KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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ALT B | LINEAR MOTION | SECTION 2 | QUESTION 23 | KCSE 2010 | FORM 3 LEVELThe figure below is a velocity - time graph for a car that travelled from t = 0 to t = 60, where t is time in seconds. Use the graph to calculate:
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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 | SURFACE AREA OF SOLIDS | SECTION 2 | QUESTION 20 | KCSE 2010 | FORM 2 LEVELThe diagram below represents a pipe whose cross-section is shaded. The pipe has internal radius of 0.26m and an external radius of 0.3m.
ALT B | QUADRATIC EQUATIONS | SECTION 1 | QUESTION 19 | KCSE 2010 | FORM 3 LEVELThe length and width of a rectangular plot of land are given as (7x + 5) m and (x + 10) m respectively.
ALT B | MATRICES & TRANSFORMATIONS | SECTION 1 | QUESTION 17 | KCSE 2010 | FORM 4 LEVELThe points A(6,1), B(3,2), C(4,5) and D (9,5) are vertices of an object ABCD as shown in the figure below.
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. ALT B | rotation | SECTION 1 | QUESTION 15 | KCSE 2010 | FORM 2 LEVELThe figure below shows a quadrilateral ABCD and its image A'B'C'D' under a rotation. Determine:
(a) the centre of rotation; (2 marks) (b) the angle of rotation. (1 mark) 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 | AREA PART OF A CIRCLE | SECTION 1 | QUESTION 13 | KCSE 2010 | FORM 2 LEVELThe figure below is a circle centre 0 of radius 10.5 cm. Angle AOB = 150°. Calculate the area of the shaded part of the circle, correct to 4 significant figures. (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 | AREA OF QUADRILATERALS | SECTION 1 | QUESTION 11 | KCSE 2010 | FORM 2 LEVELThe figure below shows a trapezium KLMN in which KN is parallel to LM, KN = 20 cm, MN = 12 cm, LM = 8 cm and ∠KNM = 36°. Calculate the length of the perpendicular from M to KN and hence find the area of the trapezium. (4 marks)
ALT B | LINEAR INEQUALITIES | SECTION 1 | QUESTION 10 | KCSE 2010 | FORM 2 LEVELSolve the inequality 3x - 2 < 10 + x ≤ 2 + 5x. (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 | VOLUME & CAPACITY | SECTION 1 | QUESTION 8 | KCSE 2010 | FORM 2 LEVELThe base of a rectangular water tank is 4 m long and 3.5m wide. The tank contains 21 000 litres of water. Calculate the height of the water in the tank. (3 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 | LOGARITHMS | SECTION 1 | QUESTION 5 | KCSE 2010 | FORM 2 LEVELUse logarithms to evaluate (43.2 X 0.015) / ∛0.00679 (4 marks)
ALT B | AREA OF A RECTANGLE | SECTION 1 | QUESTION 4 | KCSE 2010 | FORM 2 LEVELThe length of a rectangular floor of a hall is 35.2m. If the diagonal of the floor is 37.7m, Calculate the area of the floor. (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)
PROBABILITY | PAPER 1 | SECTION B | KCSE 1997 | FORM 3 LEVELThe water supply in a town depends entirely on two water pumps, A and B. The probability of pump A filling is 0.1, and the probability of pump B failing is 0.2. Calculate the probability that:
LONGITUDES & LATITUDES | KCSE 1997 | PAPER 1 | SECTION B | FORM 4 LEVELA ship leaves an island (5°N, 45°E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.
(take 1 nautical mile to be 1.853 Km and the radius of the earth to be 6370 Km) 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. |
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