Mathematics Paper 1 Questions and Answers - Moi Kabarak High School Mock 2020/2021

Instructions to candidates

• The paper contains two setions:Section I and Section II
• Answer ALL the questions in Section I and strictly any five questions from Section II
• Show all the steps in your calculations, giving your answers at each stage.
• Marks may be given for correct working even if the answer is wrong,
• Non-programmable silent electronic calculators and KNEC mathematical tables may be used, except unless stated otherwise.

SECTION I 
Answer all the questions in this section.

1. Evaluate without using a calculator   (3 marks)
     
2. The third number of four consecutive odd numbers is 2n+3. Their sum is 1768. Find the numbers.  (3 marks)
3. Peter bought a shirt and sold it to Kamau at a profit of 10%. Kamau sold the same shirt to Rony at a price of Kshs 2700/= thus making a loss of 15%. Find the price Kamau bought the shirt from Peter.   (3 marks)
4. The interior angles of an irregular hexagon are 108°, 162° and 90°. The remaining three angles are all equal. Find the value of the largest exterior angles.  (3 marks)
5. A,B and C are three points on a straight line (in that order) on horizontal ground. A and B are on the side of C. At C stands a vertical tower 173.2m high. The distance from A to B is 100m and the angle of elevation of the top of the tower from A is 30°. Find the angle of elevation of the top of the tower from B.  (3 marks)
6. The figure below shows a prism ABCDEF with BC=8cm and EB=8cm
   
   Draw the net for above prism.  (3 marks)
7. The line whose equation is 2x − 3y=12 cuts the x-axis and y-axis at A and B respectively. Find the equation of the line equidistant from A and B.  (3 marks)
8. Given that q=7^x express the equation 7^{2x − 1} + 6 × 7^{x − 1} =1 interval of q.Hence or otherwise,find the value of x in the equation 7^{2x − 1} + 6 × 7^{x − 1} =1.   (3 marks)
9. Simplify completely   (4 marks)
   2x+y    −   2y+x 
   x² −xy      xy−y²
10. Solve the inequality hence list the integral values of x satisfying the inequality.  (3 marks)
    3x − 4  ≤ 2 ≥  x+1
       −3                 4
11. Given A(2,7), B(−6,−21) and C(1,3.5). Show that the points A,B and C are collinear.  (3 marks)
12. In a certain hospital, patients are treated by two doctors in consultation rooms. On average, one doctor takes 3 minutes while the others takes 5 minutes to treat a patient. If the two doctors start to treat patients at the same time, find the shortest time it takes to treat 200 patients. (3 marks)
13. Water flows through a cylindrical pipe of diameter 4.2cm at a speed of 50m/minute. Calculate the volume of water delivered by pipe per minute in litres.  (3 marks)
14. From a ship C, a lighthouse A is 20km away on a bearing of 060°,while a lighthouse B is 30km on a bearing of 300°. Calculate the direct distance between the light houses to 3 sf. (4 marks)
15. Use reciprocal and square root tables to evaluate √0.007056 +    3    to 4 decimal places  (3 marks)
                                                                                                23.4
16. Evaluate without using mathematical table or calculator. (3 marks)
    

SECTION II (50 marks)
Answer only five questions in this section

17. The table below shows marks scored by 140 candidates in a test.
    

    Marks	1-10	11-20	21-30	31-40	41-50
    No. of candidates	8	23	55	36	18

    
    
    1. Calculate the mean mark   (3 marks)
    2. Calculate the median mark  (3 marks)
    3. State the modal class  (1 marks)
    4. Draw a frequency polygon for the marks   (3 marks)
18. Two towns A and B are 365km apart. A bus left town A at 8;15a.m and travelled towards town B at 60km/hr. At 9.00a.m a car left town B towards town A at a speed of 100km/hr. The two vehicles met at town c which lies between town A and B.
    1. Find the time of the day the two vehicles met.  (4 marks)
    2. Find the distance between towns A and C. (2 marks)
    3. At town C the driver of the car took 1 hour for lunch and followed the bus back to town B. Find how fast must the car move to arrive at town B same time as the bus. (4 marks)
19. In the figure below ABCDEFGH is a frustum of a right pyramid.The altitude of the frustum is 2cm
      
