Mathematics Paper 1 Questions and Answers - Kassu Jet Joint Mock Exams 2023

Instructions

• This paper consists of two sections: Section I and Section 11.
• Answer ALL questions in section I and ANY five questions in section 11.
• All answers and workings must be written on the question paper in the spaces provided below each question.
• Show all the steps in your calculation, giving your answer at each stage in the spaces below each question.
• Non — Programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.

QUESTIONS

1. Evaluate 
   
   
2. Given that x°,x+40°, x+70°, x+20°, x-30°, 2x+40° and 3x-40° are interior angles of a cerain polygon. give the name of the polygon hence, find the value of x. (4 marks)
3. At point A, Roberto observed the top of a tall building at an angle of 32° . After walking for 112 meters towards the foot of the building he stopped at point B where he observed it again at an angle of 60°. Calculate the height of the building giving your answer to the nearest whole number. (3 marks)
4. Simplify the   
5. Find the gradient of the tangent to the curve y = 2x3 + 2x — 1 at x = —1, hence find the equation of the normal to the curv at the tangent point. (3 marks)
6. A Kenyan bank buys ans sells foreign currencies as shown below:
   

   	Buying in Ksh.	Selling in Ksh.
   1 Hongkong dollar	16.98	17.54
   1 South African rand	6.84	7.17

   
   A tourist arrives in Kenya with 106,000 Hongkong dollars and changed the 60% of the amount to Kenya shillings. While in Kenya she spent Ksh. 408,889 and changed the balance to South African rand before leaving for south Africa. How much altogether did he have in South African rands. (4 marks)
7. If =7, y = 6 and z = 4, evaluate (3 marks)
   xy/4+x-y/2z
8. Josephat makes a basic monthly salary of Ksh. 2,700. As a vendor, he must sell Ksh. 30000 worth of items per month. He also makes a 10% commission on all sales beyond the monthly quota. There is also an additional 10% bonus on top of the normal commission rate for any sales beyond Ksh. 39,000. If Jose sold Ksh. 42,000 worth of items this month, what is his total salary for the month to the nearest shillings? (3 marks)
9. Given that the area of the trapezium CDEB isRG cm2, find the length EA marked X. (3 marks)
10. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter IS 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of O. 6 g.(3 marks)
11. Without using tables or calculators evaluate 0.18×0.0432/2.16
12. .A two-digit number is such that three times the sum of its digits is less than the value of the number by 8 when the order of the two digits is reversed, the value of the number increases by 9. Find the number. (3 marks)
13. Use tables of reciprrocals and cube roots to evaluate 1.8+15.84 to 2 decimal places
14. A trader bought two brands of coffee P and Q. Brand P costs Ksh 80 per kg and brand Q costs Ksh. 100 per kg. She mixed the two brands and sold the mixture at Ksh. 110 per kg. If she made a 25% profit, determine the ratio P : Q per kilogram in the mixture.
15. Solve the following linear inequalities and represent the solution as a combined inequality
    x-z<3x+4
    5x-3≤x+5
16. Given that find x if p²-Q²=1

SECTION TWO (50 MARKS)
Answer any FIVE questions in this section

17. The heights of 100 maize plants were measured to the nearest centimeter and the results recorded in the table shown below.
    

    Height          x cm	Frequency (f)
    25-29	5
    34	12
    35 - 39	18
    40 44	30
    45 49	17
    50 54	11
    55 59	7

    
    
