Mathematics Paper 1 Questions and Answers - Momaliche Post Mock 2020 Exam

INSTRUCTION TO CANDIDATE’S:

• This paper consists of TWO sections: Section I and Section II.
• Answer ALL the questions in Section I and any five questions from Section II.
• Answers and working must be written.
• 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 where stated otherwise.

SECTION I: (50 MARKS)
Answer all the question in this section in the spaces provided:

1. Evaluate                   (3mks)
    
2. Use square roots, reciprocal and square tables to evaluate to 4 significant figures the expression;
   (0.06458)^½ + (    2    )²      (4mks)
                        (0.4327)
3. Three similar 21-inch television sets and five similar 17-inch television cost Ksh.129,250. The difference between the cost of two 21-inch television sets and four 17-inch television sets is Ksh. 22,000. Calculate the price of a 21- inch television set and that of 17-inch television set. (3mks)
4. Simplify: (3 marks)
   
5. Solve for x in the equation. (3 Marks)
   9^(x-1) x 3^(2x+1) = 243
6. A classroom measures ( x + 2) m by ( x – 5)m. If the area of the classroom is 60m².Find its length. (3 mks )
7. A tourist exchanged X US dollars for Kenya shilling when he arrived in Kenya. He spent three days in the country and paid Ksh 45,600 for expenses. He later left the country and exchanged the remainder back to US dollars. He went back with 1200 dollars. Find the value of X to the nearest dollar.                      (3mks)
   Buying 1 US dollar = Ksh.98.36
   Selling 1US dollar = Ksh.98.54 
8. Three similar pieces of timber of length 240cm, 320cm and 380cm are cut into equal pieces. Find the largest possible area of a square which can be made from any of the three pieces. (3mks)
9. A regular polygon is such that its exterior angle is one eighth the size of interior angle.
   Find the number of sides of the polygon. (3 mks)
10. Given that sin (2θ + 30) = Cos (θ − 60). Find the value of tan θ to two decimal places.
    (2 mks)
11. The figure below shows a histogram.
    
    Fill in the table below the missing frequencies. (3mks)
    

    Length in x cm	Frequency
    7.5≤ x ≤ 9.5	12
    9.5≤ x ≤ 11.5
    11.5≤ x ≤ 15.5
    15.5≤ x ≤ 21.5

12. A straight line L₁ is perpendicular to another line L₂ whose equation is 3y+4x=12. If the two lines meet at point P which lies on the x-axis, find:
    1. The co-ordinate of point P (1mk)
    2. The equation of line L1 in the form y=mx+c (3mks)
13. The heights of two similar pails are 12cm and 8cm. The larger pail can hold 2 litres. What is the capacity of the smaller pail? Give your answer to 2 decimal places. (3mks)
14. Two matrices A and B are such that A= (k 4 3 2) and B = (1 3 3 −4) Given that the determinant of AB = 10, find the value of k. (3mks)
15. 1000cm³ of milk was shared by three children, Nick, Soita and Swalleh in the ratio
    ¼: ½ : ¹/₅,What volume did Soita get: (2mks)
16. Given that log a = 0.30 and log b = 0.48 find the value of log b² (2 mks)                                                                                                                      a 

SECTION II
Answer any five questions in this section.

17. The distance between two towns A and B is 760 km. A minibus left town A at 8:15a.m and traveled towards B at an average speed of 90km/h. A matatu left B at 10:35a.m and on the same day and travelled towards A at an average speed of 110km/h.
    1.  
       1. How far from A did they meet? (4mks)
       2. At what time did they meet? (2mks)
    2. A motorist starts from his home at 10:30 a.m on the same day and traveled at an average speed of 100km/h. He arrived at B at the same time as the minibus. Calculate the distance from B to his home. (4mks)
18. The coordinates of a triangle ABC are A(1, 1) B(3, 1) and C (1, 3).
    1. Plot the triangle ABC. (1 mark)
    2. Triangle ABC undergoes a translation vector 2 2 . Obtain the image of A' B' C ' under the transformation, write the coordinates of A' B' C'. (2 marks)
    3. A' B' C' undergoes a reflection along the line X = 0, obtain the coordinates and plot on the graph points A" B" C", under the transformation (2 marks)
    4. The triangle A" B" C" , undergoes an enlargement scale factor -1, centre origin. Obtain the coordinates of the image A'" B"' C"'. (2 marks)
    5. The triangle A"' B"' C"' undergoes a rotation centre (1, -2) angle 1200. Obtain the coordinates of the image Aiv Biv Civ. (2 marks)
    6. Which triangles are directly congruent. (1 mark)
19. The income tax rates in a certain year are as shown below.
    

