MATHEMATICS PAPER 1 - KCSE 2019 STAREHE PRE MOCK EXAMINATION (WITH MARKING SCHEME)

SECTION I (50 MARKS)
Answer all the questions from this section

1. Simplify (3 marks)
   

2. Nyongesa spent a total of sh 970 on buying 3 text books and 5 pens. If he had bought 2 text books and 8 pens he would have saved sh 90. Find the cost of one text book. (3 marks)

3. The volumes of two similar solid cones are 1080cm³ and 1715cm³. If the curved surface area of the smaller cone is 840cm², find the curved surface area of the larger cone. (4 marks)

4. The exterior angle of a regular polygon is a quarter the size of an interior angle. Determine the number of sides of the polygon. (3 marks)

5.  where  is an acute angle. Without using mathematical tables or calculator, find:
   1. Sin Θ (2 marks)
   2. Tan (90-Θ) (1 mark)

6. Solve the inequality  and give your answer as a compound inequality      (3 marks)

7. Simplify  (3 marks)
   

8. Boaz comes to Kenya with 5 600 Euros which he exchanges to Kenya Shillings. While in Kenya he spends Kshs 280 700 touring various parts of Mombasa County and donates Kshs 120,000 to a school for the blind. He then converts the remaining amount to sterling pounds and leaves Kenya. The exchange rates at the time were as follows:
   

   Currency	Buying (Kshs)	Selling (Kshs)
   1 Euro	105.63	105.98
   1 Sterling pound	120.23	120.54

   
   Calculate the amount of sterling pounds that he had as he was leaving Kenya.   (3 marks)                                                                    

9. Traffic lights at three different functions show green light at the intervals of 10 seconds, 12 seconds and 15 seconds. They all show green at 1.00pm. At what time had they previously shown green together? (3 marks)

10. Find the area of the shaded region in the figure below. (3 marks)
    

11. The point M ( ¹/₂ , 1) is the mid – point of points A (a,-3) and B (4,b). Find the values of a and b and hence the magnitude of  AB   (3 marks)

12. Calculate the volume of 2kg of a cork if the density of the cork is 0.25g/cm³. (3 marks)

13. Solve the equation 2x²+4x+1=0 using completing the square method.      (3 marks)

14. PQRS is a trapezium in which PQ and SR are parallel. If PQ = 7cm, SR = 3cm, QR = 5cm and the area of PQRS is 18cm², calculate the height PS. (3 marks)

15. PQRS is a cyclic quadrilateral and O is the center of the circle. Angle QOS = 150⁰.
    
    Find the size of:
    1. Angle QPS (2 marks)
    2. Angle QRS (1 mark)

16. The heights of two vertical poles UV and XY are 15m and 8m respectively. They area 32m apart and on a horizontal ground as shown in the figure below.
    
    Calculate the angle of elevation of V from Y       (3 marks)

SECTION II (50 MARKS)
Answer FIVE questions ONLY from this section

17.  
    1. Given the matrix  ,find its inverse matrix Q (2 marks)
    2. Two friends Kamara and Teso, bought bulls at sh b per bull and goats at sh g per goat. Kamara spent sh.96,000 in buying 5 bulls and 24 goats while Teso spent sh 93,000 in buying 4 bulls and 30 goats
       1. Form a matrix equation to represent this equation (1 mark)
       2. Use the inverse matrix Q^-1 in (a) above to find the cost of one bull and that of one goat   (3 marks)
       3. Kamara sold all his animals at a profit of 30% per bull and 40% per goat. Teso sold his animals at a profit of 25% per bull and 50% per goat. Determine who made more profit and by how much.      (4 marks)

18. A bus left Kampala travelled towards Dar-es-Salaam at an average speed of 70km/h. after 3 ¹/₂hrs, a car left Dar-es-Salaam and travelled along the same road towards Kampala at an average speed of 90km/h. the distance between Kampala and Dar-es-Salaam is 1077km.
    Find:
    1. The distance of the bus from Kampala when the car left Dar-es-salaam (2 marks)
    2. The distance of the bus from Dar-es-Salaam when the car left the bus (4marks)
    3. After the car met the bus, the car stopped for 30 minutes. The car then continued with its journey and reached Kampala at the same time the car reached Dar-es-Salaam. At what new average speed between the meeting point and Kampala car move.   (4marks)

19. The following table shows masses to the nearest kilogram, of 200 animals in Moseti’s farm.
    

    Mass (kg)	40-49	50-59	60-69	70-79	80-89	90-99	100-109
    frequency	9	25	58	52	30	16	10

    
    
    1. Using the assumed mean of 74.5, find the actual mean (4 marks)
    2. Find the median mass (3marks)
    3. Calculate the standard deviation of the data (3marks)

20. The diagram below represents a glass in form of a frustum of a cone, with milk to a depth of 8cm. the internal radius of the glass bottom is 3cm while the radius of a circular surface of milk is 5cm.
    
    
    1. How many litres of milk correct to 2 significant figures are in the glass? (3marks)
    2. A metallic hemisphere solid accidentally drops inside the milk. The level of glass in milk then rises by 6mm. if no milk splashed out of the glass when the solid dropped in, find
       1. The volume of the hemisphere solid (4marks)
       2. The radius of the hemisphere solid (3marks)

21. In January, 2008, Kelly and Wasanga contributed sh 455,040 and sh 682,560 respectively and used the money to start a business. They agreed that the profit from the business would be shared as from the business would be shared as follows.
    24% to be shared equally
    36% to be shared in their ratio of contribution
    40% to be retained for the running of the business.
    1. The total profit for the year was 2008 was sh 750,000
    2. The difference in their total shares of profits      (4 marks)
    3. Calculate the amount that was retained for the running of the business. (2marks)
    4. In January 2009, Wasanga took his whole share of profit to a bank that offered a compound interest at the rate of 6% per annum. If the interest was compounded semi-annually, calculate his total interest in the bank in December 2011. (4marks)

22. A rectangular tree nursery measuring 16m by 14 m is situated at the centre of a rectangular piece of land. A path of uniform width runs all around the tree nursery. The width of the path is x metres and the area of the piece of land 360m2. The path is graveled at the cost sh 75 per square metre.
    Determine
    1. The value of x (5marks)
    2. The dimensions of the field (2marks)
    3. Calculate the cost of gravelling the path (3marks)

23. The diagram below shows a vertical electricity pole TR supported by two wires PT and QT. the points PQ and R are collinear and on the horizontal ground. The angle of elevation of T from P is 37⁰ and the distance between P and Q is 10m
    
    Given that the length of PT is 20m, calculate to the nearest whole numbers
    1. The length of the wire QT (3marks)
    2. The angle of elevation of T from Q (3marks)
    3. The height of TR of the electricity pole (2marks)
    4. The length of P from R (2marks)

24. Two vertices of the triangle are A(3,6) and B(7,12)
    1. Find the equation of the line AB (3marks)
    2. Find the equation of the perpendicular bisector of line AB (4marks)
    3. Given that AC is perpendicular to AB and the equation of line BC is y=-5x+47, find the co-ordinates of C             (3marks)

MARKING SCHEME