MATHEMATICS PAPER 1 - 2019 KCSE Prediction Questions Set 2

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

1. Evaluate (4 marks)
   
2. Without using logarithm tables or calculators, solve for x in the equation 12^2x+1 = 4^2x+1 (3 marks)
3. Use square, reciprocal and square root tables to evaluate, correct to 4 s.f the expression below (3 marks)
   
4. The line L₁ with equation 2x + 3y = 4 is reflected along the line y=0. Find the equation L₂. Give your answer in the form, ax + by − c = 0 (3 marks)
5. A tour company in Kenya received US dollar 100,00. The money was converted into sterling pounds in a bank whose exchange rate is given below
   F

   	Buying (Kshs)	Selling (Kshs)
   1 US Dollar	100.20	100.98
   1 Sterling Pound	131.13	132.11

   If the money was erroneously converted back to kshs, find the percentage loss made. Give your answer correct to 3 d.p. (3 marks)
6. The figure below shows a solid made by pasting twp equal regular tetrahedron
   
   
   1. Draw a net of the solid (2 marks)
   2. If each face is an equilateral triangle of sides 5 cm, find the surface area of the solid (2 marks)
7. The straight line whose equation is 5y − 7x + 35 = 0 passes through points P, R and Q. If point Q is on the X axis, point P on the Y axis and point R is such that 2PR = 3RQ, find the equation of line AR in double intercept form given point A (3, −3) (3 marks)
8. In the figure below O is the center of the circle and DOB is the diameter. Find the value of Y if angle AOD = 120^o. (2 marks)
   
9. Solve the inequality and state the integral values that satisfies it (3 marks)
   
10. Without using mathematical tables or calculators simplify the expression (3 marks)
    
11. Without using a calculator or mathematical tables, evaluate (3 marks)
    
12. Evaluate (3 marks)
    
13. Use logarithms tables only to find the value of (4 marks)
    
14. The image of triangle PQR after a rotation of 180^o about (2,3) is P'Q'R. If P'Q'R is given a translation (½) the final image is P''(4, 6), Q''(3,7), and R'(3,5). Find the coordinates of the object without the use of a Cartesian plane (3 marks)
15. A bird flew from a point P(3, −4) to a point Q(−6, 10) and then  to a point R (−24, 38)
    1. Write the two vectors representing the birds movement in terms of the unit vectors (2 marks)
    2. Show that points P,Q and R are collinear (1 mark)
16. In the figure below BE//DC, AD = 8 cm, AB = √41 and AE = 5 cm
    
    Find the area of the quadrilateral DEBC (3 marks)

SECTION II (50 MARKS)
Answer any five questions from this section

17. The figure below shows a trough whose cross-section is a triangle of equal lengths. The trough which is 8 meters long initially contains water to a depth of 10 cm and water flows into the trough at the rate of 20 litres per minute. If the length of each side of the larger triangle is four times the previous depth of water in the trough, calculate to the nearest minute the time it takes to fill the trough (10 marks)
    
18. Machana starts walking towards the next village 24 km away at noon. He walks for half an hour at an average speed of 8 km/hr before his friend catches up with him and offers him a lift on his bicycle which moves at an average speed of 25km/hr. It takes him 2.5 minutes to board the stationary bicycle.
    1. Determine how far he walks before he is given the lift (2 marks)
    2. At what time did his friend start if the two are neighbors (3 marks)
    3. How much longer would he take to complete the journey if he head not been given the lift (5 marks)
19. The table below shows the masses (measured to the nearest kg) of 200 people
    

    Mass (kg)	40-49	50-59	60-69	70-79	80-89	90-99	100-109
    No. of people	9	27	70	50	26	12	6

    1. Draw and ogive for the above data (4 marks)
    2. Use your graph to estimate 
       1. The median mass (1 mark)
       2. The number of people whose mass lies between 70.5 kg and 75.5 kg (1 mark)
    3. From your graph, find
       1. The lower quartile (1 mark)
       2. The upper quartile (1 mark)
       3. The inter-quartile range (2 marks)
20. The figure below shows two intersecting circles with their centres A and B on same side of the chord PQ. Given that AP = 4 cm, radius BP=3 cm the chord PQ = 5.1 cm and the joining A to B is perpendicular to PQ.
    
    Determine
    1. The length AB (3 marks)
    2. The shaded area (7 marks)
21.  
    1. Draw the graph of y=½x²(4−x) fro −1≤x≤4 using an interval of 0.5.
    2. Use your graph tp solve the equation ½x²(4−x) − ½(x + 3) = 0  (3 marks)
    3. What is the equation in x whose solutions are the values of x in (b) above (1 marks)
    4. For what ranges of values of x is x²(4−x) greater than x+3 (2 marks)
22. Five towns A,B,C,D and E are situated such that A is 200km from B on a bearing of N50^oE. C is 300 km from B on a bearing of 150^o. D is 350km on a bearing of s60^oW from C. E is 200 km from D and the bearing of D from E is S80^oE, using a scale of 1 cm to represent 50 km
    1. Draw the diagram representing the positions of the towns (6 marks)
    2. From the diagram determine,
       1. The distance and bearing of A from E in compass bearing (2 marks)
       2. The compass bearing of D from B (2 marks)
23. The figure below is a cross-section of a 3 dimensional representation of a company logo. It is in the shape of a hemisphere and a conical frustum with dimensions given for the cross section. The height of the frustum is 5 cm
    
    
    1. Calculate the surface are of the solid (6 marks)
    2. calculate the volume of the metal used  to make the logo (4 marks)
24. The new Nairobi cinema hall has a maximum sitting capacity of 468 people with 3 long special benches and 2 short ones. The long benches take two more people than the shorter ones. The new management finds this arrangement crowded and decides that by having one more person on each long bench, he can take out some rows and still retain the same number of  people. If one row of benches was taken out, Find the original number of people per row (10 marks)