    Income (k₤ – p.a	Rate (KSh. per ₤)
    1 – 4200	2
    4201 – 8000	3
    8001 – 12600	5
    12601 – 16800	6
    16801 and above	7

    Omar pays Sh. 4000 as P.A.Y.E per month. He has a monthly house allowance of KSh.10800 and is entitled to a personal relief of KSh. 1,100 per month. Determine:
    1. his gross tax per annum in Kshs (2 Marks)
    2. his taxable income in K₤ per annum (2 marks)
    3. his basic salary in Ksh. per month (2marks)
    4. his net salary per month (2 marks)
20. The diagram below shows two circles, centre A and B which intersect at points P and Q.
    Angle PAQ = 70°, angle PBQ = 40° and PA = AQ = 8cm.
    
    Use the diagram to calculate
    1. PQ to correct to 2 decimal places (2 Marks)
    2. PB to correct to 2 decimal places (2 Marks)
    3. Area of the minor segment of the circle whose centre is A (2 mks)
    4. Area of the minor segment of the circle whose centre is B (2mks)
    5. Area of the shaded region. (2mks)
21. Three Kenyan warships A, B and C are at sea such that ship B is 450km on a bearing of 0300 from ship A. Ship C is 700km from ship B on a bearing of 1200. An enemy ship D is sighted 1000km due south of ship B.
    1. Taking a scale of 1cm to represent 100km locate the position of the ships A, B, C and D.      (4 Marks)
    2. Find the compass bearing of:
       1. Ship A from ship D (1 Mark)
       2. Ship D from ship C (1 Mark)
    3. Use the scale drawing to determine
       1. The distance of D from A (1 Mark)
       2. The distance of C from D (1 Mark)
    4. Find the bearing of:
       1. B from C (1 Mark)
       2. A from C (1 Mark)
22. The figure below shows triangle OPQ in which OS = ¹/₃ OP and OR = ¹/₃ OQ. T is a point on QS such that QT = ³/₄ QS
    
    
    1. Given that OP = p and OQ = q, express the following vectors in terms of p and q.
       1. SR (1 Mark)
       2. QS (2 Marks)
       3. PT (2 Marks)
       4. TR (2 Marks)
       5. show that point PTR are collinear. (3mks)
23. In the figure below DA is a diameter of the circle ABCDE centre O. TCS is a tangent to the circle at C, AB = BC and angle DAC = 38°
    
    Giving reasons, determine the following angles:
    1. ∠DCT        (2 marks)
    2. ∠DEA        (2 marks)
    3. ∠ACB        (2 marks)
    4. ∠BDC        (2 marks)
    5. ∠BOA        (2 marks)
24.  
    1.  
       1. Fill the table below for the function.
          y = 2x² + 5x – 12 for − 8≤ x ≤ 4                   (2 marks)
          

          x

          −8

          −7

          −6

          −5

          −4

          −3

          −2

          −1

          0

          1

          2

          3

          4

          2x2

          128

          18

          2

          32

          5x

          −40

          −15

          5

          20

          −12

          −12

          −12

          −12

          −12

          y

          76

          −9

          −5

          40

       2. Using the table, draw the graph of the function y = 2x² + 5x – 12. Use the scale 1cm to 1 unit on the x-axis and 1cm for 10 units for the y – axis
          (4 marks)
    2. Use the graph drawn above to solve the following equations.
       1. 2x² + 5x – 12 = 0         (2 marks)
       2. 3 – 7x – 3x² = 0            (2 marks)

MARKING SCHEME

1.  
   
2. √(6.458 ×10⁻²) + 2 (¹/_0.43272)²   
   2.541 + (2.311)²                          
   = 2.541 + 2(5.307)                     
   = 2.541 + 10.61                          
   =13.155                                            
3. x + 5y = 129250               
   2x - 4y = 22000                 
   6x + 10y = 258500−          
   6x − 12y = 66000
           22y = 192500
              y = 8750
             x = 28,500            
4.  
    
