Mathematics Paper 1 Questions - Londiani Joint Mock Exams 2022

Instructions

• Write your name, index number, school, date and signature in spaces provided above.
• The paper contains two sections I and II.
• Answer all questions in section I and any five questions from section II in the spaces provided below each question.
• Show all the steps in your calculations giving your answers at each stage in the spaces below each question.
• Marks may be given for correct working even if the answer is wrong
• Any negligent and slovenly work will be penalised
• Non-programmable silent electronic calculator and mathematical tables may be used except where stated otherwise.
• Candidates should check the question paper to ascertain that all the pages are printed as indicated and that no questions are missing
• Write the answer in English

For Examiner’s Use Only
SECTION I

SECTION II

QUESTIONS

SECTION I (50 MARKS)
ANSWER ALL THE QUESTIONS IN THIS SECTION

1. Evaluate: (3mks)
2. Find the value of k in the quadratic expression x² - kx + 49 that will make it a perfect square? (3mks)
3. Solve for x in the equation: 27^x x 3^{(2x - 2)} = 9^{(x + 2)} (3mks)
4. Three bells ring at regular interval of 9 min, 15 min and 21 min. The bells ring at 5.45 p.m. by 10.00 a.m. next day, how many times will they have rung together? (3mks)
5. From a point 20m away on a level ground the angle of elevation to the bottom of the window is 27º and the angle of elevation of the top of the window is 32º . Calculate the height of the window. (3mks)
6. The currency exchange rates of a given bank in Kenya are as follows;
   

   Currency	Buying	Selling
   1 sterling pound	135.50	135.97
   1 US dollar	72.23	72.65

   A tourist arrived in Kenya with 5,000US dollars which he converted to Kenya shillings upon arrival. He spent Ksh.214,500 and converted the remaining to sterling pounds. How many pounds did he receive? (3mks)
7. Given that (90 - a ) = 1/2, find without using trigonometric tables the value of;
   1. cos a (2mks)
   2. tan(90º - a) (2mks)
8. The sum of the interior angles of a regular polygon is 1260º. Find the number of sides of the polygon; hence give the name of the polygon. (3mks)
9. Find the integral values of x which satisfy the following inequalities;
   2x + 3 > 5x - 3 > -8  (3mks)
10. Given that log 2=0.3010, log 3=0.4771 and log 7=0.8451, find without using tables the value of log 42. (3mks)
11. The mean of n numbers is 15. If the same numbers together with 20 have a mean of 16, find the value of n (3mks)
12. Use reciprocal and square tables to calculate to 4 significant figures the value of 0.4766² + 1/2754 (3mks)
13. A shirt whose marked price is Ksh.800 is sold to a customer after allowing him a discount of 13%. If the trader makes a profit of 20%, find how much the trader paid for the shirt. (3mks)
14. In the figure below, ABCD is a cyclic quadrilateral. Point O is the centre of the circle. ∠ABO = 30º and ∠ADO = 40º.
    
    Calculate the size of angle;
    1. ∠BAD (2mks)
    2. ∠BCD (2mks)
15. Using a pair of compasses and a ruler only construct a triangle ABC such that AB = 4 cm, BC = 6 cm and angle ABC = 135º (3mks)
16. The figure below shows a net of a solid which is not drawn to scale.
    
    Sketch the solid ABCDEF with ABCD as the base. (3mks)

SECTION II (50MKS)
ANSWER ANY FIVE (5) QUESTIONS IN THIS SECTION

17. The masses of 40 students were measured to the nearest kilogram and recorded as shown below.
    52 58 54 x y 53 56 51 43 41 53 58 54 65 58 59 49 63 49 49 47
    45 46 52 52 55 52 55 49 47 53 63 42 45 46 48 60 49 48 53
    1. Find x and y if x + y =110
       y - x = √64 (2mks)
    2. Using a class interval of 5, and starting with 40 as the lower limit, make a frequency distribution table for the above data. (2mks)
    3. From the above data:
       1. State the modal class (1mks)
       2. Calculate the mean mass (2mks)
       3. Calculate the median mass (3mks)
18. The figure below shows a frustum. The top and bottom radii are 5cm and 10cm respectively, while the vertical height of the frustum is 12cm.
    
    Find the:-
    1. Slant height of the frustum. (3mks)
    2. Curved area of the frustum. (3mks)
    3. Volume of the frustum. (4mks)
19. A triangle ABC has vertices A(2,1), B(5,2) and C(0,4).
    1. On the grid provided plot the triangle ABC. (2mks)
       
    2. A¹B¹C¹ is the image of ABC under a translation . Plot A¹B¹C¹ and state its coordinates. (2mks)
    3. Plot A¹¹B¹¹C¹¹ the image of A¹B¹C¹ after a rotation about the origin through a negative quarter turn. State its coordinates. (3mks)
    4. A¹¹¹B¹¹¹C¹¹¹ is the image of A¹¹B¹¹C¹¹ after a reflection on the line y = 0. Plot A¹¹¹B¹¹¹C¹¹¹ and state its coordinates. (3mks)
20. A group of people planned to contribute equally towards a water project which needed Ksh. 2,000,000 to complete. However 40 members of the group withdrew from the project. As a result each of the remaining members were to contribute Kshs. 2,500 more.
    1. Find the original number of members in the group (5mks)
    2. Forty five percent of the value of the project was funded by constituency Development fund (CDF). Calculate the amount of contribution that would be made by the remaining members. (3mks)
    3. Members contribution were in terms of labour provided and money contributed. If the ratio of the value of labour to the money contribution was 6:9. Calculate the total amount of money contributed by the members (2mks)
21.                      
    1. A line, L₁ passes through the points (3, 3) and (5, 7). Find the equation of L₁, in the form of y = mx + c where m and c are constant. (3mks)
    2. Another line L₂ is perpendicular to L₁ and passes through (-2, 3) Find:
       1. The equation of L₂ (3mks)
       2. The x- intercept of L₂ (1mk)
    3. Determine the point of intersection of L₁ and L₂. (3mks)
22.                    
    1. find A^-1 the inverse of matrix (2mks)
    2. Mr. Rotich bought 5 Biology books and 6 Chemistry book for a total of Ksh 2,440. Mrs. Njuguna bought 7 Biology books and 9 Chemistry books for a total of Ksh 3,560.
       1. Form matrix equation to represent the above information. (1mk)
       2. Use matrix method to find the price of a Biology book and that of Chemistry book. (4mks)
    3. A school bought 36 Biology books and 50 Chemistry books. A discount of 5% was allowed on each Biology book whereas 8% was allowed on each Chemistry book. Calculate the percentage discount on the cost of all the books. (3mks)
23. A particle moves such that t seconds after passing a given point O, its distance S metres from O is given by S= t (t-2) (t-1)
    1. Find its velocity when t = 2 seconds (3mks)
    2. Find its minimum velocity (2mks)
    3. find the time when the particle is momentarily at rest (3mks)
    4. Find its acceleration when t=3 seconds (2mks)
24. A bird flies from tree P to another tree Q which is 50m on a bearing of 030º from P. From Q it flies 80m on a bearing of N60ºW to another tree R and finally flies due South to another tree S which is on a bearing of 320º from P.
    1. using the scale 1cm = 10m, construct an accurate scale drawing showing the positions of P,Q,R, and S (4mks)
    2. by measurement from your scale drawing determine;
       1. the distance and bearing of R from P (2mks)
       2. the distance and bearing of S from Q (2mks)
       3. the distance of S from P (1mk)
       4. the distance of S from P (1mk)