    Calculate:
    1. The altitude of the pyramid   (2 marks)
    2. The volume of the frustum  (2 marks)
    3. The angle between the bases of the frustum and the face ABGF  (3 marks)
    4. The angle between base of the frustum and face ABHE (3 marks)
20.  
    1. Triangle A(−4, 1),B(−2, 2) and C(−3,3) is mapped onto A^lB^lC^l by enlargement scale factor −1 centre (0,3). On the grid provided draw the triangle ABC and its image A^lB^lC^l. State the co-ordinates of A^lB^lC^l 
       (4 marks)
    2. Triangle A^lB^lC^l is mapped onto A^llB^llC^ll by reflection on the line x + y =0, Draw the image A^llB^llC^ll and state its co-ordinates   (3 marks)
    3. Find the matrix of transformation which maps triangle A^llB^llC^ll onto ∆ABC  (3 marks)
21. A particle moves along a straight line such that its velocity V m/s from a given point is V=3t² − 10t +3 where t is time in seconds. Find; 
    1. Acceleration of the particle when t=2 seconds (2 marks)
    2. The time taken to reach the maximum height (3 marks)
    3. The distance covered during the 5^th second (3 marks)
    4. maximum velocity attained  (2 marks
22.  
    1. Peter, John and Ronny working together take 30 minutes to slash a piece of land. peter and Ronny together take 40 minutes while peter and John together take 45 minutes. How long would each one of them take to slash the same piece of land (6 marks)
    2. Two types of sugar P and Q are such that P costs sh. 50 per kg and Q costs sh.60 per kg. In what proportion must P and Q be mixed so that by selling the mixture at shs 64.80 a profit 20% is realized.     (4 marks)
23. In the figure below SBT is the tangent to the circle at B. O is the centre of the circle. CB=3cm, AB=6cm and angle BAC=32°.
    
    Find;
    1. The diameter of the circle   (2 marks)
    2. Angle BOT  (2 marks)
    3. Angle ACB  (2 marks)
    4. Angle AMB (2 marks)
    5. Angle CBT  (2 marks)
24.  
    1. The table below shows values of x and some values of y for the curve y=2x³ + x² − 5x + 2 for −3 ≤ x ≤ 2. Complete the table (2 marks)
       

       X	−3	−2	−1	0	1	2
       y=2x3 + x2 − 5x + 2	−28			2	0

    2. On the grid provided, draw the graph of y=2x³ + x² − 5x + 2 for −3 ≤ x ≤ 2   (4 marks)
    3.  
       1. Use your graph to solve 2x³ + x² − 5x + 2 = 0   (1 marks)
       2. By drawing a suitable straight line on the graph solve the equation 
          2x³ + x² − 5x + 2 = 6x + 12  (3 marks)

Marking Scheme

1. 
   
   = 11.8(7+5)(7−5)  =   11.8 × 12 × 2
             −24                        −24
   =−11.8
2. 2n−1+2n+1+2n+3+2n+5=1768
        8n+8=1768
             8n=1760
              2n=440
   No.= 439, 441, 443, 445
3. let Peter=x                                            
   Kamau=1.1x                                              
   Rony=0.85(1.1)x =2700
         x=    2700     
              0.85 × 1.1
         x=2887.70
   
   ALT
   100 × 2700
         85
   =3176.50
   100 × 3176.50
         110
   =2887.70
4. (180−108)+(180 −162)+90+(6−3)x =360
                72+18+90+3x=360
                                  3x=180
                                   x=60
   (exterior angles = 72, 18, 90, 60)
   largest=90°
5. 
   
      Tan 30  =    173.2  
                     (100+BC)
    100 +BC =   173.2  
                      Tan 30
   100 +BC =300
           BC  = 300−100
            BC =200m
   Tan θ =173.2
                200
         θ =40.89°
6.  
   
7. 3y=2x−12
     y=²/₃x − 4
   y=⁻³/₂
   A(6, 0)
   B(0,−4)
   M(3,−2)
   y+2 = −3
   x−3     2
   2y+4=−3x+9
   2y=−3x+5
8. 7^2x·7⁻¹ + 6×7^x·7⁻¹=1
   ^q2/₇ + ⁶/₇q =1
   q² + 6q=7
   q² + 6q −7=0
   q² +7q−q−7=0
   q(q+7) −1(q+7)=0
   (q+7)(q−1) =0
       q=−7
   q=1
9. 2x+y    −   2y+x  =y(2x+y) − x(2y+x
   x(x–y)      y(x−y)            xy(x−y)
          
10. 3x−4  ≤ 2     2≥ x+1
      −3                      4
    3x−4≥−6       8≥x+1
    3x≥−2           7≥x
    x≥⁻²/₃  
       ⁻²/₃≤x≤7
    =0, 1, 2, 3, 4, 5, 6, 7
11. AB=KBC
    
    −8  = 7k
    −28    24.5k
         k =⁸/₇
    AB = ⁸/₇BC
    AB//BC
    Since B is common ∴ ABC are collinear
12. 1min =¹/₃ + ¹/₅ = ⁸/₁₅
                                      200
                            =200 × ¹⁵/₈
                             =375minutes
13. C.S.A=²²/₇ × ^4.2/₂ × ^4.2/₂ =13.86cm²
     Rate=50m/min =5000cm/1min
                13.86 × 500   l/min
                      1000
            =69.3litres per minute
14.  
    
