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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ALT B  GRAPHICAL METHODS   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 24Some water is heated in a beaker and then left to cool for 12 minutes. After the heating is stopped, the relationship between the water temperature C, in degrees centigrade and the time t, after heating is given as C = 100 1/2 T^2.
ALT B  vectors ii   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 23The figure below shows a triangle OAC in which B is the midpoint of OC and D is the midpoint of AC.
Given that OA = 2i + 5j and OB = 4i + j,
ALT B  AREA APPROXIMATION   FORM 4 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 22A quadrant (a quarter of a circle) of radius 10 cm is drawn on the grid below. The quadrant is divided into 5 vertical strips.
ALT B  TRIGONOMETRY I   FORM 2 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 21Triangle ABC is such that AB = 4 cm, BC = 7 cm and angle ABC = 100°. Calculate to 2 decimal places:
ALT B  PROBABILITY   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 20A bag contains 5 yellow (Y) balls and 3 blue (B) balls. All the balls are identical except for the colour. A ball is drawn at random from the bag without replacement and its colour noted. A second ball is draw at random from the same bag and its colour also noted.
ALT B  STATISTICS II   FORM 4 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 19The table below represents the number of streams in 20 schools.
Calculate: (a) the mean number of streams per school; (3 marks) (b) the variance; (5 marks) (c) the standard deviation correct to 2 decimal places. (2 marks) ALT B  SEQUENCE AND SERIES   FORM 3 LEVEL  SECTION II  PAPER 2  KCSE 2010  QUESTION 18The terms of an Arithmetic sequence are 2,5,8,11, ...
ALT B  COMMERCIAL ARITHMETIC II   FORM 3 LEVEL  SECTION ii  PAPER 2  KCSE 2010  QUESTION 17A shop sells a certain type of fridge at a cash price of Ksh 80 000. If the fridge is bought on Hire Purchase (H.P), a deposit of Ksh 24 000 is paid. A customer is also charged 15% per annum simple interest on the balance of the cash price after deposit is paid. Khamala bought one such fridge on H.P. He paid the balance plus the interest in 5 equal monthly instalments.
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  COMMERCIAL ARITHMETIC II   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 15A building was valued at Ksh 720 000 on 1st January 2007. The value of the building appreciated at 2% per annum in the first year. The value of the building then depreciated at the rate of 5% for the next 2 years. Calculate the value of the building at the end of year 2009. (3 marks)
ALT B  LONGITUDES AND LATITUDES   FORM 4 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 14The positions of two points A and B on the surface of the earth are A(32.8°N, 26°E) and B(21.2°S, 26°E).
Calculate in kilometres the shortest distance between A and B. (Take the radius of the earth to be 6370 km and π = 22/7) (3 marks) ALT B  graphical methods   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 13The table below gives values of two variables x and y obtained from an experiment.
(a) On the grid provided below, plot the values of y against x and draw the line of best fit. (2 marks) ALT B  CIRCLES, CHORDS AND TANGENTS   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 12In the figure below, PRQS is a circle of radius 17cm. Line PQ is a diameter of the circle and is perpendicular to chord RS at T.
ALT B  SEQUENCE AND SERIES   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 11The second term of a geometric sequence is 24 and the fifth term is 192. Find the first term of the sequence. (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  STATISTICS I   FORM 2 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 8The piechart below represents the expenditure of a family in a certain month on maize, meat, vegetables, fruits and milk.
During that month, the family spent equal amounts of money on milk and fruits.
ALT B  COMPOUND PROPORTIONS   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 7An inlet pipe fills an empty water tank in 8 hours while an outlet pipe empties the full tank in 5 hours. When the tank is full, the inlet and outlet pipes are opened at the same time. Calculate:
ALT B  logarithms i   FORM 2 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 1and give the answer correct to 5 significant figures. [2 marks]
ALT B  quadratic equations   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 3Solve by factorisation, the quadratic equation:
2x²3x50 = 0 (3 marks) ALT B  FORMULA AND VARIATIONS   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 4ALT B  Circles, Tangents and Chords   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 5The figure below shows a circle centre O and external point X.
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. 
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