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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 2001PP1QN24

21/7/2020

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Form 4 Mathematics


A plane flying at 200 knots left an airport A (300S, 310E) and flew due North to an airport B ( 300 N, 310E)
  • (a) Calculate the distance covered by the plane, in nautical miles
  • (b) After a 15 minutes stop over at B, the plane flew west to an airport C ( 300N, 130E) at the same speed.
Calculate the total time to complete the journey from airport C, though airport B.
Answer

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN23

21/7/2020

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Form 3 Mathematics


​The probability of three darts players Akinyi, Kamau, and Juma hitting the bull's eye are 0.2, 0.3 and 1.5 respectively.
  • (a) Draw a probability tree diagram to show the possible outcomes
  • (b) Find the probability that:
    • (i) All hit the bull's eye
    • (ii) Only one of them hit the bull's eye
    • (iii) at most one missed the bull’s eye
Answer
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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN22

21/7/2020

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Form 4 Mathematics


(a) Complete the following table for the equation y = x3 + 2x3
Picture

  • (b) On the grid provided draw the graph y = x3 + 2x2 for -3 ≤ x ≤ 1.5. Take the scale: 2cm for 1 unit on the x- axis and 1 cm for 1 unit on y – axis
  • (c) By drawing a suitable line on the same grid, Estimate the roots of the equation: x3 + 2x2 – x – 2 =0

Answer

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN21

21/7/2020

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Form 4 Mathematics



(a) The gradient function of a curve is given  by 
Picture
Find the equation of the curve, given that y = 3, when x = 2
(b) The velocity, vm/s of a moving particle after seconds is given: v = 2t3 + t2 – 1. Find the distance covered by the particle in the interval 1 ≤ t ≤ 3.
Answer
Picture
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN20

21/7/2020

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Form 3 Mathematics


In the figure below, points O and P are centers of intersecting circles ABD and BCD respectively. Line ABE is a tangent to circle BCD at B. Angle BCD = 420

Picture
  • (a) Stating reasons, determine the size of
  • (i) ∠GBD
  • (ii) Reflex ∠BOD
  • (b) Show that ∆ ABD is isosceles
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN19

21/7/2020

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Form 3 Mathematics



The figure below shows a parallelogram OPQR with O as the origin, OP = p and OR =  r, Point T divides RQ in the ratio 1: 4 PT Meets OQ at S.
Picture
​(a) Express in terms of p and r the vectors
  • (i) OQ
  • (ii) OT
(b) Vector OS can be expressed in tow ways: mOQ or OT + n TP, Where m and n are constants express OS in terms of
  • (i) m, n and r
  • (ii) n, s and r
Hence find the:
  • (iii)  Value on m
  • (iv) Ratio OS: SQ
Answer
Picture
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN18

21/7/2020

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Form 4 Mathematics



The coordinates of the vertices of rectangle PQRS are P (1,1), Q (6,1), R ( 6,4) and S(1,4)
Picture
Answer 18.A
Picture
Answer 18.B
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN17

21/7/2020

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Form 3 Mathematics



The table shows income tax rates
Picture
​A company employee earn a monthly basic salary of Kshs 30,000 and is also given taxable allowances amounting to Kshs 10, 480.
  • (a) Calculate the total income tax
  • (b) The employee is entitled to a personal tax relief of Kshs 800 per month. 
Determine the net tax.
  • (c) If the employee received a 50% increase in his total income, calculate the corresponding percentage increase on the income tax.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN16

21/7/2020

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Form 2 Mathematics



The position vectors for points P and Q are 4i + 3 j + 6 j + 6 k respectively. Express vector PQ in terms of unit vectors I, j and k. Hence find the length of PQ, leaving your answer in simplified form.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN15

21/7/2020

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Form 2 Mathematics



A town N is 340 km due west of town G and town K is due west of town N. A helicopter Zebra left G for K  at 9.00 am. Another helicopter Bufalo left N for K at  11.00 am. Helicopter Buffalo traveled at an average speed of 20 km/ h faster than Zebra. If both helicopters reached K at 12.30 pm find the speed of helicopter Buffalo.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN14

21/7/2020

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Form 1 Mathematics



The interior angles of the hexagon are 2x0, ½ x0 + 400, 1100, 1300 and 1600. Find the value of the smallest angle.