    BA =√(30²+20²−2×30×20×Cos 120)
    BA=√1900
    BA=43.6km
15. √70.56×10⁻⁴
    8.4× 10⁻² + 3×0.04274
    0.084 + 0.128
    =0.2122
16.  
    

17. Marks	1-10	11-20	21-30	31-40	41-50
    No. of candidates	8	23	55	36	18
    fx	44	356.5	1402.5	1278	819

     Σfx = 3900
    1. Mean
       3900  =  27.86
        140 
    2. Median mark
       20.5 + (70−31)10
                  (   55   )
        =27.59
    3. Modal class  21-30
    4.  
       
       
       
18.  
    1. Relative speed=60+100=160Km/hr
       Relative distance= 365 −(⁴⁵/₆₀ × 60)
                               =320km
          320  =   2hrs
          160     +9       
                       11.00a.m
       ALT
       
       ⁴⁵/₆₀ × 60 = 45km
       ∴  x  =  320−x
          60      100
       100x =19200−60
       160x =19200
            x=120km
       120  =2hrs
        60
       9+2=11.00am
       
       
    2. 45 + 120=165km
    3. Bus=60 × 1 =60km
       Bus to cover 140km
       Car to cover 200km
       200  = 140
         x        60
       x=200 × 60
                140
       x=85.71km/h
19.  
    1. Altitude of pyramid
       
       h+2 = 8
          h      4
       h+2 =2
          h
       h+2=2h
        h=2
       height=4cm
    2. Volume of frustum
       ¹/₃×8×5×4 −¹/₃×4×2.5×2
           =53.33 − 6.667
           =46.67cm³
    3.  
       
        tan θ =²/_1.25
              θ =57.99°
    4.  tan θ =²/_3.75
               θ =28.07º
20.  
    1. 
       
    2. A^ll(−5,−4), B^ll(−4,−2), C^ll(−3,−3)
    3. 
       
       −5a−4b=−4    −5c−4d=1
       −4a−2b=−2    −4c−2d=2
         5a+4b=4       −5c−4d=1
         8a+4b=4       −8c−4d=4
             a=0             3c = −3
             b=1               c=−1
                                   d=1
          
21.  
    1. Acceleration
       v=3t² − 10t + 3
       a=^dv/_dt=6t−10
    2. time taken
       3t² − 10t + 3=0
       3t² − 9t −t+ 3=0
       3t(t−3)−1(t−3)=0
       (t−3)(3t−1)=0
          t=3s
          t=¹/₃s
    3. distance covered during 5th second
       
                 =(125−125+15)−(64−80+12)
                 =15−(76−80
                 =15−−4
                 =19metres
    4. maximum velocity
       Acceleration=0
       6t−10=0
         6t=10
           t=¹⁰/₆ 
             t=⁵/₃ =1²/₃sec
       v=3(⁵/₃) − 10(⁵/₃) +3
       v=8.333−16.67+3
        =−5.34m/s
22.  
    1. P+J+R =¹/₃₀
       P+R = ¹/₄₀
       P+J =¹/₄₅
       ¹/₄₅ + R =¹/₃₀
                 R = ¹/₃₀ − ¹/₄₅
              R=¹/₉₀ Rony = 90mins
               J= ¹/₃₀ − ¹/₄₀ = ¹/₁₂₀  John=120mins
              P= ¹/₄₀ − ¹/₉₀ = ¹/₇₂  peter=72mins
    2. let be n:1
       (50n +60)  120 =64.80
       (  n + 1  )   100
       (50n + 60)1.2 =64.8n + 64.8
       60n + 72 =64.8n +64.8
              4.8n = 7.2
                 n=³/₂ 
                 ³/₂ : 1
                  =3:2
23. 
            
    1. Diameter of circle
       CA=√(6² + 3²)= √45
                             =6.708cm
    2. Angle BOT 
       • 64°
    3. Angle ACB
       • 58°
    4. Angle AMB
          116 = 58°
            2
    5. Angle CBT
       • 32°
24.  
    1. 
       

       X	−3	−2	−1	0	1	2	3
       y=2x3 + x2 − 5x + 2	−28	0	6	2	0	12	50

    2. 
       
    3.  
       1. X_l =–2,1
       2. 2x³ + x² − 5x + 2 = 6x + 12
                                   y=6x +12
                    X_l =–2,−1