5. 9^(x-1) x 3^(2x+1) = 243
   Change to base 3                        
   3^2(x-1)x 3^(2x+1) = 3⁵
   2 (x – 1) + 2x + 1 = 5               
   2x – 2 = 2x + 1 = 5
   4x – 1 = 5
   4x = 6
   x = 1.5                                    
6. (x + 2 ) ( x – 5 ) = 60
   x² – 5x + 2x – 10 = 60
   x² – 3x – 70 = 0
   x² – 10x + 7x – 70 = 0
   x ( x – 10) + 7(x – 10) = 0
   ( x – 10) ( x +7) = 0
   x = 10 x = -7
   Length 10 + 2 = 12m
7. 98.54 x 1200 = 118248
   45600 + 118248
   = 163848÷98.36 =1665.7991 = 1666 dollars
8. HCF of 240, 320 and 380
   

   	120	320	380
   2	120	160	190
   2	60	80	95
   5	12	16	19

   HCF = 2 x 2 x 5 = 20 cm
   Area = 20² = 400cm²
9. ¹/₈x + x = 180
   ⁹/₈x = 180
   x = 180 x 8
           9
   = 160
   Exterior ˂ = 18 x 160 = 20
   No. of sides 360 = 18
                      20
10. 2θ + 30 + θ - 60 = 90
    3θ = 120
      θ = 40
    Tan 40 = 0.81
11. ¹²/₂ = 1.2 x k
    k = 6   = 5
         1.2
    

    Length in x cm	Frequency
    7.5≤ x ≤ 9.5	12
    9.5≤ x ≤ 11.5	5 x 1.6 = 16
    11.5≤ x ≤ 15.5	5 x 0.8 x 4 = 16
    15.5≤ x ≤ 21.5	5 x 2 x 6 = 60

      
12.  
    1. at P y= o ∴ 3(0) + 4(x) = 12
                  x = 3 
                     = P(3,0)
    2. y= −⁴/₃ x + 3       m1 = −⁴/₃ m2 =³/₄
       y – 0 = ³/₄
        x−3
       4y = 3x – 9 
       ∴  Y = ³/₄x– 2¹/₄
13. L. S. F= 12 : 8 = 3 : 2
    V.S. F = 27 : 8
    27 = 2litres
    8 =      ?
     8  x 2= 16 litres
    27         27
    (¹⁶/₂₇ x 1000) cm³
    = 592.592593cm³ =592.59cm³
14. AB= (K 4 3 2)  (1 2 3 −4)  = (K+12 2K−16 9 −2)
    −2(K+12) −9 (2K−16)=10
    −2K−24−18K+144=10
    −20K = −110
    ∴ K=5.5
15. Total ration ¼ + ½ + ¹/₅ = 5+10+4 = 19
                                                20         20
    Vol. Shared = 19 x 1000 = 950cm³
                         20
    Soita =  ½   x 950
              ¹⁹/₂₀
    10 x 950 = 500cm³
    19
16. log b² = log b² − log a
         a
    2(0.48) – 0.30
    0.96 – 0.30
    = 0.66
17.  
    1. V.R = 90+110 = 200km/h
       10.35a.m – 8.15a.m = 2hrs 20min = 2 ¹/₃ hrs
       Distance covered by matatu by 10.35cm
       = ⁷/₃ x 90 = 210km
       Remaining distance 760 – 210 = 550km
       Time taken = 550 = 2 ¾ hrs
                           200
       Distance minibus had moved = ¹¹/₄ x 90 = 247.5km
              Distance from A = 210 + 247.5
                                      = 457.5km
    2. They met at   10.35
                        +   2.45
                            13.20
                       = 1320hrs or 1:20pm
    3. By 10.30a.m minibus had covered
       ⁹/₄ x 90 = 202.5km
       Time taken by minibus to B
       760 – 202.5 = 6⁷/₃₆hrs = 6.19hrs
              90
       Distance covered by the motorist in this time.
       6.19 x 100 = 619km
18. 
    
