Maths F5 Topical Test 3 _E_ by speedracerijok

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                         TOPICAL TEST 3: TRANSFORMATION III


  PAPER 1

 1 Diagram 1 shows five quadrilaterals         If the area of the shaded region is          image of point (–3, 3) under the
   are drawn on a Cartesian plane.             240 cm2, calculate the area, in cm2,         combined transformation VU are
                                               of trapezium PQRS.                           A (3, 10)        C (4, 10)
                                               A 30              C 80                       B (3, 9)         D (2, 7)
                                               B 60              D 90
                                                                                         8 Diagram 7 shows five congruent
                                            5 Diagram 5 shows a point P is plotted         trapeziums are drawn on a Cartesian
                                              on a Cartesian plane.                        plane.




                 Diagram 1
    Which of the quadrilaterals, A, B, C
    and D is the image of M under a
    clockwise rotation of 90° about
    centre (1, 0)?                                                                                     Diagram 7
                                                          Diagram 5                         Transformation P is a clockwise
 2 Diagram 2 shows five triangles are
                                               Transformation M is a reflection in          rotation of 90° about the centre (1,
   drawn on square grids.
                                               the line y = x. Transformation N is a        0). Transformation Q is a reflection
                                               clockwise rotation of 90° about the          in the line x = 4. Which of the
                                               centre (4, 2). Find the coordinates of       shapes, A, B, C and D is the image
                                               the image of point P under the               of shape X under the combined
                                               combined transformation NM.                  transformation QP?
                                               A (5, 1)
                                               B (3, 2)                                  9 Diagram 8 shows a kite.
                                               C (4, 1)
                 Diagram 2                     D (5, 2)
    Which of the triangles, A, B, C and
                                            6 Diagram 6 shows a point S is plotted
    D, is the image of triangle P under a
                                              on a Cartesian plane.
    rotation of 180° about the centre O?

 3 Diagram 3 shows two trapeziums P
   and Q. Q is the image of P under an
   enlargement.
                                                                                                    Diagram 8 Rajah 8
                                                                                            Transformation P is a clockwise
                                                                                            rotation of 90° about point E.
                                                                                            Transformation Q is an enlargement
                                                          Diagram 6                         with centre K and with a scale factor
                                              Transformation Q is a reflection in the       of 2. Find the coordinates of the
                 Diagram 3                    line x = 3. Transformation R is a             image of point H under the
    Which of the points, A, B, C and D                                                      combined transformation QP.
                                              translation  3  . Find the coordinates      A (5, 3)         C (6, 3)
    is the centre of enlargement?                          4
                                                                                            B (5, 2)         D (6, 2)
                                              of the image of point S under the
 4 In Diagram 4, trapezium PTUV is            combined transformation RQ.
   the image of trapezium PQRS under                                                     10 Diagram 9 shows a triangle X with a
                                              A (5, 1)         C (0, 2)                     point K.
   an enlargement.
                                              B (8, 0)         D (5, 2)


                                            7 Transformation U is a translation   
                                                                                  4 .
                                                                                  1
                                              Transformation V is an enlargement
                                              about the centre (0, 1) and a scale
                                              factor of 3. The coordinates of the

                 Diagram 4
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                                                 Given Q = Translation  1  ,                   B (–2, 2)
                                                                        2                     C (2, –2)
                                                                                                 D (–2, –2)
                                                      R = Translation  2 ,
                                                                         1 
                                                                                             19 Given J = Rotation of 180° about a
                                                      S = Clockwise rotation of 90°
                                                           about (2, 2),                                  point (4, 0),
                                                      T = Rotation 180° about the                    K = Reflection in the line
                                                           point (3, 3).                                  y = –x.
                                                The combined transformation that                The image of point (3, 0) under the
                 Diagram 9                      maps M onto N is                                combined transformation JK is
    Given R = Rotation of 180° about            A QS               C TQ                         A (8, 3)
              point (2, 2),                     B RS               D QT                         B (–6, –3)
          S = Enlargement with centre        14 P is a reflection in the line y = –2            C (8, 4)

