Mathematics Paper 2 Questions - Londiani Joint Mock Exams 2022

INSTRUCTIONS TO CANDIDATES

1. Write your name and index number in the spaces provided above.
2. Sign and write date of examination in the spaces provided above.
3. This paper consists of two sections; Section I and Section II.
4. Answer All questions in Section I and only Five questions from section II
5. All answers and working must be written on the question paper in the spaces provided below each question.
6. Show all the steps in your calculations giving answers at each stage in the spaces provided below each question.
7. Marks may be given for correct working even if the answer is wrong.
8. Non-programmable silent electronic calculators and KNEC Mathematical tables may be used except where stated otherwise.
9. Candidates should answer questions in English.

For examiner’s use only.
Section I

Section II

QUESTIONS

SECTION 1 (50 MARKS)

1. Evaluate using squares, cubes and reciprocal tables (4 marks)
   
2. Make x the subject in  = K (3 marks)
3. Ali deposited Ksh.100,000 in a financial institution that paid simple interest at the rate of 12.5% p.a. Mohamed deposited the same amount of money as Ali in another financial institution that paid compound interest. After 4 years, they had equal amounts of money. Determine the compound interest rate per annum to 1 decimal place. (3 marks)
4. Simplify  (3 marks)
5. Expand [1 - 2x]⁴ , hence find the value of [1.02]⁴ correct to 3 significant figures. (3 marks)
6. If sin x = 2b and cos x = 2b√3, find the value of b (3 marks)
7. Find the relative error in given that , a=77ml , b = 23ml, c = 36ml and d = 16ml (3 marks)
8. Without using a calculator or mathematical tables, express  in surd form and simplify. (3 marks)
9. The equation 3x² - 8px + 12 = 0 has real roots. Find the value of P. (2 marks)
10. A construction company employs 200 artisans and craftsmen in the ratio 1:3 every week. An artisan is paid 2 ½ times as much as a crafts man. At the end of 3 weeks the company paid ksh 1485000 to those employees. Find how much each artisan and each craftsman is paid. (a working week has six days) (3 marks)
11. A dam containing 4158m³ of water is to be drained. A pump is connected to a pipe of radius 3.5cm and the machine operates for 8 hours per day. Water flows through the pipe at the rate of 1.5m per second. Find the number of days it takes to drain the dam. (4 marks)
12. Two brands of coffee Arabica and Robusta costs sh.4,700 and sh.4,200 per kilogram respectively. They are mixed to produce a blend that costs shs.4,600 per kilogram. Find the ratio of the mixture. (3 marks)
13. Under a transformation represented by a matrix , a triangle of area 10cm² is mapped onto a triangle whose area is 110cm². Find x (3 marks)
14. Find the distance between the centre 0 of a circle whose equation is 2x² + 2y² + 6x + 10y + 7 = 0 and a point B(-4, 1). (3 marks)
15. Solve for x in the equation: (log₂x)² + log₂8 = log₂x⁴ (4 marks)
16. The figure below shows a circle inscribed in an isosceles triangle ABC. If Q, P and R are the points of contact between the triangle and the circle, O is the centre of the circle, BO = 19.5cm and BQ = 18 cm. Find the radius of the circle and hence the length of the minor arc PQ. (3 marks)
    

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

17. Income tax is charged on annual income at the rates shown below.
    

    Taxable Income K£	Rate (shs per K£)
    1 – 1500	2
    1501 – 3000	3
    3001 – 4500	5
    4501 – 6000	7
    6001 – 7500	9
    7501 – 9000	10
    9001 – 12000	12
    Over 12000	13

    A certain headmaster earns a monthly salary of Ksh. 8570.. He is entitled to tax relief of Kshs. 150 per month.
    1. How much tax does he pay in a year. ( 6 mks)
    2. From the headmaster’s salary the following deductions are also made every month;
       W.C.P.S 2% of gross salary
       N.H.I.F Kshs. 1200
       House rent, water and furniture charges Kshs. 246 per month.
       Calculate the headmaster’s net salary. (4 mks)
18.                          
    1.                        
       1. Taking the radius of the earth, R = 6370 km and π = 22/7 calculate the shorter distance between the two cities P (60ºN , 29ºW) and Q (60ºN, 31ºE) along the parallel of latitude. (3mks)
       2. If it is 1200Hrs at P, what is the local time at Q. (3mks)
    2. An aeroplane flew due South from a point A (60ºN, 45ºE) to a point B. The distance covered by the aeroplane was 800km. Determine the position of B. (4mks).
19.                        
    1. Draw ∆PQR whose vertices are P(1,1)Q(-3,2) and R(0,3) on the grid provided (2marks)
       
    2. Find and draw the image of ∆PQR under the transformation whose matrix is  and label the image P’Q’R’ (2mks)
    3. P’Q’R’ is then transformed into P¹¹ Q¹¹ R¹¹ by the transformation with the matrix Find the co-ordinates of  P¹¹ Q¹¹ R¹¹ and draw  P¹¹ Q¹¹ R¹¹ (3marks)
    4. Describe fully the single transformation which maps PQR onto  P¹¹ Q¹¹ R¹¹ and find the matrix of this transformation (3marks)
20.                  
    1. Complete the table for y = Sin x + 2 Cos x. (2mks)
       

       X	0	30	60	90	120	150	180	210	240	270	300
       Sinx	0			1.0		0.5		-0.5			-0.87
       2 cos x	2			0		-1.73		-1.73			1.0
       Y	2			1.0		-1.23		-2.23			0.13

    2. Draw the graph of y = Sin x + 2 cos x. (3mks)
       
    3. Solve sinx + 2 cos x = 0 using the graph. (2mks)
    4. Find the range of values of x for which y ≤ -0.5 (3mks).
21. A bag contains 3 red, 5 white and 4 blue balls. Two balls are picked without replacement. Determine the probability of picking.
    1. 2 red balls 2mks
    2. Only one red ball 2mks
    3. At least a white ball 2mks
    4. Balls of same colour. 2mks
    5. Two white balls 2mks
22.                        
    1. Draw the graph of the function (4mks)
       y = 10+3x – x²      for           –2<x <5
       
    2. use of the trapezoidal rule with 5 stripes, find the area under the curve from x = -1 to x = 4. 2mks
    3. Find the actual area under the curve from x = -1 to x = 4. 2mks
    4. Find the percentage error introduced by the approximation. 2mks
23. The figure below is a cuboid ABCDEFGH such that AB = 8cm, BC = 6cm and CF 5cm.
    Determine (a) the length
    1. AC (2mks)
    2. AF (2mks)
       
    3. The angle AF makes with the plane ABCD. (3mks)
    4. The angle AEFB makes with the base ABCD. (3mks)
24. If (x - 1¹/₈), x and (x + 3/2) are the first three consecutive terms of a geometric progression;
    1. Determine the values of x and the common ratio. (4 marks)
    2. Calculate the sum of the first 6 terms of this progression. (3 marks)
    3. Another sequence has the terms
       -13, -16, -19, ……………………………-310.
       Find the sum of this sequence. (3 marks)

MARKING SCHEME