Category: Integration

The curve of the equation y = x+ 2x2, has x = ½ and x = 0 as x-intercepts. The area bounded by the x-axis, x = ½ and x = 3 is shown by the sketch below.

13/5/2023

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The curve of the equation y = x+ 2x², has x = ½ and x = 0 as x-intercepts. The area bounded by the x-axis, x = ½ and x = 3 is shown by the sketch below.

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Evaluate

13/5/2023

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KCSE REVISION QUESTION AND ANSWERS ON INTEGRATION, DIFFERENTIATION AND GRAPHICAL METHODS MODEL05052023001

10/4/2023

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QUESTION

ANSWER

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A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t]2 - 5t – 12

30/11/2021

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INTEGRATION | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t² - 5t – 12

Find;
(a) The value of t when P is instantaneously at rest. (2mks)

(b) An expression for the distance, S metres, moved by P after t seconds given that when t = 0, s = 0 (2mks)

(c) The total distance traveled by P in the first 3 seconds after passing point Q. (3mks)

(d) The distance of P from Q when the acceleration is zero. (3mks)

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A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity is given by the equation

25/10/2021

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A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity is given by the equation

2t² – 10t + 12 find;

a) The values of t when p is instantaneously at rest (2mks)

b) An expression for the distance moved by P after t seconds (2mks)

c) The total distance traveled by P in the first 3 seconds after passing point O. (3mks)

d) The distance of P from O when acceleration is zero

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K.C.S.E Mathematics Q & A - MODEL 2018PP2QN16

21/9/2020

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Form 4 Mathematics

answer

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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.16

17/9/2020

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Form 4 Mathematics

The acceleration, a ms^-2, of a particle is given by a =25 – 9t², where t in seconds after the particle passes fixed point O.If the particle passes O, with velocity of 4 ms^-1, find:

(a) An expression of velocity V, in terms of t ( 2 marks)
(b) The velocity of the particle when t = 2 seconds ( 2 marks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN22

15/9/2020

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Form 4 Mathematics

The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
a)Find
i)The equation of the curve
ii)The value of x at which the curve cuts the x – axis
b) Determine the area enclosed by the curve and the x – axis

answers

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.13

15/9/2020

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Form 4 Mathematics

The gradient function of a curve is given

If the curve passes through the point, (0, 2), find its equation.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN13

10/9/2020

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Form 4 Mathematics

Evaluate

answer

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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN23

4/9/2020

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Form 4 Mathematics

The equation of a curve is given by y = 5x − 1/2 x²
(a) On the grid provided, draw the curve of y = 5x − 1/2 x² for 0 ≤ x ≤ 6
(b) By integration, find the area bounded by the curve, the line x =6 and the x-axis.
(c) (i) On the same grid as in,(a).draw the line y = 2x.
(ii) Determine the area bounded by the curve and the line y = 2 x.

answers

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN020

4/9/2020

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Form 4 Mathematics

The diagram below is a sketch of the curve y =x² + 5.

a)
- i)Use the mid –ordinate rule, with six strips to estimate the area enclosed by the curve, the x – axis and the y – axis and line x =3. (4mks)
- ii) Calculate the same area using the integration method. (2mks)
b) Assuming the area calculated in (a) (ii) _______________ calculate the percentage error made when the mid – ordinate rule is used.

ANSWER

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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 2012PP2QN13

1/9/2020

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Form 4 Mathematics

The graph below shows the relationship between distance s metres and time t seconds in the interval 0 ≤ t ≤ 6.

(a) the average rate of change of distance between t =3 seconds and t =6 seconds;
(b) the gradient at t = 3 seconds.

answers

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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN22

31/8/2020

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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) the y - intercept of the curve.
(b) (i) Determine the stationery 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 2011PP1QN21

27/8/2020

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Form 4 Mathematics

(a) Using the trapezium rule with seven ordinates, estimate the area of the region bounded by the curve y = -x² +,6x+ 1, the lines x = 0, y = 0 and x = 6.
(b) Calculate: (i) the area of the region in (a) above by integration;
(iii) the percentage error of the estimated area to the actual area of the region,correct to two decimal places.

answers

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K.C.S.E Mathematics Q & A - MODEL 2009PP2QN16

21/8/2020

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Form 4 Mathematics

A particle moves in a straight line with a velocity V ms^-1. Its velocity after t seconds is given by V= 3t² – 6t-9.
The figure below is a sketch of the velocity-time graph of the particle

