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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~Topically Analyzed

K.C.S.E Mathematics Q & A - MODEL 1999PP2QN24

30/6/2020

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Form 2 Mathematics



​The diagram below shows a right pyramid VABCD with V as the vertex. The base of the pyramid is rectangle ABCD, WITH ab = 4 cm and BC= 3 cm. The height of the pyramid is 6cm.
Picture
  • (a) Calculate the 
    • (i) length of the projection of VA on the base
    • (ii) Angle  between the face VAB and the base
  • (b) P is the mid- point of VC and Q is the mid – point of VD. Find the angle between the planes VAB and the plane ABPQ
answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN24

Related Questions on Trigonometry I

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN23

30/6/2020

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Form 4 Mathematics



The transformation R given by the matrix
Picture

  • (a) Determine the matrix A giving a,b,c and d as fractions
  • (b) Given that A represents a rotation through the origin determine the angle of rotation
  • (c) S is a rotation though 1800 about the point (2, 3). Determine the image of (1,0) under S followed by R.

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN22

30/6/2020

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Form 4 Mathematics



  • (a) Complete the table below, giving your values correct to 2 decimal places.
Picture


  • b) On the grid provided, draw the graphs of y = tan x and y = sin ( 2x + 300) for 00 ≤ x 700
    Take scale: 2 cm for 100 on the x- axis
                       4 cm for unit on the y- axis
    Use your graph to solve the equation tan x- sin ( 2x + 300 ) = 0

Answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN22

Related Questions on Trigonometry III

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN21

30/6/2020

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Form 1 Mathematics



The diagram below shows a garden drawn to scale of 1: 400. In the garden there are already tow trees marked A and B. The gardener wises to plant more trees. There are a number of rules he wishes to apply.
Picture
​Rule 1: Each new tree must be  an  equal distance from both trees A and B.
Rule 2: Each new tree must be at least 4 m from the edges of the garden.
Rule 3: Each new tree is at least 14 m from tree B.
  • (a) Draw the  locus given by each  of these rules on the diagram
  • (b) If the  new trees are to be planted 4m apart, show on your  diagram the possible planting points for  the new trees.
Answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN21

Related Questions on Scale Drawing

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN20

30/6/2020

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Form 3 Mathematics



  • (a)The first term of an arithmetic progression is 4 and the last term is 20. The sum of the term is 252. Calculate the number of terms and the common differences of the arithmetic progression
  • (b) An Experimental culture has an initial population of 50 bacteria. The population increased by 80% every 20 minutes. Determine the time it will take to have a population of 1.2 million bacteria.
ANSWER
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN20

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN19

30/6/2020

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Form 2 Mathematics



Patients who attend a clinic in one week were grouped by age as shown in the table below:
Picture
  • ​i. Estimate the mean age
  • ii. On the grid provided draw a histogram to represent  the distribution 
    1 cm to represent 5 unit on  the horizon axis
    2  cm to represent 5 units on the vertical axis
Answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN19

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN18

30/6/2020

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Form 1 Mathematics



A tower is on a bearing of 0300 from a point P and a distance of elevation of the top is 150 and the angle  of depression of the foot  of the tower is 10.
  • a)     Find the height of the tower
  • b)     A point Q is on the same horizon plane as point P. The tower is on a bearing 3300 from Q and at a distance of 70 m.
Answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN18

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN17

30/6/2020

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Form 1 Mathematics



​A retailer bought 49 kg of grade I rice at Kshs. 65 per kilogram and 60 kg of grade II rice at Kshs 27.50 per kilogram. He mixed the two types of rice.
  • (a) Find the buying price of one kilogram of the mixture
  • (b) He packed the mixture into 2 kg packets
    • (i) If he intends to make a 20% profit find the selling price per  packet
    • (ii) He sold 8 packets and then reduced the price by  10% in order to attract customers. Find the new selling price per packet.
    • (iii) After selling of the remainder at reduced price, he raised the price so as to realize the original goal of 20% profit overall. Find the selling price per packet of the remaining rice.
Answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN17

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN16

30/6/2020

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Form 4 Mathematics




Find the equation of the tangent to the curve
Y = (x2 + 1) (x - 2) when x = 2

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN15

30/6/2020

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Form 3 Mathematics



A construction firm has tractors T1 and T2. Both tractors working together can complete a piece of work in 6 days while T1 alone can  complete the work in 15 days. After two tractors had worked together for four days, tractor T1 broke down.
Find the time it takes tractor T2 to complete the remaining work.
Answers
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN15