    A^I = (1 1) + (2 2) = (3 3)
    B^I = (3 1) + (2 2) = (5 3)
    C^I = (1 3) +(2 2) = (3 5)
    A^II =(−5,3)  B^II = (−3, 3) C^II = (−3,5)
    A^III = (3,−3) B^III = (5, −3) C^III = (3,−5)
    A^IV = (−0.6, −3.8) B^IV =( −2, −2.8) C^IV = (−3,−5)
    Object and image 1, image 3, image 4,
19. 1. (4000 x 12) + (1100 x 12)
       = Sh. 61,200
    2. 1^st slab 4200 x 2= 8400
       2^nd slab 3800 x 3 = 11400
       3^rd slab 4600 x 5 = 23000 = 42800
       4^th slab y x 6 = (61,200 – 42800)
       y = K₤ 3066.67
       Taxable income= (12600 + 3066.67)
       = K₤ 15666.67
    3. 15666.67 x 20 − 10800
               12
       = KSh. 15,311.12
    4. 26111.12 – 4000
       = Sh. 22,111.12
20.  
    1. PQ = 2(8sin 35)
       = 9.177 = 9.18
    2. =8sin 35
          sin 20
       = 13.42
    3. Area of minor segment circle centre A
       ⁷⁰/₃₆₀ x 3.142 x 8 x 8 −½ x 8 x 8sin 70 = 9.03
    4. Area of minor segment circle centre B
       ⁴⁰/₃₆₀ x 3.142 x 13.42² –½ x 13.42 x 13.42 x sin 40
        = 4.99cm²
    5. Area of shaded region = Area of Δs
       APQ and PQB – Area =(30.07+57.88)−(9.03+4.99)
           =73.93cm²
21.  
    1.  
       
    2.  
       1. N20°W
       2. S42°W
    3.  
       1. 6.4 x 100km = 640km
       2. 8.8 x 100km = 880km
    4.  
       1. 300°
       2. 268°
22. 
    
    OS = ¹/₃OP QT = ¾OS  OR = ¹/₃OQ
    1. SR = SO + OR
       =¹/₃P + ¹/₃Q
       = ¹/₃(Q – P)
    2. QR = QO + OS
       = Q + ¹/₃P
       = ¹/₃P – Q
    3. PT = PS + ST
       = −²/₃P + ¼(−QS)
       = −²/₃p + ¼ (Q − ¹/₃P)
       =−²/₃ + ¼q − ¹/₁₂p
       = −²/₃ − ¹/₁₂p + ¼q
       =−⁹/₁₂p + ¼q
       = ¼q − ¾p
    4. TR = TQ + QR
       = −¾ QR − ²/₃Q
       = −¾(¹/₃p – q)− ²/₃Q
       = −¼p + ¾q − ²/₃q
       9Q-8Q
          12
       = −¼P + ¹/₁₂Q
       = ¹/₁₂Q −¼P
       PT = ¼Q − ¾P
       TR = ¹/₁₂Q −¼P
       ∴ PT = 3TR or ¹/₃PT = RT
       Common point T
       PT is a multiple of TR
       PT = 3TR
       Hence PTR are collinear
23.  
    1. ∠DCT = 38°-the angle which the chord makes with tangent is equal to the angle subtended by the same chord in the alternate segment of the circle
    2. ∠DEA = 90°-Diameter subtends right angle at any point on the circumference of the circle
    3. ∠ACB = 26°- The base angles of isosceles triangle are equal
    4. ∠BDC = 26°-Angles subtended on the circumference by the same arc in the same segment are equal
    5. ∠BOA = 52°-The angle which an arc subtends at the centre is twice that it subtends at any point on the circumference of the circle
24.  
    1. 
       

       x	−8	−7	−6	−5	−4	−3	−2	−1	0	1	2	3	4
       2x2	128	98	72	50	32	18	8	2	0	2	8	18	32
       5x	−40	−35	−30	−25	−20	−15	−10	−5	0	5	10	15	20
       −12	−12	−12	−12	−12	−12	−12	−12	−12	−12	−12	−12	−12	−12
       y	76	51	30	13	0	−9	−14	−15	−12	−5	6	21	40

       
       B1 – For half + correct values B1B1 for all values.
    2.  
       1. 2x² + 5x – 12 = y
          2x² + 5x – 12 = 0
                            0 = y
          x = −4 or 1.5
       2. (2x² + 5x – 12 = y)3
          (3x² + 7x –3 = 0)2
          (6x² +15x – 36 = 3y) − (6x² + 14x – 6 =0)
           x – 30=3y
          y=¹/₃x-10
          x=–4.6, 2.4