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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

QUESTION AND ANSWER ON GRADIENT AND EQUATIONS OF A CURVED LINE  MODEL06012023011

5/1/2023

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The velocity V m/s of a particle in motion is given by   V=3t^2-2t+5. Calculate the distance travelled by the particle between t= 2 seconds and t = 6 seconds.

11/12/2022

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The velocity V m/s of a particle in motion is given by   V=3t2-2t+5.Calculate the distance travelled by the particle between t= 2 seconds and t = 6 seconds.              (3 marks) 
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Differentiate with respect to x

27/11/2021

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Differentiate with respect to x    ​(3mks)

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN07

24/9/2020

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Form 4 Mathematics


Find the coordinates of the turning point of the curve y= x²-14x +10 
answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP1QN24

23/9/2020

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Form 4 Mathematics


The equation of a curve is y=x3+x2-x-1
(i) Determine the stationary point of the curve
(Îi) the nature of the stationary points in (a) (i) above.
(b) Determine:
(i) the equation of the tangent to the curve at x = 1;
(ii) the equation of the normal to the curve at x = 1.
answers
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.17

23/9/2020

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Form 4 Mathematics



A curve is represented by the function y = 1/3 x3 + x2 – 3x + 2

(a) Find dy/dx         (1 mark)

(b) Determine the values of y at the turning points of the curve y = 1/3 x3 + x2 – 3x + 2     ( 4 marks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN24

21/9/2020

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Form 4 Mathematics


The equation of a curve is given as y=1/3x3-4x+5
 Determine:
(a) The value of y when x = 3;
(b) The gradient of the curve at x = 3;
(c) The turning points of the curve and their nature.
answers
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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN19

20/9/2020

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Form 4 Mathematics


The distance covered by a moving particle through point O is given by the equation, s = t3 - 15t2 + 63t — 10.
 Find:
(a) distance covered when t = 2
(b) the distance covered during the 3rd second;
(c) the time when the particle is momentarily at rest;
(d) the acceleration when t = 5.
answers
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.16

19/9/2020

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Form 4 Mathematics



A stone is thrown vertically upwards from a point O After t seconds, the stone is S metres from O Given that S= 29.4t – 4.9t2,

Find the maximum height reached by the stone ( 3 marks)

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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.21

18/9/2020

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Form 4 Mathematics



The gradient of a curve at point (x,y) is 4x – 3. the curve has a minimum value of – 1/8

(a) Find

(i) The value of x at the minimum point ( 1 mark)

(ii) The equation of the curve ( 4 marks)

(b) P is a point on the curve in part (a) (ii) above. If the gradient of the curve at P is -7, find the coordinates of P ( 3 marks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP1QN24

16/9/2020

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Form 4 Mathematics


The equation of a curve is given as y = 2x3 -9/2 x2 -15x + 3.
(a) Find: (i) the value of y when x = 2;
(ii) the equation of the tangent to the curve at x = 2.
 (b) Determine the turning points of the curve.
answers
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.22

16/9/2020

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Form 4 Mathematics



A particle moves in a straight line. It passes though point O at t = O with velocity v= 5m/s. The acceleration a m/s2 of the particle at time t seconds after passing through O is given by a = 6t + 4
(a) Express the velocity v of the particle at time t seconds in terms of t
(b) Calculate
(i) The velocity of the particle when t = 3
(ii) The distance covered by the particle between t = 2 and t = 4

Answer
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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN23

14/9/2020

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Form 4 Mathematics


The equation of a curve is y = 2x3 + 3x2.
 a)Find
i)The x – intercept of the curve
ii) they-intercept of the curve
 b i)Determine the stationary points of the curve
 ii)For each point in (b) (i) above, determine whether it is a maximum or a minimum
c) Sketch the curve.
answers
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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN10

13/9/2020

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Form 4 Mathematics


The gradient of the tangent to the curve y = ax3 + bx at the point (1,1) is -5 , Calculate the values of a and b.
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN22

11/9/2020

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Form 4 Mathematics


A particle was moving along a straight line. The acceleration of the particle after t seconds was given by (9 -3t) ms-2. The initial velocity of the particle was 7 ms-1.
 Find:
 a) the velocity (v) of the particle at any given time (t);
 b) The maximum velocity of the particle;
c)the distance covered by the particle by the time it attained maximum velocity
answers
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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.18

11/9/2020

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Form 4 Mathematics



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K.C.S.E Mathematics Q & A - MODEL 2015PP1QN24

10/9/2020

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Form 4 Mathematics


The gradient of the curvey y = 2x3 – 9x2 + px – 1 at x = 4 is 36.
 a)Find :
 i) the value of p;
 ii)The equation of the tangent to the curve at x = 0.5.
b) Find the coordinates of the training points of the curve
answers
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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.5

9/9/2020

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Form 4 Mathematics



The velocity V ms, of a moving body at time t seconds is given by V = 5t2 – 12t + 7
Find its acceleration after 2 seconds.
Answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP2QN15

8/9/2020

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Form 4 Mathematics


The gradient of a curve is given by dy/dx = x2 - 4x4- 3. The curve passes through the point (1,0). Find the equation of the curve.
answer
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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN021

8/9/2020

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Form 4 Mathematics



  • a)
    • i) Find the coordinated of the stationary points on the curve y = x2 – 3x + 2 (2mks)
    • ii) For each stationary point determine whether it is minimum or maximum.
  • b) In the space provided below, sketch the graph of the Function y = x2 – 3x + 2 (2mks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN24

7/9/2020

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Form 4 Mathematics


The equation of acurve is given by y = x3 – 4x2 – 3x
(a) Find the value of y when x = -1
(b) Determine the stationary points of the curve
(c) Find the equation of the normal to the curve at x = 1
answers
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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN016

3/9/2020

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Form 4 Mathematics



The velocity Vms-1 of particle in motion is given by V =3t2 – t +4, where t is time in seconds.

Calculate the distance traveled by the particle between the time t=1 second and t=5 seconds.

aNSWER
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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN21

2/9/2020

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Form 4 Mathematics


The displacement, s metres, of a moving particle from a point O, after t seconds is given by, s = t3 – 5t2 + 3t + 10
a) Find s when t =2.
b) Determine:
 i. The velocity of the particle when t = 5 seconds;
ii. The value of t when the particle is momentarily at rest.
c) Find the time, when the velocity of the particles is maximum.
answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP2QN24

2/9/2020

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Form 4 Mathematics


The acceleration of a body moving along a straight line is (4 - t) m/s2 and its velocity is v m/s after t seconds.
 (a) (i) If the initial velocity of the body is 3 m/s, express the velocity v in terms of t.
 (ii) Find the velocity of the body after 2 seconds.
 (b) Calculate: (i) the time taken to attain maximum velocity;
(ii) the distance covered by the body to attain the maximum velocity.
answers
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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN024

31/8/2020

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Form 4 Mathematics



The displacement s metre of a particle moving along straight line after t seconds is given by. S = 3t + 3/2 t2 – 2t3
  • a) Find its initial acceleration
  • b) Calculate:
    • i) The time when the particle was momentarily at rest.
    • ii) Its displacement by the time it comes to rest momentarily
  • c) Calculate the maximum speed attained.
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