KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
Comprehensive Answers and Marking Schemes KNEC Certified
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:
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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. SURFACE AREA OF SOLIDS | KCSE 1997 | PAPER 1 | FORM 2 LEVEL | SECTION BThe figure below shows a portable kennel.
MATRICES | FORM 3 LEVEL | KCSE 1997 | SECTION B | PAPER 1The figure on the grid shows a triangular shaped object ABC and its image A'B'C'. (a)
(d) Hence find the area of the image A” B” C LINEAR EQUATIONS | FORM 2 LEVEL | KCSE 1997 | PAPER 1 | SECTION BThe coordinates of the points P and Q are (1, -2) and (4, 10) respectively. A point T divides the line PQ in the ratio 2:1.
VECTORS I | FORM 2 LEVEL | PAPER 1 | SECTION B | KCSE 1997In the figure below, OA is equal to A, OB is equal to B, AB is equal to BC, and OB is to BD in a ratio of 3:1. (a) Determine
​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.
COMMERCIAL ARITHMETIC II | QUESTION 21 | KCSE 1996 | FORM 3 LEVEL | SECTION BKubai saved Kshs 2,000 during the first year of employment. In each subsequent year, he saved 15% more than the preceding year until he retired.
statistics ii | kcse 1996 | question 19 | paper 2 | section bIn an agricultural research centre, the length of a sample of 50 maize cobs was measured and recorded. The recorded measurements are presented in the frequency distribution table below. Calculate
ANGLE PROPERTIES OF A CIRCLE | FORM 2 LEVEL | KCSE 1996 | PAPER 2 | SECTION BIn the figure below, AOC represents a diameter of the circle with center O. The length of AB is equal to BC, and the angle ACD measures 25 degrees. The line EBF is a tangent to the circle at point B. Additionally, point G is located on the minor arc CD.
QUESTION 24 | KCSE 2023 | VECTORS I | PAPER 2 | FORM 2 LEVELIn the following figure OABC is a trapezium. OA is parallel to CB and OA = 3 CB. M is the midpoint of AB. (a) Given that OA = 3a and OC = c express in terms of a and c.
QUESTION 23 | KCSE 2023 | INTEGRATION | PAPER 2 | FORM 4 LEVELThe following figure is a sketch of a curve whose equation is y = 3x² - 9x. The curve cuts the x-axis at O(0, 0) and at R(3, 0). The curve cuts the line y and Q. The coordinates of Q is (4, 12). Line RN is perpendicular to PQ at N.
QUESTION 22 | KCSE 2023 | LOCI | PAPER 2 | FORM 4 LEVELIn this question, use a ruler and a pair of compasses only. The following figure is drawn to scale. It shows sides AB and AD of a trapezium ABCD in which AB and DC are parallel. Angle DAB = 40° and vertex C is not shown.
QUESTION 21 | KCSE 2023 | LINEAR PROGRAMMING | PAPER 2 | FORM 4 LEVELAn express train operates between two towns. The train pulls x coaches on first class and y coaches on economy class. Each first class coach can hold 72 passengers while each economy class coach can hold 120 passengers.
The table below shows values of x and some values of y for the curve y = 14+ 10x 8x² - 4x³.1/1/2024 QUESTION 20 | KCSE 2023 | TRIGONOMETRY III | PAPER 2 | FORM 3 LEVEL
QUESTION 19 | KCSE 2023 | pROBABILITY | PAPER 2 | FORM 3 LEVEL
QUESTION 18 | KCSE 2023 | COMMERCIAL ARITHMETIC II | PAPER 2 | FORM 3 LEVELA welfare group invested Ksh 75 000 in shares and another Ksh 75 000 in a piece of land for a period of 5 years. The shares appreciated in value at a rate of 6% per annum (p.a) for a period of 3 years. In the remaining period of 2 years, the shares appreciated in value at a rate of 4.5% every 6 months. During the 5 years, the piece of land appreciated in value at a constant annual rate. At the end of the 5th year, the values of the two investments were equal.
QUESTION 17 | KCSE 2023 | SEQUENCES & SERIES | PAPER 2 | FORM 3 LEVELThe first term of an arithmetic progression (A.P.) is a and the common difference d. The 7th term of the A.P. is 11. The sum of the first 12 consecutive terms of the A.P. is 123.
QUESTION 16 | KCSE 2023 | 3d geometry | PAPER 2 | FORM 3 LEVELP, Q and R are points on a level ground. Q is 4.5 m south of P. R is to the east of P and 5.3 m from Q. A vertical post at P is supported by a cable of length 3.5 m. The cable joins the top T of the post to point R.
Calculate the angle between the cable and the level ground correct to 2 decimal places. (3 marks) QUESTION 15 | KCSE 2023 | differentiation | PAPER 2 | FORM 4 LEVELThe gradient function of a curve is given by dy/dx = 3 - 4x. If the curve passes through the point (-1, 10), find the equation of the curve. (3 marks)
QUESTION 14 | KCSE 2023 | LINEAR MOTION | PAPER 2 | FORM 3 LEVELA stone was thrown upwards from a point 8 metres above the ground. The following graph shows the height, h metres of the stone above the ground at time / seconds in the interval 0 ≤ t ≤ 4. Determine the rate of change of h at t = 2 seconds. (3 marks)
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