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN14

30/6/2020

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Form 3 Mathematics



The points P. Q and R lie on a straight line. The position vectors of P and R  are 2i + 2j + 13k and  5i – 3j + 4k respectively. Q divides PR internally in the ratio 2:1
Find the
(a) Position  vector of Q.
Answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN14

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN13

30/6/2020

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Form 1 Mathematics



The number of people who attended an agricultural show in one day was 510 men, 1080 women and some children. When the information was represented on a pie chart, the combined angle for the men and children was 2160. Find the angle representing the children.
answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN13

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN12

30/6/2020

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Form 3 Mathematics



Solve the equation
8s2 + 2s – 3 = 0
Hence solve the equation
8 sin2Ө + 2sinӨ - 3 = 0  for 00 ≤ θ ≤ 1800

answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN12

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN10

30/6/2020

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Form 3 Mathematics




Use binomial expression to evaluate (0.96)5 correct to 4 significant figures
answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN10

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN09

30/6/2020

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Form 2 Mathematics


Two towns A and B are 220 km apart. A bus left town A at 11. 00 a.m. and traveled towards B at 60 km/h. At the same time, a matatu left town B for town A and traveled at 80 km/h. The matatu stopped for a total of 45 minutes on the way before meeting the bus. Calculate the distance covered by the bus before meeting the matatu.
answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN09

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN08

30/6/2020

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Form 1 Mathematics


The figure below shows a solid made by passing two equal regular tetrahedra.
Picture
  • (a) Draw a net solid
  • (b) If each face is an equilateral triangle of side 5 cm find the surface area of the  solid
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN07

30/6/2020

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Form 2 Mathematics


The equation of a line is 
\[-\frac{3}{5}x + 3y = 6\]
Find the:
  • (a) Gradient of the line
  • ​(b) Equation of a line passing through point (1,2) and perpendicular to the given line.
Answers
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN07

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN06

30/6/2020

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Form 3 Mathematics



Solve for x 
\[(log_{3}x^{2}) - \frac{1}{2} log_{3} = \frac{3}{2}\]
ANSWER
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN06

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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN05

30/6/2020

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In the month of January, an insurance salesman earned Kshs 6750 which was a  commission of 4.5% of the premium paid  to the company.
answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN05
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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN04

30/6/2020

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Simplify
\[\sqrt{2x \times 5^{2x}2^{-x}}\]
answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN04
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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN03

30/6/2020

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The mass of a mixture A of beans and maize is 72 kg. The ratio of beans to maize is 3:5 respectively
  • (a) Find the mass of maize in the  mixture
  • (b) A second mixture of B of beans and maize of mass 98 kg in mixed with A. The final ratio of beans to maize is 8:9 respectively. Find  the ratio of  beans to maize in B
Answer
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN03
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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN02

30/6/2020

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​Find the range of x if 2 ≤ 3 – x < 5
Answers
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN02
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K.C.S.E Mathematics Q & A - MODEL 1999PP2QN01

30/6/2020

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Use logarithms to evaluate 
\[[\frac{6.79\times 0.3911}{log 5}]^{\frac{3}{4}}\]
ANSWER
K.C.S.E Mathematics Q & A - MODEL 1999PP2QN01
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K.C.S.E Mathematics Q & A - MODEL 1999PP1QN24

25/6/2020

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Free 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1


The graph below consists of a non- quadratic part ( 0 ≤ x ≤ 2) and a quadrant part ( 2 ≤ x 8) The quadratic part is y = x2 – 3x + 5, 2 ≤ x ≤ 8
Picture
(a) Complete the table below   (1 mark)
Picture
  • ​(b) Use the trapezoidal rule with six strips to estimate the area enclosed by the  curve, x = axis and the line x = 2 and x = 8 (3 marks)
  • (c) Find the exact area of the region given in (b) (3 marks)
  • (d) If the trapezoidal rule is used to estimate the area under the curve between x = 0 and x = 2, state whether it would give an under- estimate or an over- estimate. Give  a reason for your answer (1 mark)
ANSWER
K.C.S.E Mathematics Q & A - MODEL 1999PP1QN24
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K.C.S.E Mathematics Q & A - MODEL 1999PP1QN23

25/6/2020

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Free 1999 K.C.S.E Mathematics Topical Question & Answers Paper 1

The diagram below shows a cross- section of a bottle. The  lower part ABC is a hemisphere of radius 5.2  cm and the upper part  is a frustum of a cone. The top radius  of the  frustum is one third of the radius of the hemisphere. The hemisphere part is completely filled water as shown  in the diagram.
Picture
When the container is inverted, the water now completely fills only the frustum part.
  • (a) Determine the  height of the frustum part
  • (b) Find the surface area of the frustum part of the bottle.