# MATHEMATICS PAPER 1 - 2019 MOKASA II MOCK EXAMINATIONS

INSTRUCTIONS TO CANDIDATES

• This paper consists of two sections: Section I and Section II
• Answer ALL questions from section I and ANY FIVE from section II
• Show all the steps in your calculation
• Non – Programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.

SECTION I 50 MARKS

1. Without using mathematical tables or calculator, evaluate:

Leaving the answer as a fraction in its simplest form.                                (2 marks)
2. Use prime factors to evaluate
(3 marks)
3. Solve for m in the equation:    (3 marks)
4.
1. Find the greatest common divisor of the term.                                    (1 mark)
2. Hence factorize completely this expression
(2 marks)
5. Solve for x if
(3 marks)
6. A car dealer charges 10% commission for selling a car. He received a commission of Ksh. 27,500 for selling a car. How much did the owner received from the sale of his car if the dealer added an extra charges of 5 %.                                   (3 marks)
7. Two similar cylinders have diameter of 7cm and 21cm. If the larger cylinder has a volume of 6237cm³. Find the heights of the two cylinders.                      (3 marks)
8. A sector of radius 12 cm subtends and angle of 700 at the centre. If the sector is folded to form a cone, calculate ;
1. The area of the curved part of the cone                                                  (2 marks)
2. The radius of the cone formed.                                                                  (2 marks)
9. Find all the integral values of x which satisfy the inequality              (3 marks)

10. The table below shows four principal crops produced in Kenya in the years 2000 and 2001. Use it to answer the questions below.
1. Using a radius of 5 cm, draw a pie chart to represent crop production in the year 2000.                                                                                                                (3 marks)
2. Calculate the percentage increase in wheat production between the years 2000 and 2001.                                                                                                            (1 mark)

 CROP AMOUNT IN METRIC TONNES YEAR 2000 2001 Wheat Maize Coffee Tea 70,000 200,000 98,000 240,000 13,000 370,000 55,000 295,000
1. Construct line AB 12.2 cm. Use a line X which meets line AB at A such that angle XAB is  to divide line AB into 8 proportional parts.                    (3 marks)
2. The cost of providing a commodity consists of transport, labour and raw material in the ratio 8:4:12 respectively. If the transport cost increases by 12% labour cost 18% and raw materials by 40%, find the percentage increase of producing the new commodity.                                                                                                      (3 marks)
3. A line L1 passes through point (-1,1) and perpendicular to the line L2 which makes an angle of 18.434948820 with the x-axis. Find the equation of L1 giving your answer in the double intercept form.                                                            (4 marks)
4. Given that and  find          (4 marks)
5. The exterior angle of a regular polygon is equal to one-third of the interior angle. Calculate the number of sides of the polygon and give its name.    (3 marks)
6. In the figure below, shows an irregular solid with a uniform cross-section. Complete the sketch, showing the edges clearly.                                          (2 marks)

SECTION II (50 MARKS)

(Answer ANY FIVE questions in the spaces provided)

1. The figure below shows a frustrum container with base radius 8 cm and top radius 6 cm. The slant height of the frustrum is 30cm as shown below. The container 90 percent full of water.
1. Calculate the surface area of the frustrum                                               (3 marks)
2. Calculate the volume of water. (4 marks)
3. All the water is poured into a cylindrical container of circular radius 7cm, if the cylinder has the height of 35cm; calculate the surface area of the cylinder which is not in contact with water. (3 marks)
2. Complete the table below for the function
(2 marks)
 x -3 -2 -1 0 1 2 3 4 -x3 27 8 0 -8 2x2 18 8 2 0 -4x 8 0 -16 2 2 2 2 2 2 2 2 2 y 26 2 -6 -46

1. On the grid provided below draw the graph of  for                   (3 marks)

1. Use the graph to estimate the roots of . (2 marks)
2. By drawing a suitable line on the graph solve the equation    (3 marks)
2. A lorry left Malaba for Nairobi, 500 km away at 6.00 am and travelled at an average speed of 60km/h. After travelling for 1hour it stopped for 30 minutes to unload some luggage then proceeded with its average speed. A coast bus left Nairobi for Malaba at 8.00 am and travelled at an average speed of 90km/h. Calculate
1. The distance travelled by the lorry before the bus started its journey. (2 marks)
2. The time of the day the two vehicles met                                                (4 marks)
3. How far from Malaba when they met.                                                      (3 marks)
4. The time the bus reached Malaba if it travelled continuously without stopping.        (1 mark)
3. The table below shows measurements in metres made by a surveyor in her field book. (Distance are given in metres)
 F 50 C 120 B 280 250 200 150 100 40 A E 40 D 100 B 50
1. Using the representative fraction scale of a map is , Draw the accurate measurements of the field   (3 marks)
2. Calculate the area of the field in hectares    (5 marks)
Using the above scale:
3. Calculate actual circumference of the circular maize farm of radius 2.1cm on the map in kilometres.  (2 marks)
1. The table below shows the marks of 100 candidates in an examination:
1. Draw a cumulative frequency curve to represent above data                (3 marks)
 Marks 1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 No of students 4 9 16 24 18 12 8 5 3 1

2. Using the graph determine:
3. the upper quartile                                                                                    (1 mark)
4. estimate how many students passed, if 55 marks is the pass mark.    (2 marks)
5. find the pass mark if 70% of the students are to pass                    (2 marks)
6. the range of marks obtained by the middle 80% of the students   (2 marks)
2. A ball is thrown upwards with a velocity of 40 m/s.
( Take acceleration due to gravity to be 10m/s)
1. Determine the expression of its height above the point of projection    (3 marks)
2. Find the velocity and height after 2 seconds and 3 seconds                  (2 marks)
3. Find the distance moved by the ball between t=1s and t=2s            (2 marks)
4. Find the maximum height attained by the ball.                                     (3 marks)
3. A transformation represented by the matrix maps P(0,0), Q(2,0), R(2,3) and S(0,3) onto P’, Q’, R’, S’
1. On the grid provided draw the quadrilateral PQRS and P’Q’R’S’    (3 marks)

2. Determine the area of PQRS , Hence or otherwise find the area of P’Q’R’S’  (2 marks)
3. A transformation represented by the matrixmaps P’Q’R’S’ onto P’’Q’’R’’S’’. On the same Cartesian plane draw and state the coordinates of P’’Q’’R’’S’’                                                                                                         (3 marks)
4. Determine the matrix of transformation that would map P’’Q’’R’’S’’ onto PQRS (2 marks)
4. In the figure below, OB = b and OA = a. If Y divides line OA in the ratio 11:-3 and OX:XB=2:-1,

1. Find in terms of a and b the vectors:
2. XA   (1 mark)
3. BY (1 mark)
4. If XD=hXA and BD=kBY, express OD in terms of
1. a, b and h (1 marks)
2. a, b and k   (1 mark)
5. using the results in (b) above, find the values of k and h hence find XD:DA and BD:DY.  (6 marks)

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