MATHEMATICS PAPER 1 - KCSE 2019 MARANDA MOCK EXAMINATION

SECTION A (50MKS)            
Answer ALL the questions in this section in the spaces provided.

1. Without using a calculator, evaluate leaving the answer as a fraction in its simplest form (3mks)                                                                    

2. Solve for x in the equation  (3 marks)

3. The length of a solid prism is 10cm, its cross-section is an equilateral triangle of side 6cm. Find the total surface area of the prism.   (3mks)

4. In the figure below ABCDE is a cross-sections of a solid. The solid has uniform cross-section. Given that BG is a base edge of the solid, complete the sketch, showing the hidden edges with broken lines (3mks)
   

5. A shopkeeper sell two types of pangas, type x and type y. Twelve type x pangas and five type y pangas cost sh. 1260, while nine type x pangas and fifteen type y pangas cost sh. 1620. Musembi bought nineteen type y pangas. How much did he pay for them?   (4mks)

6. Ntutu had cows, sheep and goats in his farm. The number of cows was 32 and number of sheep was twelve times the number of cows. The number of goats was 1344 more than the number of sheep. If he sold ¾ of the goats, find the number of goats that remained. (4mks)

7. Given below is a line PQ. Without using a protractor construct another line through P making an angle of 37 ½ ^o with PQ. Using the constructed line subdivide BC into 7 equal parts (4mks) 
      

8. Given that OA =(4,5) and OB = (-3,8) find the mid-point m of AB       (2mks)

9. Simplify (3 MKS)
   

10. In the triangle, AB = 8.5cm, AC = 10cm and ABC = 90^o
    
    Calculate:-
    1. The length of BC   (1mk)
    2. The length of BD   (2mks)

11. Simplify   leaving the answer in the form     a   + b √c   where   a,b, and c are rational number.       (3mks) 

12.  Two matrices A and B are such that Given that the determinant of AB = 4, find the value of K.     (3mks)

13. A minibus covered a distance of 200km at an average speed of 100km/h. it travelled at a speed of 80km/h for 3/5 of its journey. At what speed did it travel the remaining part of the journey? (3mks)

14. The table below shows marks scored by 40 students in a mathematics test.
    

    Marks	30-39	40-49	50-59	60-69	70-79
    No of students	2	9	14	7	8

    
    Calculate the median mark (2mks)

15. Juma paid sh. 180 for a book after getting a discount of 10%. the shopkeeper made a profit of 20% on the sale of the set book. What percentage profit would the shopkeeper have made if no discount was allowed.?   (3mks)

16. A rectangular tank has a hole in it such that 11cm3 of water leaks out every 5 seconds. Using a ᴫ as 3.142, calculate
    1. the capacity of the water lost from the tank every hour (2mks)
    2. The time it takes to fill a cylindrical tank of radius 30cm and height 30cm into which the leaking water drains in hours to 4 significant figures (2mks) 

SECTION II (50MARKS)
ANSWER ANY FIVE QUESTIONS FROM THIS SECTION IN THE SPACES PROVIDED.

17. A line L passes through points (-2, 3) and (-1, 6) and perpendicular to a line P at (-1,6)
    1. Find the equation of L   (2mks)
    2. Find the equation of P in form ax + by = c where a,b, and c are constants   (2mks)
    3. Given that another line Q is parallel to L and passes through point (1,2) find the x and y intercept of Q (3mks)
18. Two shopkeepers Juma and Wanjiku bought some items from a wholesaler. Juma bought 18 loaves of bread, 40 packets of milk and 5 bars of soap while Wanjiku bought 15 loaves of bread, 30 packets of milk and 6 bars of soap. The prices of loaf of bread, a packet of milk and a bar of soap wereksh, 45ksh 50 and ksh, 150 respectively.
    1. Represent
       1. the number of items bought by Juma and Wanjiku using a 2 x 3 matrix (1mk)
       2. The price of items bought using a   3 x 1 matrix   (1mk)
    2. Use the matrix I (a) above to determine the total expenditure incurred by each person and hence the difference in their expenditure.   (3mks)
    3. Juma and Wanjiku also bought rice and sugar. Juma bought 36kg of rice and 23kg of sugar and paid ksh, 8160. Wanjiku bought 50kg of rice and 32kg of sugar and paid ksh, 11,340. Use the matrix method to determine the price of one kilogram of rice and one kilogram of sugar. (5mks)

19. The table below shows how income tax wascharged on income earned in a certain year.
    

    Taxable income per year (Kenya Pounds)	Rate (shilling per Kenya Pound)
    1   -   3630 3631   - 7260 7261   - 10890 10891   - 14520	2 3 4 5

    
    Mr. Gideon is an employee of a company and earns a salary of Ksh. 15,200 per month. He is housed by the company and pays a nominal rent of Ksh. 1050 per month. He is married and is entitled to a family relief of Ksh. 450per month
    1. Calculate his taxable income in k£ p.a.   (2mks)
    2. Calculate his gross tax per month.   (4mks)
    3. Calculate his net tax per month   (2mks)
    4. Calculate his net salary per month   (2mks)

20. The diagram below shows a triangle ABC with A(3,4)   B(1,3) and C(2,1)
    1. Draw   ∆ A’B’C’ the image of a   ∆ABC under a rotation of +90 about   (0,0)     (2mks
    2. Draw   ∆A”B”C” the image of     ∆ A’B’C’ under a reflection in the lines   y = x   (2mks)
       
    3. Draw     ∆ A”’B”’C”’ the image of   ∆ A ”B”C” under a rotation of   - 90^o about (0.0) (2mks)
    4. Describe a single transformation that maps   ∆ABC onto∆ A’’’B’’’ C’’’         (2mks)
    5. Write down the equations of the lines of symmetry of the quadrilateral   B B”A”’A’   (2mks)

21. The diagram below shows the speed time graph for a train travelling between two stations. The train starts from rest and accelerates uniformly for 150 seconds. It then travels at a constant speed for 300 seconds and finally decelerates uniformly for 200 seconds
    
    Given that the distance between the two stations is 10,450m, calculate the
    1. Maximum speed in km/h the train attained (3mks)
    2. Acceleration (2mks)
    3. Distance the train travelled during the last 100 seconds (2mks)
    4. Time the train takes to travel the first half of the journey. (3mks)
22. The table shows the mark scored by students in a maths exams
    1. Draw a cumulative frequency curve   (3mks)
    2. Use your graph to determine
       1. The median (1mk)
       2. The quartile deviation   (1mk)
       3. The number of students who scored above 67   (1mk)
    3. Use an assumed mean of 64.5 to calculate the standard deviation of the above data. (4mks)

23. A circular lawn is surrounded by a path of uniform width of 7M. the area of the path is 21% that of the lawn
    1. calculate the radius of the lawn (4mks)
    2. Given further that the path surrounding the lawn is fenced on both sides by barbed wire on posts at intervals of 10 metres and 11 metres on the inner and outer sides respectively. Calculate the total number of posts required for the fence   (4mks)
    3. Calculate the total cost of the post if one post cost shs.105 (2marks)

24. The displacement , S metres of a moving particles after t seconds is given by S = 2t³- 5t²   +   4t   +   2
    Determine
    1. The velocity of the particle when t = 3seconds   (3mks)
    2. The value of t when the particle is momentarily at rest   (3mks)
    3. The displacement when the particle is momentarily at rest   (2mks)
    4. The acceleration of the particles when   t = 3 seconds   (2mks)

MARKING SCHEME