Category: Form 4 Level

QUESTION AND ANSWER ON STATISTICS II MODEL06012023007

5/1/2023

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QUESTION ON LONGITUDES AND LATITUDES MODEL06012023001

5/1/2023

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QUESTION AND ANSWER ON LOCI MODEL06012023006

5/1/2023

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QUESTION AND ANSWER ON MATRICES AND TRANSFORMATION MODEL06012023013

5/1/2023

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

5/1/2023

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QUESTION AND ANSWER ON STATISTICS II MODEL06012023015

5/1/2023

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QUESTION AND ANSWER ON MATRICES AND TRANSFORMATION MODEL06012023008

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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A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

2/12/2021

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(a) A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

On the grid provided, show the figure ABCD and its final image under the successive transformations ERS. (6mks)

(a) ERS =

(b) Find the matrix representing the single transformation mapping the image found in (a) above
back to the object figure ABCD. (2mks)

(c) A(2,2), B(2,0) and C(3,2) are co-ordinates of the vertices of triangle ABC. Triangle ABC undergoes a shear factor 3 parallel to the x-axis. Determine the coordinates of A’B’C’ (2mks)

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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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Complete the table for y = Sin x + 2cos x

29/11/2021

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TRIGONOMETRY III | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

(a) Complete the table for y = Sin x + 2cos x. (2mks)

(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

(d) Find the range of values of x for which y≤-0.5. (3mks)

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TAKING THE RADIUS OF THE EARTH R=6370 KM AND PIE=22/7, CALCULATE THE SHORTEST DISTANCE BETWEEN THE TWO CITIES P(60]0 N,29]0 E) ALONG THE PARALLEL OF LATITUDE.

29/11/2021

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LONGITUDES AND LATITUDES | Distance between two points along the small and great circles in nautical miles and kilometres. | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

(a) (i) Taking the radius of the earth, R= 6370km and π = 22/7, calculate the shortest distance between the two cities P(60^oN, 29^oW) and Q(60^oN, 31^oE) along the parallel of latitude. (3mks)

(ii) If it is 1200hrs at P, what is the local time at Q. (3mks)

(b) An aeroplane flew due south from a point A (60^oN, 45^oE) to a point B. the distance covered by the aeroplane was 8000km. determine the position of B. (4mks)

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Differentiate with respect to x

27/11/2021

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Differentiate with respect to x (3mks)

Worked Answer:

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T is a transformation represented by the matrix

27/11/2021

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T is a transformation represented by the matrix

Under T, a square of area 10cm square is mapped onto a square of area 110cm square find the value of x. (3mks)

Worked Answer:

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A number of people are asked to cut 20cm lengths of string without measuring. Later 100 pieces are collected and measured correct to the nearest 1/10cm. the data below was collected.

22/11/2021

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PAPER 1, SECTION B, STATISTICS II, FORM 4 LEVEL, 10 MARKS

A number of people are asked to cut 20cm lengths of string without measuring. Later 100 pieces are collected and measured correct to the nearest 1/10cm. the data below was collected.

Using 19.7 as a working mean calculate:

(a) Mean (4mks)

(b) Standard deviation (5mks)

(c) State the modal class (1mk)

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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 2019PP2QN24

24/9/2020

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Form 4 Mathematics

(b) On the grid provided draw PQRS and its image P'Q'R'S’

(ii) On the same Grid draw P"Q"R‘S”.
(d) (i) Find a single matrix that maps P"Q"R’S" onto P’Q’R’S’.
(ii) Describe fully the transformation thai maps P"Q”R"S" onto P’Q’R’s’.

answers

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN22

24/9/2020

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Form 4 Mathematics

The amount of money contributed by a group of students during a fundraising for a needy student was as shown in the table below.

(a) On the grid provided draw an ogive to represent the data.
(b) Use the graph to estimate:
(i) The median;
(ii) The quartile deviation;
(iii) The percentage number of students who contributed at least Ksh 750.50.

answers

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN21

24/9/2020

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Form 4 Mathematics

A workshop makes cupboards and tables using two artisans A and B every cupboard made requires 3 days of work by artisan A and 2 days of work by artisan B. Every table made requires 2 days of work by artisan A and 2 days of work by artisan B.
In one month artisan A worked in less than 24 while artisan B Worked for Not More Than 18 Days.
The workshop made x cupboards and y tables in that month.
(a) Write all the inequalities which must be satisfied by x and y.
(b) Represent the inequalities in (a) on the grid provided.
(c) The workshop makes a profit of Ksh 6 000 on each cupboard and Ksh4 000 on each table.
Find the number of cupboards and the number of tables that must be made for maximum profit and hence determine the maximum profit.

