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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

K.C.S.E Mathematics Q & A - MODEL 1998PP2QN21

10/5/2023

Comments

 

Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

ANSWERS
K.C.S.E Mathematics Q & A - MODEL 1998PP2QN21
Comments

K.C.S.E Mathematics Q & A - MODEL 1998PP2QN24

13/6/2020

Comments

 

Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

​A draper is required to supply two types of shirts A and type B.
The total number of shirts must not be more than 400. He has to supply more type A than of type B however the number of types A shirts must be  more than 300  and the number of type B shirts not be less than 80.
Let x be the number of type A shirts and y  be the number of types B shirts.
  • (a) Write down in terms of x and y all the linear inequalities representing the information above.
  • (b) On the grid provided, draw the inequalities and  shade the unwanted regions
    Type A: Kshs 600 per shirt
    Type B: Kshs 400 per shirt
    • (i) Use the graph to determine the number  of shirts of each type that should be  made to maximize the profit.
    • (ii) Calculate the maximum possible profit.
answer
K.C.S.E Mathematics Q & A - MODEL 1998PP2QN24
Comments

K.C.S.E Mathematics Q & A - MODEL 1998PP2QN23

13/6/2020

Comments

 

Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

The figure below represents a rectangle PQRS inscribed in a circle centre 0 and radius 17cm . PQ = 16 cm.
Picture
​Calculate
  • (a) The length PS of the rectangle
  • (b) The angle POS
  • (c) The area of the shaded region
answer
K.C.S.E Mathematics Q & A - MODEL 1998PP2QN23
Comments

K.C.S.E Mathematics Q & A - MODEL 1998PP2QN22

13/6/2020

Comments

 

Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

    Two aeroplane P and Q leaves an airport at the same time.  P lies on a bearing of 2400 at  900 km/ h while Q flies due  east  at 750 km/ h.
    • (a) Using a scale of 1 cm to represents 100km, make a scale drawing  to show the position  of the aeroplane after 40 minutes.
    • (b) Use the scale drawing to find the distance between the two aeroplane after 40 minutes.
    • (c) Determine the bearing
      • (i)  P from Q
      • (ii) Q from P
      ANSWERS
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN22
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN20

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      • (a) Find the value of x at which the curve y= x- 2x2 – 3 crosses the x- axis
      • (b) s(x2 – 2x – 3)dx
      • (c) Find the area bounded by the curve y = x2 – 2x – 3, the axis and the lines x= 2 and x = 4
      Answers
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN20
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN19

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      In the figure below, QOT is a diameter. ∠QTR = 480, ∠TQR = 760 and ∠SRT = 370
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN19
      Calculate
      • (a) ∠RST
      • (b) ∠SUT
      • (c) ∠Obtuse RUT
      • (d) ∠PST
      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN19
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN18

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      ​(a) Complete the table below for the value of y =  2 sin x + cos x.
      (a) Complete the table below for the value of y = 2 sin x + cos x.


      • (b) Using the grid provided draw the graph of y = 2 sin x + cos x for 00. Take 1 cm represent 300on the x- axis and 2 cm to represent 1 unit on the axis.
      • (c) Use the graph to find the range of x that satisfy the inequalities 2 sin x cos x > 0.5

      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN18
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN17

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      ​A cylindrical water tank is a diameter 7 meters and height  2.8 metre
      • (a) Find the capacity  of the water tank in litres
      • (b) Six members of a family use 15 litres per day. Each day 80 litres are used for cooking and washing and a further 60 litres are wasted.
      Find the number of complete days a full tank of water would last the family.
      ANSWERS
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN17
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN16

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      The triangular prism shown below  has  sides AB= DC = EF = 12 cm. The ends are equilateral triangle of sides 10cm. The point N is the midpoint FC.
      The triangular prism shown below has sides AB= DC = EF = 12 cm. The ends are equilateral triangle of sides 10cm. The point N is the midpoint FC.
      • ​(a) Find the length of
        • (i) BN
        • (ii) EN
      • (b) Find the angle between the line  EB and the plane CDEF
      ANSWERS
      The triangular prism shown below has sides AB= DC = EF = 12 cm. The ends are equilateral triangle of sides 10cm. The point N is the midpoint FC.
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN15

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      ​A river is flowing at uniform speed of 6 km/ h. A canoeist who can paddle at 10 km/h through still water wishes to go straight across the river.
      Find the direction, relative to the bank in which he should steer.
      answers
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN15
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN14

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      A science club is made up  of boys and girls. The club has  3 officials. Using a tree diagram or otherwise find the probability that:
      • (a) The club official are all boys
      • (b) Two of the officials are girls
      ANSWERS
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN14
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN13

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2


      • (a) Write down the simplest expansion ( 1 + x)6
      • (b) Use the expansion up to the fourth term to find the value  of ( 1.03)6 to the nearest one  thousandth.

