Basic Mathematics Past Paper 2024 PDF - Exam Paper

PRESIDENT’S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT KIBAHA TC, BAGAMOYO DC AND KINONDONI MC (KIBAKI) FORM FOUR JOINT PRE-NATIONAL EXAMINATION 041 BASIC MATHEMATICS Time: 3 Hours...

PRESIDENT’S OFFICE REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT KIBAHA TC, BAGAMOYO DC AND KINONDONI MC (KIBAKI) FORM FOUR JOINT PRE-NATIONAL EXAMINATION 041 BASIC MATHEMATICS Time: 3 Hours YEAR: 2024 INSTRUCTIONS 1. This paper consists of sections A and B with a total of fourteen (14) questions. 2. Answer all questions 3. Each question in section A carries six (06) marks while each question in section B carries ten (10) marks. 4. All necessary working and answers for each question must be shown clearly 5. NECTA’s mathematical tables and non-programmable calculators may be used. 6. Write your Examination Number on every page of your answer booklet(s). 7. Where necessary use the following constants;  pi=π=3.14  Radius of the Earth, r =6370 km 3 −3  1 cm =10 litre Page 1 of 5  SECTION A (60 MARKS) Answer all questions in this section. 1 (a) The cost of construction of the line of the standard gauge railway (SGR) from Dar Es. Salaam to mainland was shs. 8488456019500. Write this numerical amount of money in words. (b) Evaluate the expression 1.0 3+2. 428571 and leave your answer in fractional form. (c) The sum of two numbers is twenty-three. Twice the larger number is four more than four times the smaller. What are the numbers? 2 (a) Prove that the following expression is a rational number. √ 3+2 √2−√ 3−2 √ 2 (Hint: start rationalising by squaring the expression). (b) Find the solution set for the equation 2 log x=log 4 +log ( 2 x −3 ) 3 (a) The class has thirty students. Twenty students study physics while twelve study both. physics and chemistry. If eight students study neither physics nor chemistry, how many students studies chemistry? (b) The knock-out match is the one which emerges with a winner, no draw match. The football experts predict the outcome of two knock-out matches. The first match is of Simba against Yanga, the second is of Real Madrid against Barcelona. The chance of Simba to win is 0.74 while that of Real Madrid to win is 0.65. What is the probability that both Yanga and Barcelona will win their matches? 4 (a) ´ which passes to points C (2 ,1) and D(6 ,1) is perpendicular to the line AB The line CD ´. ´ which passes through the point B( 5 , 3 ). Find the equation of the line AB. (b) (i) Define the word “solution”. (ii) Find the value of k which makes the following simultaneous equations to have no solution { y x −1= 5 15 k y x− =1 40 8 5 (a) 3 15 If sin A= and cos B= , where A and B are acute angles, find the exact value of. 5 17 sin( A +B). (b) The direction of vectors is such that the positive ray of the x-axis is zero degrees and anticlockwise rotation is positive. Three forces of magnitude 6 N, 5 N and 10 N are acting on the same load. The directions of the forces are 70°, 160° and 240° respectively. Find the Page 2 of 5  resultant force. 6 (a) 1 ( ) 2 =5 to evaluate the expression x + 1 2. Use the sentence x + 2 x x (b) Six people working 8 hour a day take ten days to finish a certain job. How long will i take for two people working 12 hour per day to finish the same job? 7 (a) The bank has a condition that on repaying back the borrowed loan the customer must be. charged the interest rate of 8% per annum. John the customers of the bank borrowed shs. 28,000,000. How much did he own after two years and five months. (b) Show that the solution set for the sentence (2¿¿ x−1) ( 3 y+1 ) =(3¿ ¿2) ( 23 ) ¿ ¿ is an equation of a straight line. 8 (a) Find the ratio of the sum of the first ten terms of the series. 2 4 8 log x +log x +¿ log x + ¿ log x +¿ ¿ ¿ ¿… to the first term. (b) Florida deposited sh. 48,000,000/= in a bank for three years at 4% per annum. Find the compound interest she earned if the interest is compounded at every three months. 9 (a) A fish pond has a shape of a triangle whose sides are 15 m, 10 m and 8 m long. If the depth of the pond. is 4 m, how many litres of water are needed to fill the pond? (b) The company stared a business on April 01, 2023 with capital of shs. 600,000 April 2, 2023: Purchased goods for cash shs. 400,000 April 3 Bought goods from Peter on credit shs. 100,000 April 4, 2023: Sold goods for cash shs. 300,000 April 5, 2023: Paid cash to Peter shs. 20,000 April 5, 2023: Paid salary for cash shs. 150,000 April 8, 2023: Paid goods on credit to Deus shs. 250,000 April 8, 2023: Paid transport expenses for cash shs. 120,000 Prepare the cash account using these transactions. 10. (a) Find the value of k which makes the equation 2 5 k x + 5 x − =0 4 to have equal roots. (b) Two points A and B on a straight coastline are 1 km apart, B being due East of A. If a ship is observed on bearings 167° and 205° from A and B respectively, what is its distance from the coastline? Page 3 of 5  SECTION B (40 MARKS) Answer all questions in this section. 11. The table below is the weight of patients measured in kilogram-force (kgf). 4 4 5 5 7 6 4 4 5 7 9 8 8 7 2 3 7 6 1 7 5 6 4 3 9 6 4 4 5 6 9 7 9 3 0 1 3 8 5 8 6 5 3 6 6 4 4 4 4 3 5 0 8 5 8 5 6 6 3 5 4 4 7 4 5 4 5 3 5 5 8 5 4 5 9 4 5 6 3 3 (a) Prepare the frequency distribution table representing the given data by using the classes 31 − 40, 41 − 50,…, 81 – 90. (b) Use the distribution table prepared in (a) to determine the measures of the central tendency. 12. (a) Define the following terms in relation to the spherical shape of the Earth (i) meridian (ii) longitude (b) An aeroplane flies from Rome (41° N, 12° E) towards Port Clarence (65° N, 168 ° W). The altitude of its path is 15 km above the sea level. Calculate the shortest distance that can be covered by the aeroplane for the journey from Rome to Port Clarence. (c) (i) Sketch a net of a regular tetrahedron. (ii) A tetrahedron is made of the base which is an equilateral triangle. The length of each slant edge of the tetrahedron is 20 m while that of each side of its base is 30 m. Calculate the shortest distance from the apex of the tetrahedron to its base. 13. (a) Two chords, AB and CD of a circle whose radius is 13 cm are equal and parallel. If each chord is 12 cm long, find the distance between them. (b) ´ passes to points A( 0 ,−5) and B(0 , 8). Use the line AB The line AB ´ to answer the following questions: (i) ´. Find the reflection matrix which defines the reflection through the line AB (ii Use the reflection matrix obtained from (i) to find the image of P(−5 ,−3) under reflection ) ´. through that line AB 14. The function is defined as f ( x)=⌊ x ⌋ −x where n ≤ x< n+ 1 (a) Sketch the graph of f ( x )=⌊ x ⌋ −x , given that −3< n< 3 (b Vitamin, protein and fat are nutrients in spinach and groundnuts. Spinach contains 20, 40 and 30 ) units of vitamin, protein and fat respectively. Groundnuts contain 50, 20 and 40 units of vitamin, protein and fat respectively. The cost of spinach per kilogram is shs. 5000. The cost of Page 4 of 5 groundnuts per kilogram is shs. 3000. If the minimum requirement is 800 units of vitamin, 1000 units of protein and 1200 units of fat, how much spinach and groundnuts should be bought to satisfy the conditions. Page 5 of 5