answers

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN20

24/9/2020

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Form 4 Mathematics

A ship left point P(10°S, 40°E) and sailed due East for 90 hours at an average speed of 24 knots to a point R.(Take 1 nautical mile (nm) to be 1.853 km and radius of the earth to be 6370 km)
(a) Calculate the distance between P and R in:
(i) nm;
(ii) km.
(b) Determine the position of point R.
(c) Find the local time, to the nearest minute, at point R when the time at P is 11:00a.m.

answers

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN19

24/9/2020

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Form 4 Mathematics

The figure KLMN below is a scale drawing of a rectangular piece of land of length KL = 80m

(a) On the figure, construct
(i) The locus of a point P which is both equidistant from points L and M It and from lines KL and LM.
(ii) the locus of a point Q such that ∠KQL = 90°.
(b) (i) Shade the region R bounded by the locus of Q and the Locus of points equidistant from KL and LM.
(ii) Find the area of the region R in m². (Take ℼ= 3.142).

answers

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN14

24/9/2020

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Form 4 Mathematics

The vertices of a triangle PQR are P(-3, 2), Q(0,-1) and R(2, -1). A transformation matrix maps triangle PQR onto triangle P’Q' R' whose vertices are P'(-7, 2), Q'(2, -1) and R’(4, -1).
Find M^-1, the transformation that maps P'Q'R' onto PQR.

answer

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN11

24/9/2020

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Form 4 Mathematics

The figure ABCDEFGH represents a box.

The top lid of the box is opened such that the height OT is 35cm. Calculate the:
(a ) angle the top lid makes with the plane FGHE;
(b) length BE, correct to 2 decimal places.

answers

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

Topically Analysed

​(a) A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

On the grid provided, show the figure ABCD and its final image under the successive transformations ERS. (6mks)

(b) Find the matrix representing the single transformation mapping the image found in (a) above back to the object figure ABCD. (2mks)

​(c) A(2,2), B(2,0) and C(3,2) are co-ordinates of the vertices of triangle ABC. Triangle ABC undergoes a shear factor 3 parallel to the x-axis. Determine the coordinates of A’B’C’ (2mks)

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)

TRIGONOMETRY III | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

(a) Complete the table for y = Sin x + 2cos x. (2mks)

​(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

​(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

(d) Find the range of values of x for which y≤-0.5. (3mks)

LONGITUDES AND LATITUDES | Distance between two points along the small and great circles in nautical miles and kilometres. | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

(a) (i) Taking the radius of the earth, R= 6370km and π = 22/7, calculate the shortest distance between the two cities P(60oN, 29oW) and Q(60oN, 31oE) along the parallel of latitude. (3mks)

(ii) If it is 1200hrs at P, what is the local time at Q. (3mks)

(b) An aeroplane flew due south from a point A (60oN, 45oE) to a point B. the distance covered by the aeroplane was 8000km. determine the position of B. (4mks)

Differentiate with respect to x ​(3mks)

Worked Answer:

​T is a transformation represented by the matrix

Under T, a square of area ​10cm square is mapped onto a square of area 110cm square find the value of x. (3mks)

​Worked Answer:

​A number of people are asked to cut 20cm lengths of string without measuring. Later 100 pieces are collected and measured correct to the nearest 1/10cm. the data below was collected.

​Using 19.7 as a working mean calculate:

​(a) Mean (4mks)

​(b) Standard deviation (5mks)

​(c) State the modal class (1mk)

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

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(a) A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

(b) Find the matrix representing the single transformation mapping the image found in (a) above
back to the object figure ABCD. (2mks)

(c) A(2,2), B(2,0) and C(3,2) are co-ordinates of the vertices of triangle ABC. Triangle ABC undergoes a shear factor 3 parallel to the x-axis. Determine the coordinates of A’B’C’ (2mks)

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)

(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

(a) (i) Taking the radius of the earth, R= 6370km and π = 22/7, calculate the shortest distance between the two cities P(60^oN, 29^oW) and Q(60^oN, 31^oE) along the parallel of latitude. (3mks)

(b) An aeroplane flew due south from a point A (60^oN, 45^oE) to a point B. the distance covered by the aeroplane was 8000km. determine the position of B. (4mks)

Differentiate with respect to x (3mks)

T is a transformation represented by the matrix

Under T, a square of area 10cm square is mapped onto a square of area 110cm square find the value of x. (3mks)

Worked Answer:

A number of people are asked to cut 20cm lengths of string without measuring. Later 100 pieces are collected and measured correct to the nearest 1/10cm. the data below was collected.

Using 19.7 as a working mean calculate:

(a) Mean (4mks)

(b) Standard deviation (5mks)

(c) State the modal class (1mk)