      ANSWER
      Picture
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN12

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      Find x if:

      \[-3 log 5 + log x^{2} = log \frac{1}{125}\]

      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN12
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN11

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      A balloon, in the form of a sphere of radius 2 cm, is blown up so that the volume increase by 237.5%. Determine the new volume  of balloon in terms of π
      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN11
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN10

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      Given that P = 3 y express the equation 32y – 1 + 2 × 3y-1= 1 in terms of AP. Hence or  otherwise find the value of y in the equation 32y – 1 + 2 × 3y-1= 1
      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN10
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN09

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      In the figure, KLMN is a trapezium in which KL is parallel to NM  and KL = 3 NM
      Given that KN = w, NM = u and ML = v
      Show that 2 u = v= w

      In the figure, KLMN is a trapezium in which KL is parallel to NM and KL = 3 NM
      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN09
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN08

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      In the figure below a line XY and three points. A,B  and C are given. On the figure construct 
      • (a) The perpendicular bisector of AB
      • (b) A point P on line xy such that ∠APB = ∠ACB
      Picture
      answer
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN08
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN07

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      ​A manufacturer sells bottle of fruit juice to a trader at a profit of 40%. The trader sells it for Kshs 84 at a profit of 20%. Find:
      • (a) The  trader’s buying price
      • (b) The cost  of manufacture of one bottle
      answer
      A manufacturer sells bottle of fruit juice to a trader at a profit of 40%. The trader sells it for Kshs 84 at a profit of 20%. Find
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN06

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      ​During a certain period, the exchange  rate were follows:
      • 1 sterling pound = Kshs. 102.0
      • 1 sterling pound = Kshs. U.S dollar
      • 1 U.S dollar = Kshs. 60.6
      A school management intended to import textbooks worth Kshs 500,00 from U.K. It changed the money to  sterling pounds.  Later the management found out that books were cheaper in U.S.A. Hence it changed the sterling pounds to dollars. Unfortunately, a financial crisis arose and the money had to be reconverted to Kenya shillings.
      Calculate the total amount of money the management ended up with.

      ANSWERS
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN06
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN05

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      ​A  plot of land was valued at Kshs 50,000 at the start of 1994. It appreciated by 20% during 1994. Thereafter, every year, it appreciated by  10% of its previous years value.
      • ​a. The value of the land at the start of 1995
      • b. The value of the land at the end  of  1997

      answer
      Picture
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN04

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

      In the figure below ABC = 300, ACB = 900, AD = 4√3 and DC = 4cm

      Picture
      Picture
      Calculate the length of:
      • (a) AC
      • (b) BC

      ANSWER
      Picture
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN03

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2


      ​Simplify as far as possible, leaving your  answer in the form of surd

      Picture

      ANSWER
      Picture
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN02

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2


      Simplify the expression:

      Picture

      ​Hence solve the equation:

      Picture

      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN02
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN01

      13/6/2020

      Comments

       

      Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2


      ​Use logarithms to evaluate:

      \[55.9 \div (0.2621 \times 0.01177)^{\frac{1}{5}}\]


      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP2QN01
      Comments

      K.C.S.E Mathematics Q & A - MODEL 1998PP1QN25

      7/6/2020

      Comments

       
      25. If a fowl is treated, probability of dying is 1/10 while if not treated the probability is 7/10 calculate the probability that, a fowl picked at random from the 36 fowl is

      If a fowl is treated, probability of dying is 1 ⁄ 10 while if not treated the probability is 7 ⁄ 10 calculate the probability that, a fowl picked at random from the 36 fowl is

      • (i) treated with the drug and  will die
      • (ii) Not treated with the drug and will die
      • (iii) Not treated  with the drug and will not die

      ANSWER
      K.C.S.E Mathematics Q & A - MODEL 1998PP1QN25
      Comments
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