KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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 SCALE DRAWING  FORM 2 LEVEL  SECTION II  PAPER 1  ALT B  KCSE 2011  QUESTION 23 A piece of land is in the shape of a quadrilateral ABCD. Point B is 450 m east of A. Point D is 500 m from A on a bearing of 310°. Point C is 700 m from D on a bearing of 080°.
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 ANGLES AND PLANE FIGURES  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 14 The sum of interior angles of a regular polygon is 1620°. Calculate the number of sides of the polygon. (2 marks)
 geometrical constructions  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 11 Using a ruler and a pair of compasses only, construct triangle ABC such that AB = 4.5 cm, BC = 8.1 cm and angle CBA = 60°. Measure angle CAB.
(3 marks) A support cable of length 6.5 m is fixed on a vertical pole at a distance of 0.9 m from the top.22/3/2024  LENGTH  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 9 A support cable of length 6.5 m is fixed on a vertical pole at a distance of 0.9 m from the top. The cable is anchored on the ground at a distance of 2.5 m from the foot of the pole. Determine the height of the pole. (3 marks)
 GCD  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 7 Three metal rods of lengths 234 cm, 270 cm and 324 cm were cut into shorter pieces, all of the same length, to make window grills.
Calculate the length of the longest piece that can be cut from each of the rods and hence the total number of pieces that can be obtained from the rods. (4 marks)  TIME  FORM 1 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 3 On a certain day a journalist started travelling at 0850 hours to attend a meeting. He travelled for 6½ hours and then rested for 1 hour 45 minutes. He attended the meeting for 3% hours and travelled for 35 minutes to a hotel.
Determine the time, in 12hour clock system, the journalist arrived at the hotel. (3 marks) 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) 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 DRAWINGBEARING  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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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 440 ÷ 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 
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