Category: Matrices And Transformations

KCSE REVISION QUESTION AND ANSWERS ON MATRICES AND TRANSFORMATION MODEL05052023003

10/4/2023

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KCSE REVISION QUESTION AND ANSWERS ON MATRICES AND TRANSFORMATION MODEL05052023003

QUESTION

ANSWER

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QUESTION AND ANSWER ON MATRICES AND TRANSFORMATION MODEL06012023013

5/1/2023

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QUESTION AND ANSWER ON MATRICES AND TRANSFORMATION MODEL06012023008

5/1/2023

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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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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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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 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 2005.PP2.QN.18

22/9/2020

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Form 4 Mathematics

Triangles ABC and A”B”C” are drawn on the Cartesian plane provided. Triangle ABC is mapped onto A”B”C” by two successive transformations

(a) Find R ( 4 marks)

(b) Using the same scale and axes, draw triangles A’B’C’, the image of triangle ABC under transformation R ( 2 marks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2018PP2QN15

21/9/2020

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Form 4 Mathematics

answer

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K.C.S.E Mathematics Q & A - MODEL 2018PP1QN20

20/9/2020

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Form 4 Mathematics

The diagram below shows triangle ABC with vertices A(-1, -3), B(1, -1) and C(0,0), and line M.

(a) Draw triangle A'B'C' the image of triangle ABC under a reflection in the line M.

(i) Draw triangle A"B"C"
(ii) Describe fully the transformation represented by matrix T.
(iii) Find the area of triangle A’B'C' hence find area of triangle A"B"C".

answers

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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN18

17/9/2020

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Form 4 Mathematics

The vertices ofa rectangle ABCD are: A(0,2), B(0,4), C(4,4) and D(4,2). The vertices of its image under a transformation T are; A’(0,2) , B’(0,4) , C’(8,4) and D’(8,2).
On the grid provided, draw the rectangle ABCD and its image A’B’C’D’ under T.
(ii) Describe fully the T.
(iii) Determine the matrix of transformation.
(b). On the same grid as in (a), draw the image of rectangle ABCD under a shear with line x =-2 invariant and A(0, 2) is mapped onto A”(0,0).

answers

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.21

16/9/2020

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Form 3 Mathematics

Triangle ABC is the image of triangle PQR under the transformation

(b) Triangle ABC in part (a) above is to be enlarged scale factor 2 with centre at (11, -6) to map onto A’B’C. Construct and label triangle A’B’C’ on the grid above.

(c) By construction find the coordinates of the centre and the angle of rotation which can be used to rotate triangle A’B’C’ onto triangle A” B” C”, shown on the grid above.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN23

15/9/2020

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Form 4 Mathematics

A quadrilateral with vertices at K (1, 1), L (4, 1), M (2, 3) and N (1, 3) is transformed by a matrix

a) Determine the coordinates of the image
(b)On the grid provided draw the object and the image.
c)i)Describe fully the transformation which maps KLMN onto K’L’M’N
ii) Determine the area of the image
d) Find a matrix which maps K’L’M’N’ onto KLMN.

answers

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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN03

14/9/2020

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Form 4 Mathematics

answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN24

11/9/2020

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Form 4 Mathematics

a) Determine the coordinates of the image
b) On the grid provided draw the object and the image
c i)Describe fully the transformation which maps KLMN onto K'L'M'N'
ii)Determine the area of the image.
d)Find a matrix which maps K'L'M'N' onto KLMN

answers

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K.C.S.E Mathematics Q & A - MODEL 2014PP2QN07

8/9/2020

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Form 4 Mathematics

In a transformation, an object with an area of 5 cm² is mapped onto an image whose area is 30cm². Given that the matrix of the transformation is

answer

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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN16

3/9/2020

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Form 4 Mathematics

The vertices of triangle T are A(1, 2), B(4, 2) and C(3, 4). The vertices of triangle Tʹ, the image of T are Aʹ(1/2 ,1) , Bʹ(2,1) and Cʹ(3/2. 2).

answer

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K.C.S.E Mathematics Q & A - MODEL 2012PP2QN18

1/9/2020

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Form 4 Mathematics

(ii) On the same grid draw O" A" B" C".
(c) Find the single matrix that maps O" A" B" C" onto OABC.

answers

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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN11

31/8/2020

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Form 4 Mathematics

answer

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K.C.S.E Mathematics Q & A - MODEL 2011PP2QN19

28/8/2020

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Form 4 Mathematics

The vertices of a rectangle are A(-l,-l), B(-4 ,-l),C(-4-3) and D(-l,-3).

answers

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K.C.S.E Mathematics Q & A - MODEL 2009PP2QN20

21/8/2020

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Form 4 Mathematics

Triangle PQR shown on the grid has vertices p(5,5), Q(10, 10) and R(10,15)

a) Find the coordinates of the points p‟, Q‟ and R‟ and the images of P, Q and R respectively under transformation M whose matrix is

b) Given that M is a reflection;
i) draw triangle P‟Q‟R‟ and the mirror line of the reflection;
ii) Determine the equation of the mirror line of the reflection
c) Triangle P” Q” R” is the image of triangle P‟Q‟R‟ under reflection N is a reflection in the y-axis.
i) draw triangle P”Q”R”
ii) Determine a 2 x2 matrix equivalent to the transformation NM
iii) Describe fully a single transformation that maps triangle PQR onto triangle P”Q”R”

answers

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K.C.S.E Mathematics Q & A - MODEL 2009PP2QN09

20/8/2020

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Form 4 Mathematics

answer

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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN17

19/8/2020

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Form 2 Mathematics

In the figure below (not drawn to scale), AB = 8cm, AC= 6cm, AD= 7cm, CD= 2.82 cm and angle CAB =50⁰

Calculate, to 2 decimal places
a) The length BC,
b) The size of angle ABC,
c) The size of angle CAD,
d) The area of triangle ACD
b) Express vector NM in terms of OB

OP = OM + 2 MN, find the coordinates of P.

answers

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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN10

18/8/2020

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Form 4 Mathematics

Points A(2,2)and B(4,3) are mapped onto A‟(2,8) and b‟ (4,15) respectively by a transformation T.
Find the matrix of T.

answer

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K.C.S.E Mathematics Q & A - MODEL 2002PP1QN022

14/8/2020

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Form 4 Mathematics

A triangle T whose vertices are A (2,3) B(5,3) and C (4,1) is mapped onto triangle T¹ whose vertices are A¹ (-4,3) B¹ (-1,3) and C¹ (x,y) by a transformation

Find the:

(i) Matrix M of the transformation

(ii) Coordinates of C₁

b) Triangle T² is the image of triangle T¹ under a reflection in the line y = x.

Find a single matrix that maps T and T² (8mks)

Answers

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

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KCSE REVISION QUESTION AND ANSWERS ON MATRICES AND TRANSFORMATION MODEL05052023003

QUESTION

ANSWER

​(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)

​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:

Form 4 Mathematics

24

Form 4 Mathematics

14

Form 4 Mathematics

N.18

Form 4 Mathematics

15

Form 4 Mathematics

20

Form 4 Mathematics

18

Form 3 Mathematics

N.21

Form 4 Mathematics

23

Form 4 Mathematics

3

Form 4 Mathematics

24

Form 4 Mathematics

7

Form 4 Mathematics

16

Form 4 Mathematics

18

Form 4 Mathematics

11

Form 4 Mathematics

19

Form 4 Mathematics

20

Form 4 Mathematics

9

Form 2 Mathematics

17

Form 4 Mathematics

10

Form 4 Mathematics

22

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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)

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: