾
      6-a = x 2 
      a = 4.5
  22.      
    1. volume of water flowing per minute 
      = 150000 + 120000
      = 270000
      number of minutes used in filling the tank
      = 18900000
           270000
      = 70
      number of hours taken 
      = 70/60 = 11/6hrs = 1.166hrs
    2. volume of the water filled in the tank after 25minutes
      = 25 x 270000
              1000
      = 6750
      volume of the tankbe filled while the three taps are running
      = 18900 - 6750
      = 12150
      rate of filling the tank per minute
      = 270 - 20
      = 250 litres/minute
      time taken = 12150
                             250
      = 48mins 36s
      time when the tank was filled 
      = 1115hrs + 48mins 36s
      = 12:03:36pm
  23.    
    1.            
      11
    2.           
      1.  4.4 x 10 
        44 ± 1 km
      2. 240º ± 1
      3. 120º ± 1º
      4. 12.5 x 10
        125 ± 1km
  24.    
    1.      
      Marks Frequency(f) Midpoints(x) fx cf
      49.5-59.5
      59.5-69.5
      69.5-79.5
      79.5-89.5
      89.5-99.5
      5
      10
      30
      40
      15 
      54.5
      64.5
      74.5
      84.5
      94.5 
      272.5
      645.0
      2235.0
      3380.0
      1471.5 
      5
      15
      45
      85
      100 
    2. 79.5 - 89.5
    3. x = 7950
            100
      = 79.5
    4. n/2 = 50
      median = 79.5 + (50 - 45)10
                                     40
      = 80.75 
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