    
    1. Calculate to 2 d.p.
       1. the mean using assumed mean of 38 (2 marks)
       2. the standard deviation (3 marks)
    2. Draw an orgive to represent above information
    3. Using the graph, estimate the quartile deuatlon.
18. A triangular plot ABC is such that AB = 75 m, BC = 82 m and AC = 84 m.
    1. Calculate the:
       1. the area of the
       2. acute angle between the edges AB and BC. (3 marks)
       3. perpendicular height from A to BC
    2.  
       1. A tree is planted in the plot such that the tree points A, B and C. calculate the distance of the tree to 4s.f
       2. A equidistant from each of the tree from C giving your answer to 4s.f. (2 marks)
19. The figure below shows a righ solid frusum. the base is a rectangle measuring 15cm by 8cm while the top is a rectangle measuring 9cm by 4.8 cm. the height of the frustum is 12 cm. calculate its:
    1. Volume
    2. Surface area
20. Three business persons John, Felix and Susan contributed a capital of Ksh 80,000, Ksh. 12,000 and Ksh. 90,000 respectively to start a business. They agreed to share their profits as follows; 30% equally, 45% in the ratio of their contributions and the rest was saved for the running of the business. During a certain year, they made a profit of sh. 87 000. Determine:
    1. Amount shared equally
    2. Amount shared according to ratio
    3. Amount saved
    4. The share of Felix and Susan
21. A square ABCD has two of its vertices at A (2, 3) and C (8, 5).The equation of line AB is y — 2x + 1 = 0. (4 marks)
    1. Determine the equation of line BC in the form ax +by= c where a, b and c are whole numbers
    2. By calculation, determine the co-ordinate of point D
    3. Calculate the length of a side of the square ABCD to 3 significante figures
22. The graph given represents the velocity time graph of a sprinting cheetah recorded over a period of 50 seconds.
    1. Given that the acceleration of the cheetah is 2.5m/s², calculate the maximum speed attained in km/h. (3 marks)
    2. The average speed of the cheetah in the first 30 seconds. (3 marks) 
    3. The time it takes to cover three-fifths oft e whole journey. (4 marks)
23. A curve whose equation is 2y=6-12x+9x²-2x² turns at point A and B
    1. Find the coordinates of A and B
    2. determine the nature of its turning points (3 marks)
    3. A particle moving on a straight line passes a fixed point O at a velocity of 3 m/s. The acceleration of the particle t seconds after passing O is given by the equation a = 4 + 14t . Calculate its velocity two seconds later after it passes through O. (3 240
24.  
    1. Two vehicles P and Q left town T at the same time. P moved along a straight road on a bearing of 2500 at an average speed of 60 km/h. While Q was driven along a straight road on a bearing of N400E at an average speed of 40km/h. (a) Using the scale of I •.500000ff,
       determine:
       1. the positions of the two cars 6 hours later from T (3 marks)
       2. The actual distance between P and Q after 6 hours and the bearing of P from Q. (3 marks)
    2. the two cars were stationary at their new positions in (a) above at 9:00am. At 9:30 am, car P started moving on a straight road towards Q at an average speed of 30km/h. At 10:00 am, car Q started moving towards car P at an average speed of 50km/h. determine the time when the two cars met.(4 marks)

MARKING SCHEME

1. Evaluate 
   k=2.3333.....
   10k=23.3333/9k=21
   k=21/9=7/3
   k=19/90
   k=0.45.45
   10k=45.45/99k=45
   k=45/99=5/11
   2[(7/3+19/90)]÷5/11]
   =11 44/225
2. Given that x°,x+40°, x+70°, x+20°, x-30°, 2x+40° and 3x-40° are interior angles of a cerain polygon. give the name of the polygon hence, find the value of x. (4 marks)
   name heptagon
   sum of interior angles
   (n-2) 180° 
   (7-2) 180° =900°
3. At point A, Roberto observed the top of a tall building at an angle of 32° . After walking for 112 meters towards the foot of the building he stopped at point B where he observed it again at an angle of 60°. Calculate the height of the building giving your answer to the nearest whole number. (3 marks)
   tan 32 = h/112+x
   h=xtan60
   tan 32 (112+x)x= x tan 60°
   112tan32+xtan32=2tan60
   xtan 60-xtan 32
   x=112tan32/tan60-tan32
   x=112*0.6249/1.7321-0.6249
   x=63.2124
   h=63.224*17321
   h=109.490198
   height = 109
4. Simplify the 
   6x2-12x+x-2/3(x-2)(x+2)
   6x(x-2)+1(x-2)/3(x-2)(x+2)
   (6x+1)(x-2)/3(x-2)(x+2)
   6x+1/3(x+2)
   =6x+1/3x+6 
5. Find the gradient of the tangent to the curve y = 2x3 + 2x — 1 at x = —1, hence find the equation of the normal to the curv at the tangent point. (3 marks)
   
6. a+x=*1
7. A Kenyan bank buys ans sells foreign currencies as shown below:
   

   	Buying in Ksh.	Selling in Ksh.
   1 Hongkong dollar	16.98	17.54
   1 South African rand	6.84	7.17

   
   A tourist arrives in Kenya with 106,000 Hongkong dollars and changed the 60% of the amount to Kenya shillings. While in Kenya she spent Ksh. 408,889 and changed the balance to South African rand before leaving for south Africa. How much altogether did he have in South African rands. (4 marks)
8. If =7, y = 6 and z = 4, evaluate (3 marks)
   xy/4+x-y/2z
9. Josephat makes a basic monthly salary of Ksh. 2,700. As a vendor, he must sell Ksh. 30000 worth of items per month. He also makes a 10% commission on all sales beyond the monthly quota. There is also an additional 10% bonus on top of the normal commission rate for any sales beyond Ksh. 39,000. If Jose sold Ksh. 42,000 worth of items this month, what is his total salary for the month to the nearest shillings? (3 marks)
   
10. Given that the area of the trapezium CDEB isRG cm2, find the length EA marked X. (3 marks)
    
11. The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter IS 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of O. 6 g.(3 marks)
    
12. Without using tables or calculators evaluate 0.18×0.0432/2.16
    
13. .A two-digit number is such that three times the sum of its digits is less than the value of the number by 8 when the order of the two digits is reversed, the value of the number increases by 9. Find the number. (3 marks)
14. Use tables of reciprrocals and cube roots to evaluate 1.8+15.84 to 2 decimal places
    
15. A trader bought two brands of coffee P and Q. Brand P costs Ksh 80 per kg and brand Q costs Ksh. 100 per kg. She mixed the two brands and sold the mixture at Ksh. 110 per kg. If she made a 25% profit, determine the ratio P : Q per kilogram in the mixture.
    