                                                                              
              (2, 2) and a scale factor of                                                      D (–6, –4)
                                                 and Q is a translation
                                                                              2 . Find the
              2.                                                              5
    The coordinates of K under the                                                           20 Transformation F is a reflection in
                                                 coordinates of the image of                    the line y = 3.
    combined transformation SR are               M(–2, 1) under the combined
    A (–4, –1)        C (–3, –1)                                                                Transformation E is a reflection in
                                                 transformation PQ.                             the line y = x.
    B (0, –2)         D (–3, –2)                 A (0, –11)       C (–10, 0)                    State the coordinates of image of
                                                 B (–11, 0)       D (0, –10)                    point R(3, 1) under the combined
11 In Diagram 10, N is the image of M

                                                                           
   under a combined transformation JK.                                                          transformation FE.
                                             15 M is a translation
                                                                           3 and N is          A (3, 5)         C (1, 3)
                                                                           4                   B (3, 1)         D (5, 3)
                                                 translation    
                                                                5 . The image of point
                                                                3                            21 Given R = Reflection in the line y = x,
                                                                                                      S = Rotation of 180° about
                                                 (8, 2) under the combined
                                                 transformation MN is                                     the
                                                 A (0, –1)                                                origin,

                                                                                                                          
                                                                 C (0, 1)
                                                 B (0, 2)        D (1, 0)                               T = Translation
                                                                                                                          0 ,
                                                                                                                          2
            Diagram 10 Rajah 10
                                             16 In Diagram 12, Q is the image of P                     U = Enlargement at the origin
    K is a translation  4 and J is

    reflection in the line
                            3
                                               under a translation
                                                                     x .
                                                                     y                                     with a scale factor of 2.
                                                                                                 Q(2, 6) is the image of P(6, 4) under
                                                                                                 the combined transformation of
    A y = 2x                                                                                     A TR                C TS
    B y=x                                                                                        B RT                D SU
    C y= 1x                                                                                  22 Diagram 13 is drawn on square
             2
    D y=0                                                                                       grids. J', the image of J under a
                                                                                                transformation, is mapped onto J"
12 Transformation T is the translation                                                          under another transformation.
     2 and transformation S is a                            Diagram 12
     1
                                               Given the distance PQ is 10 units,
   reflection in the line y = x. The             the translation is
   coordinates of the image of point
                                                 A 2              C 8 
   (10, 2) under the combined                         6             6
   transformation ST are
   A (3, 7)          C (3, 8)                    B  6                D  6 
                                                                          2 
   B (4, 7)          D (8, 3)                      8                     
                                                                                                            Diagram 13
13 Diagram 11 shows two squares, M and       17 Given U = Reflection in the line y = x,          Which of the points, A, B, C and D
   N.                                                   V = Clockwise rotation of 90°            is the image of point M under of
                                                            about (2, 1).                        same combined transformation?
                                                Find the coordinates of image of point
                                                (4, 2) under the combined transfor-          23 Diagram 14 shows a polygon K is
                                                mation VU.                                      drawn on a Cartesian plane.
                                                A (–1, –5)                                      Transformation X is a reflection in the
                                                B (1, 5)                                        line y = 1. Transformation Y is a
                                                C (4, 1)                                        reflection in the line x = 5. Polygon K
                                                D (5, 1)                                        undergoes a combined transformation
                                                                                                YX.
                                             18 R is a reflection in the line
                Diagram 11                      y = x. The image of (2, 2) under the
                                                combined transformation R2 is
                                                A (2, 2)
© Navision (M) Sdn. Bhd. (690640-P)                                10                                                            SULIT
                                            Transformation P is a translation

                                             
                                             2
                                             3
                                                   . Transformation Q is a
                                                                                     25 In Diagram 16, K is the image of J
                                                                                        under a combined transformation.
                                            clockwise rotation of 90° about the
                                            centre (0, 7).