Calculate the distance the particle moves between t = 1 and t = 4

answer

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K.C.S.E Mathematics Q & A - MODEL 2002PP1QN020

20/8/2020

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Form 4 Mathematics

The diagram below shows a straight line intersecting the curve y = (x-1)2 + 4
At the points P and Q. The line also cuts x-axis at (7,0) and y axis at (0,7)

a) Find the equation of the straight line in the form y = mx +c.
b) Find the coordinates of p and Q.
c) Calculate the area of the shaded region. (8mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN20

13/8/2020

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Form 3 Mathematics

The gradient function of a curve is given by the expression 2x + 1. If the curve passes through the point ( -4, 6);
(a) Find:
(i) The equation of the curve
(ii) The vales of x, at which the curve cuts the x- axis
(b) Determine the area enclosed by the curve and the x- axis

ANSWERS

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K.C.S.E Mathematics Q & A - MODEL 2006PP2QN24

11/8/2020

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Form 4 Mathematics

The diagram below shows a sketch of the line y = 3x and the curve y = 4 – x² intersecting at points P and Q.

a) Find the coordinates of P and Q
(b) Given that QN is perpendicular to the x- axis at N, calculate
(i) The area bounded by the curve y = 4 – x², the x- axis and the line QN
(ii) The area of the shaded region that lies below the x- axis
(iii)The area of the region enclosed by the curve y = 4-x², the line y – 3x and the y axis

answers

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K.C.S.E Mathematics Q & A - MODEL 2006PP2QN15

10/8/2020

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Form 4 Mathematics

A particle moving in a straight line passes through a fixed point O with a velocity of 9m/s. The acceleration of the particle, t seconds after passing through O is given by a = ( 10 – 2t) m/s².Find the velocity of the particle when t – 3 seconds

answer

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K.C.S.E Mathematics Q & A - MODEL 2006PP1QN24

10/8/2020

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Form 4 Mathematics

A particle moves along straight line such that its displacement S metres from a given point is S = t³ – 5t² + 4 where t is time in seconds

Find
(a) the displacement of particle at t = 5
(b) the velocity of the particle when t = 5
(c) the values of t when the particle is momentarily at rest
(d) The acceleration of the particle when t = 2

answers

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K.C.S.E Mathematics Q & A - MODEL 2000PP2QN21

14/7/2020

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Form 4 Mathematics

The curve of the equation y = 2x + 3x², has x = - ‌⅔ and x = 0 and x intercepts. The area bounded by the axis x = - ‌⅔ and x = 2 is shown by the sketch below.

Find:

(a) (2x + 3 x²) dx
(b) The area bounded by the curve x – axis, x = ‌⅔ and x =2

Answer

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K.C.S.E Mathematics Q & A - MODEL 2000PP1QN14

8/7/2020

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Form 4 Mathematics | Topical Questions and Answers

The acceleration a m/s² of a particle moving in a straight line is given by a = 18t - 4, where t is time in seconds. The initial velocity of the particle is 2 m/s

(a) Find the expression for velocity in terms of t
(b) Determine the time when the velocity is again 2m/s

ANSWER

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

13/6/2020

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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

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

The curve of the equation y = x+ 2x2, has x = ½ and x = 0 as x-intercepts. The area bounded by the x-axis, x = ½ and x = 3 is shown by the sketch below.

QUESTION

ANSWER

INTEGRATION | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

​A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t² - 5t – 12

​Find; (a) The value of t when P is instantaneously at rest. (2mks)

(b) An expression for the distance, S metres, moved by P after t seconds given that when t = 0, s = 0 (2mks)

​(c) The total distance traveled by P in the first 3 seconds after passing point Q. (3mks)

(d) The distance of P from Q when the acceleration is zero. (3mks)

A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity is given by the equation

a) The values of t when p is instantaneously at rest (2mks)

b) An expression for the distance moved by P after t seconds (2mks)

c) The total distance traveled by P in the first 3 seconds after passing point O. (3mks)

d) The distance of P from O when acceleration is zero

Form 4 Mathematics

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Form 3 Mathematics

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Form 4 Mathematics

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Form 4 Mathematics

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Form 4 Mathematics | Topical Questions and Answers

14

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

20

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The curve of the equation y = x+ 2x², has x = ½ and x = 0 as x-intercepts. The area bounded by the x-axis, x = ½ and x = 3 is shown by the sketch below.

A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t² - 5t – 12

Find;
(a) The value of t when P is instantaneously at rest. (2mks)

(c) The total distance traveled by P in the first 3 seconds after passing point Q. (3mks)