16. Solve the following linear inequalities and represent the solution as a combined inequality
    x-z<3x+4
    5x-3≤x+5
17. Given that find x if p²-Q²=1
    

SECTION TWO (50 MARKS)
Answer any FIVE questions in this section

17. The heights of 100 maize plants were measured to the nearest centimeter and the results recorded in the table shown below.
    

    height x cm	frequency (f)	mid point		C-e
    25-29	5	32	-6			29.5
    34	12	37	-1			44.5
    35-39	18	42	4	120		49.5
    40-44	30	47	9	153	480	54.5
    45-49	17	52	14	154	1377	59.5
    50-54	11	57	19	133	2156
    55-59	7				2527

    
    
    1. Calculate to 2 d.p.
       1. the mean using assumed mean of 38 (2 marks)
       2. the standard deviation (3 marks)
          
    2. Draw an orgive to represent above information
       
    3. Using the graph, estimate the quartile deuatlon.
       Q₁=1⁄4*100=25^R=37
       Q₃=3⁄4*100=75^R=47.5
       47.5-37/2
       10.5/2
       =5.25
18. A triangular plot ABC is such that AB = 75 m, BC = 82 m and AC = 84 m.
    1. Calculate the:
       1. the area of the
       2. acute angle between the edges AB and BC. (3 marks)
          
       3. perpendicular height from A to BC
          
    2.  
       1. A tree is planted in the plot such that the tree points A, B and C. calculate the distance of the tree to 4s.f
          84/sin64.51 = 2R
          2R=84/0.4303
          2R=195.2126
          R=97.6063
       2. A equidistant from each of the tree from C giving your answer to 4s.f. (2 marks)
19. The figure below shows a righ solid frusum. the base is a rectangle measuring 15cm by 8cm while the top is a rectangle measuring 9cm by 4.8 cm. the height of the frustum is 12 cm. calculate its:
    
    
    1. Volume
       
20. Three business persons John, Felix and Susan contributed a capital of Ksh 80,000, Ksh. 12,000 and Ksh. 90,000 respectively to start a business. They agreed to share their profits as follows; 30% equally, 45% in the ratio of their contributions and the rest was saved for the running of the business. During a certain year, they made a profit of sh. 87 000. Determine:
    1. Amount shared equally
       
    2. Amount shared according to ratio
       
    3. Amount saved
       
    4. The share of Felix and Susan
21. A square ABCD has two of its vertices at A (2, 3) and C (8, 5).The equation of line AB is y — 2x + 1 = 0. (4 marks)
    1. Determine the equation of line BC in the form ax +by= c where a, b and c are whole numbers
       
    2. By calculation, determine the co-ordinate of point D
       
    3. Calculate the length of a side of the square ABCD to 3 significante figures
22. The graph given represents the velocity time graph of a sprinting cheetah recorded over a period of 50 seconds.
    1. Given that the acceleration of the cheetah is 2.5m/s², calculate the maximum speed attained in km/h. (3 marks)
    2. The average speed of the cheetah in the first 30 seconds. (3 marks) 
    3. The time it takes to cover three-fifths oft e whole journey. (4 marks)
23. A curve whose equation is 2y=6-12x+9x²-2x² turns at point A and B
    1. Find the coordinates of A and B
       
    2. determine the nature of its turning points (3 marks)
       
    3. A particle moving on a straight line passes a fixed point O at a velocity of 3 m/s. The acceleration of the particle t seconds after passing O is given by the equation a = 4 + 14t . Calculate its velocity two seconds later after it passes through O. (3 240
       
24.  
    1. Two vehicles P and Q left town T at the same time. P moved along a straight road on a bearing of 2500 at an average speed of 60 km/h. While Q was driven along a straight road on a bearing of N400E at an average speed of 40km/h. (a) Using the scale of I •.500000ff,
       determine:
       1. the positions of the two cars 6 hours later from T (3 marks)
          
       2. The actual distance between P and Q after 6 hours and the bearing of P from Q. (3 marks)
          
    2. the two cars were stationary at their new positions in (a) above at 9:00am. At 9:30 am, car P started moving on a straight road towards Q at an average speed of 30km/h. At 10:00 am, car Q started moving towards car P at an average speed of 50km/h. determine the time when the two cars met.(4 marks)