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN13

21/7/2020

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Form 3 Mathematics



Given that:
Picture
Hence, solve simultaneous equations below:

2x – 3 y = 5

-x + 2y = -3

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN12

21/7/2020

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Form 4 Mathematics



Given that sin ( x + 30)0 = cos 2x0 for 00, 00 ≤ x ≤900 find the value of x. Hence find the value of cos23x0.

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN11

21/7/2020

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Form 4 Mathematics



A particle is projected from the origin. Its speed was recorded as shown in the table below
Picture
Use the trazezoidal rule to estimate the distance covered by the particle within the 35 seconds
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN09

21/7/2020

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Form 3 Mathematics



​A poultry farmer vaccinated 540 of his 720 chickens against a disease. Two months later, 5% of the vaccinated and 80% of the un-vaccinated chicken, contracted the disease. Calculate the probability that a chicken chosen random contacted the disease.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN08

21/7/2020

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Form 1 Mathematics




Use a ruler and compasses in this question. Draw a parallegram ABCD in which AB = 8 cm, BC = 6 cm and ∠BAD = 750. By construction, determine the perpendicular distance between AB and CD.

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN07

21/7/2020

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Form 2 Mathematics




The length of a room is 4 metres longer its width. Find the length of the room if its area is 32cm2

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN06

21/7/2020

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Form 3 Mathematics



Simplify the expression
Picture
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN05

21/7/2020

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Form 2 Mathematics



A line L1 passes though point (1,2) and has a gradient of 5. Another line L2, is perpendicular to L1 and meets it at a point where x = 4. Find the equation for L2 in the form of Y = Mx + C

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN04

21/7/2020

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Form 2 Mathematics



​The diagram below represents a solid made up of a hemisphere mounted on a cone. The radius of the hemisphere are each 6 cm and the height of the cone is 9 cm.
a solid made up of a hemisphere mounted on a cone
a solid made up of a hemisphere mounted on a cone
Find the volume of the solid:
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN03

21/7/2020

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Form 2 Mathematics



Use logarithms to evaluate
use logarithms to evaluate
use logarithms to evaluate
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN02

21/7/2020

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Form 2 Mathematics



The figure below represents a kite ABCD, AB = AD = 15 cm. The diagonals BD  and AC intersect at O. AC = 30 cm and AO = 12 cm.
kite ABCD
Kite ABCD
Find the area of the kite
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN01

21/7/2020

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Form 2 Mathematics



Find the reciprocal of 0.342. Hence evaluate:
Picture
ANSWER
Picture

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K.C.S.E Mathematics Q & A - MODEL 2000PP2QN24

14/7/2020

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Form 4 Mathematics



​A theatre has a seating capacity of 250 people. The charges are Kshs. 100 for an ordinary seat and Kshs 160 for a special seat. It cost Kshs 16,000 to stage a show and the theater must make a profit. There are never more than 200 ordinary seats and for a show to take place at least 50 ordinary seats must be occupied. The number of special seats is always less than twice the number of ordinary seats.
  • (a) Taking x to be the number of ordinary seats and y the number of special seats write down all the inequalities representing the information above.
  • (b) On the grid provided, draw a graph to show the inequalities in (a) above
  • (c) Determine the number of seats of each type that should be booked in order to maximize the profit.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2000PP2QN23

14/7/2020

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Form 2 Mathematics




The diagram on the grid provided below shows a trapezium ABCD on the same grid.
  • (a)
    • (i) Draw the image A’B’C’D of ABCD under a rotation of 900 clockwise about the origin.
    • (ii) Draw the image of A”B”C”D” of A’B’C’D’ under a reflection in line y = x. State coordinates of A”B”C”D”.
  • (b) A”B”C”D” is the image of A”B”C”D under the reflection in the line x = 0. Draw the image A”B” C”D” and state its coordinates.
  • (c) Describe a single transformation that maps A” B”C”D onto ABCD.
Answer
Picture

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