                  Diagram 14
    A single transformation which is
    equivalent to YX is
                                                                                                   Diagram 16
                                                                                        Which of the following is not the
    A a reflection in the line y = x.                                                   possible combined transformation?
                                                  Diagram 15 Rajah 15
    B a rotation of 180° about the                                                      A Enlargement followed by rotation
                                            Which of the point, A, B, C and D is
      centre (5, 1).                                                                    B Enlargement followed by
                                            the image of point E under the
    C an anticlockwise rotation of 90°                                                     reflection
                                            combined transformation QP?
      about the centre (4, 4).                                                          C Reflection followed by
    D a reflection in the line y = 4.                                                      enlargement
                                                                                        D Translation followed by
24 Diagram 15 shows five points are                                                        enlargement
   drawn on a Cartesian plane.



     PAPER 2

 1 Transformation U is an anticlockwise rotation of 90°          2 Transformation U is a clockwise rotation of 90° about the
   about the centre (0, 3) and transformation V is a               origin. Transformation V is a reflection in the line x = 3.
    translation    
                   2 .
                   3
                                                                   On Diagram 2, draw the image of the triangle CDE under
                                                                   the each of following combined transformations.
                                                                    (a) VU,
    On Diagram 1, draw the image of line PQ under the              (b) UV.
    combined transformation VU.                                                                                       [4 marks]
                                             [2 marks]




                               Diagram 1



                                                                                         Diagram 2




© Navision (M) Sdn. Bhd. (690640-P)                        11                                                          SULIT
 3 Transformation G is a translation     
                                        3 .
                                        2
                                                                          6 Diagram 4 shows three trapeziums, A, B and C.

    Transformation H is an enlargement at the origin with a scale
    factor 2. State the coordinates of the image of point (1, –2)
    under each of the following combined transformations.
     (a) HG,                       (b) GH.
                                                        [4 marks]




                                                                                                  Diagram 4
                                                                            (a) Point P is the image of point Q under a reflection.
                                                                                State the coordinates of the image of point R under the
 4 Transformation A is a reflection in the line y = –x.                         same reflection.
   Transformation B is a clockwise rotation of 90° about the                                                                   [2 marks]
   centre (–2, 1). State the coordinates of the image of point (2,          (b) B is the image of A under a transformation V. C is the
   3) under each of the following combined transformations.                     image of B under a transformation W. Describe in full
    (a) AB,               (c) BA,              (e) A2,                           (i) V,
                                                         [6 marks]              (ii) W.                                        [4 marks]
                                                                            (c) State the coordiantes of the image of point R under the
                                                                                following transformations.
                                                                                 (i) VW,
                                                                                (ii) WV.                                       [4 marks]




 5 Diagram 3 shows point A drawn on a Cartesian plane.




                                                                          7 Diagram 5 shows three quadrilaterals, ABCD, JKLM and
                                                                            JPQR on a Cartesian plane.
                         Diagram 3 Rajah 3

    Transformation T is a translation    
                                        4 . Transformation U is
                                        2
    a reflection in line y = x. Transformation V is a clockwise
    rotation of 90° about the centre (0, 1).
    Transformation S is a reflection in line y = –x.
    State the coordinates of the image of point A under following
    transformations.
     (a) TV,                        (b) ST,
    (c) TS,                         (d) UV,
    (e) TU,                         (f) US.                                                       Diagram 5
                                                        [12 marks]
                                                                            JPQR is the image of ABCD under the combined
                                                                            transformation VW.
                                                                             (a) Describe the full transformation
                                                                                  (i) V,
                                                                                 (ii) W.                                [4 marks]
                                                                            (b) Given T = reflection in the line y = 2,
                                                                                      R = translation    
                                                                                                        3 .
                                                                                                        2
                                                                                State the coordinates image of S(4, 0) under following
                                                                                transformations.
                                                                                 (i) TR,
                                                                                (ii) RT.                                       [4 marks]




© Navision (M) Sdn. Bhd. (690640-P)                                  12                                                         SULIT
 8 (a) Transformation M is a translation      
                                             2 . Transformation
                                             3
                                                                          10 Diagram 7 shows four triangles, P, Q, R and S.

