KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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ALT B | TIME, DISTANCE AND SPEED | | FORM 1 LEVEL | SECTION 1 | PAPER 2 | KCSE 2010 | QUESTION 16Below is a travel timetable for a bus travelling from town P to town S via towns Q and R.
If the distance between town P and town S is 220km, calculate the average speed at which the bus travels. (3 marks)
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ALT B | SCALE DRAWING | | FORM 1 LEVEL | SECTION 1 | PAPER 2 | KCSE 2010 | QUESTION 9The area of each small square of the grid below is 64 mm².
Estimate in mm², the area of the figure drawn on the grid. (3 marks) ALT B | SCALE DRAWING | SECTION 2 | QUESTION 24 | KCSE 2010 | FORM 1 LEVELThe angle of elevation of the top of a vertical mast, viewed by an observer 50m away, was found to be 16.7°.
ALT B | SCALE DRAWING-BEARING | SECTION 2 | QUESTION 21 | KCSE 2010 | FORM 1 LEVELTowns A, B and C are located such that B is 400 km to the north of A and town C is 750 km on a bearing of 225° from town B.
ALT B | COMMERCIAL ARITHMETIC 1 | SECTION 1 | QUESTION 16 | KCSE 2010 | FORM 1 LEVELA saleswoman was paid a basic salary of Ksh12 000 per month. She also received commission in two parts as follows: 2% for sales of up to Ksh 30 000, 3 1/2% for sales above Ksh 30 000. In one month she sold goods worth Ksh 84 000. Determine the saleswoman's total earnings that month. (4 marks) FEATURED QUESTIONSFEATURED PRODUCTSOn Sale On Sale FREE GRADE 4 REVISION KITS & PAST PAPERS TERM 1 2020
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IRE Grade 7 Opener Question Paper: Understanding the Quran, Hadith, and Tawheed Review: The IRE Grade 7 Opener Question Paper provides a comprehensive assessment of students' understanding of key concepts in Islamic Religious Education. The paper focuses on three main topics: the Quran, Hadith, and Tawheed, ensuring a well-rounded evaluation of students' knowledge. The questions in the paper are thought-provoking and require students to demonstrate a deep understanding of the subject matter. The first section covers the Quran, asking students to define the term and explain the need for its revelation. It also explores the roles of Angel Jibril in the revelation process and the two stages in which the Quran was revealed. Additionally, students are required to analyze the significance of Surah Al-Fatiha and derive lessons from it. The second section delves into the Hadith, examining the teachings of Surah Al-Nasir and Suratul Al-Asri. It also discusses the circumstances under which Suratul Fill was revealed and explores the differences between the Quran and Hadith. Furthermore, the paper highlights the evolution of Hadith, its forms, and its contribution to Islamic thought and culture. Lastly, the paper addresses the concept of Tawheed, requiring students to identify the articles of Iman and define Tawheed itself. It provides an opportunity for students to showcase their understanding of this fundamental concept in Islam. The questions are appropriately challenging for Grade 7 students, encouraging critical thinking and a comprehensive understanding of the subject matter. The paper also emphasizes the importance of neatness and provides ample space for students to write their answers. Overall, the IRE Grade 7 Opener Question Paper effectively assesses students' knowledge of the Quran, Hadith, and Tawheed. It covers a wide range of topics and encourages students to think deeply about the principles and teachings of Islam. This paper serves as a valuable tool for evaluating students' grasp of key concepts in Islamic Religious Education. Three alarms are programmed to sound at intervals of 25 minutes, 30 minutes and 35 minutes.2/3/2024 ALT B | LCM | SECTION 1 | QUESTION 14 | KCSE 2010 | FORM 1 LEVELThree alarms are programmed to sound at intervals of 25 minutes, 30 minutes and 35 minutes. Given that the three alarms sound together at a particular time, determine the time, in hours, it will take for them to sound together again. (4 marks)
ALT B | RATES, RATIO & PERCENTAGE | SECTION 1 | QUESTION 12 | KCSE 2010 | FORM 1 LEVELThe price of a shirt and that of a pair of trousers are increased in the same ratio. The price of the shirt is increased from Ksh 800 to Ksh1 200. If the new price of the pair of trousers is Ksh 2 700, calculate its original price.
(3 marks) ALT B | GEOMETRICAL CONSTRUCTIONS | SECTION 1 | QUESTION 9 | KCSE 2010 | FORM 1 LEVELUsing a pair of compasses and a ruler only, construct:
(a) a triangle ABC such that AB = 6 cm, BC = 3.5cm and CA = 4 cm; (1 mark) (b) a circle to pass through the vertices of the triangle ABC. (2 marks) ALT B | FRACTIONS | SECTION 1 | QUESTION 7 | KCSE 2010 | FORM 1 LEVELWithout using a calculator, evaluate: (3 marks)
In the figure below, ABCDEF is a regular polygon. Line AB and EC are each extended to meet at G11/2/2024 ALT B | ANGLES AND PLANE FIGURES | SECTION 1 | QUESTION 6 | KCSE 2010 | FORM 1 LEVELIn the figure below, ABCDEF is a regular polygon. Line AB and EC are each extended to meet at G. Calculate the size of angle BGC. (3 marks)
ALT B | ALGEBRA & INTEGERS | SECTION 1 | QUESTION 3 | KCSE 2010 | FORM 1 LEVELGiven that x = -2, y = 3 and z = 5, evaluate [2x + 3 (y + z)] / 4yz. (2 marks)
ALT B | SQUARES & SQUARE ROOTS | SECTION 1 | QUESTION 2 | KCSE 2010 | FORM 1 LEVELUse the prime factors of 7056 to find √7056 (2 marks)
ALT B | BODMAS | SECTION 1 | QUESTION 1 | KCSE 2010 | FORM 1 LEVELWithout using a calculator, evaluate: 270 ÷ (90 x 2) + 7 x 4-40 ÷ 5. (2 marks)
GEOMETRIC CONSTRUCTION | KCSE 1997 | PAPER 1 | SECTION B | FORM 1 LEVELUsing ruler and compasses only, construct triangle ABC such that AB = 4 cm, BC = 5 cm, and ∠ABC = 120°. Measure AC.
On the diagram, construct a circle which passes through the vertex of the triangle ABC. Measure the radius of the circle. Measure the shortest distance from the centre of the circle to line BC. A commercial bank buys and sells Japanese Yen in Kenya Shillings at the rates shown below.7/1/2024 COMMERCIAL ARITHMETIC I | KCSE 1997 | FORM 1 LEVEL | PAPER 2 | SECTION AA commercial bank buys and sells Japanese Yen in Kenya Shillings at the rates shown below. A Japanese tourist at the end of his tour of Kenya was left with Kshs. 30,000 which he converted to Japanese Yen through the commercial bank. How many Japanese Yen did he get? KNEC ANSWERS
Given that 1 Japanese Yen is selling at Ksh 0.5446, we can use this rate to calculate the amount of Japanese Yen the tourist received.
The tourist had Kshs 30,000, so we can calculate the amount of Japanese Yen as follows: Amount in Japanese Yen = Kshs 30,000 ÷ Selling rate of 1 Japanese Yen Amount in Japanese Yen = Kshs 30,000 ÷ 0.5446 The calculation gives us: Amount in Japanese Yen ≈ 55,082.12 Therefore, the tourist received approximately 55,082 Japanese Yen. SCALE DRAWING - BEARING | FORM 1 LEVEL | KCSE 1996 | PAPER 2 | QUESTION 20 | SECTION BFour towns, R, T, K, and G, are arranged in the following manner: T is located 84 km directly north of R, K is positioned 60 km away from R on a bearing of 295°, and G is located 30 km away from K on a bearing of 340°. To create a scale drawing that accurately represents the relative positions of these towns, a scale of 1 cm representing 10 km will be used. Find (a) The distance and the bearing of T from K (b) The distance and the bearing G from T (c) The bearing of R from G kcse 1996 | paper 1 | section a | question 3 | commercial arithmetic | form 1 levelThe cost of 5 skirts and 3 blouses is Kshs 1750. Mueni bought three of the skirts and one of the blouses for Kshs 850. Find the cost of each item (3 marks).
COMMERCIAL ARITHMETIC I | PAPER 2 | SECTION B | KCSE 1996 FORM 1 LEVELTwo businessmen jointly purchased a minibus capable of accommodating 25 paying passengers at full capacity. The fare for a one-way trip between towns A and B was set at Kshs 80 per passenger. The minibus operated three round trips between the two towns on a daily basis. The daily cost of fuel amounted to Kshs 1500. Additionally, the driver and conductor received daily allowances of Kshs 200 and Kshs 150 respectively. An additional Kshs 4,000 per day was allocated for maintenance, insurance, and loan payments.
QUESTION 24 | KCSE 2023 | Geometrical constructions | PAPER 1 | FORM 1 LEVELIn this question, use a ruler and a pair of compasses only. Line PR is a diagonal of a quadrilateral PQRS, PR = 6 cm
QUESTION 5 | KCSE 2023 | L.C.M | PAPER 1 | FORM 1 LEVELTwo light bulbs are set to light after every 40 seconds and 60 seconds respectively. If they light exactly at the same time initially, calculate:
(a) the time, in minutes, they will take to light together again. (2 marks) (b) the number of times they would light together in the first half an hour. (1 mark) QUESTION 13 | KCSE 2021 | GEOMETRICAL CONSTRUCTION | PAPER 2 | FORM 1 LEVELThe figure below shows triangle XYZ. Using a ruler and a pair of compasses, locate a point M on the triangle such that M is 2 cm from line YX and is equidistant from lines YX and YZ. Measure length YM. (3 marks)
QUESTION 13 | KCSE 2021 | Time | PAPER 1 | FORM 1 LEVELAli left Mombasa for Nairobi on Tuesday at 2.30 a.m. He arrived in Mtito Andei after 3 hours 12 minutes. He stayed in Mtito Andei for 36 hours and then left for Nairobi. He took 5 hours Ham 25 minutes to arrive in Nairobi.
Determine the day and time in the 12 hour system Ali arrived in Nairobi. (3 marks) QUESTION 12 | KCSE 2021 | Geometrical Constructions | PAPER 1 | FORM 1 LEVELLine AB drawn below is a side of a trapezium ABCD. (a) Using a ruler and pair of compasses only, complete trapezium ABCD in which AB is parallel to DC, BAD = 67.5°, AD = 5 cm, BC = 5.5 cm and ∠ABC is acute. (3 marks)
(b) Measure the length of DC. (1 mark) The cost of one litre of Petrol is Ksh 110. John's vehicle covers 12 km on one litre of petrol.25/12/2023 QUESTION 10 | KCSE 2021 | Rates, Ratio, Percentage and Proportion | PAPER 1 | FORM 1 LEVELThe cost of one litre of Petrol is Ksh 110. John's vehicle covers 12 km on one litre of petrol. He used Ksh 2 805 on petrol to travel from town A to town B. Jane's vehicle consumes 12.5 litres of Petrol for every 100 km travelled.
Calculate the amount of money that Jane would use to travel from town A to B on the same road. (3 marks) QUESTION 5 | KCSE 2021 | Angles & Plane Figures | PAPER 1 | FORM 1 LEVELThe size of two interior angles of an irregular polygon each measures 90°. All the other remaining interior angles each measure 150°.
Determine the number of sides of the polygon. (3 marks) |
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