         N is a reflection in the line y = 5.
         State the coordinates of image of point (1, 3) under the
         following transformations.
          (i) M,
         (ii) N,
         (iii) MN.                                       [4 marks]
    (b) S(–4, 3) is the image of T under a translation   
                                                         2 . Find
                                                         3                                             Diagram 7
         the coordinates of point T.                                         (a) Triangle Q is the image of triangle P under a rotation.
                                                       [2 marks]                 State
    (c) U(4, 3) is the image of V(2, 4) under a combined                          (i) the coordinates of the centre of the rotation,
        transformation TF. Describe in full the transformation                   (ii) the angle of the rotation.
         (i) T,                                                                                                                    [2 marks]
        (ii) F.                                        [4 marks]             (b) Find the coordinates of the image of point F(2, 1)
                                                                                 under a translation    
                                                                                                        3 followed by a reflection in the
                                                                                                        1
                                                                                 line y = –1.
                                                                                                                                 [2 marks]
                                                                             (c) Triangle R is the image of triangle Q under a combined
                                                                                 transformation WV. Describe in full the transformation.
                                                                                  (i) V,
                                                                                 (ii) W.                                         [4 marks]




 9 (a) Given R is an anticlockwise rotation 90° about the centre
             (2, 2),

                                       
                                                                          11 Diagram 8 shows three points, P', Q and Q', on a Cartesian
                T is a translation
                                       2 .                                   plane.
                                       4
        State the coordinates of the image of point (1, 2)
        under each of the following transformations.
         (i) T,
        (ii) R,
        (iii) TR,
        (iv) RT.                                     [6 marks]
    (b) In Diagram 6, triangle ABC is the image of triangle
        DEF under a combined transformation WV.

                                                                                                       Diagram 8
                                                                             (a) State the values of h dan k, if point Q' is the image of
                                                                                 point Q under a translation   
                                                                                                               h .
                                                                                                               k
                                                                                                                                 [2 marks]

                                                                             (b) Find the coordinates point P, if P' is the coordinates


                             Diagram 6
                                                                                 image of P under translation      
                                                                                                                    h .
                                                                                                                    k
                                                                                                                                 [2 marks]


         Describe in full the transformation                                 (c) Given A = reflection is the y-axis,
          (i) V,                                                                       B = rotation of 90° clockwise about the centre
         (ii) W.                                         [4 marks]                         (0, 0).
                                                                                 Find the coordinates of the image of P under the
                                                                                 combined transformation AB.                 [2 marks]




© Navision (M) Sdn. Bhd. (690640-P)                                  13                                                            SULIT
12 In Diagram 9, quadrilateral JKLM is the image of                     14 Diagram 11 shows three trapeziums, ABCD, EFGH and
   quadrilateral EFGH under a transformation X whereas                     HPQR.
   quadrilateral PQRS is the image of quadrilateral JKLM under
   a transformation Y.




                                                                                                  Diagram 11

                                                                                                         
                             Diagram 9
                                                                           (a) Given T = translation
                                                                                                        2 ,
    (a) Describe in full the transformations X and Y.                                                   1
                                                    [4 marks]
    (b) By determining the image of EFGH under the combined                              V = reflection in the line y = 3,
        transformation YX, describe a single transformation                             W = reflection in the y-axis.
        which is equivalent to YX.                                               (i) Find coordinates of the image of point A under
                                                    [2 marks]                         transformation W.
                                                                                 (ii) Find the coordinates of the image of point C under
                                                                                      transformation V.
                                                                                (iii) Find the coordinates of the image of point D
                                                                                      under the combined transformation TV.
                                                                                                                                 [4 marks]
                                                                            (b) HPQR is the image of quadrilateral EFGH under a
                                                                                transformation S.
                                                                                 (i) Describe in full the transformation S.
                                                                                 (ii) If the area of EFGH is 16 cm2, calculate the area
                                                                                      of HPQR in cm2.
13 (a) Given L = reflection in the line y = x,                                                                                   [5 marks]
               M = translation      2 .
                                      1
               N = anticlockwise rotation of 90° about the
                    centre (2, 1).
        Find the coordinates of the image of point (3, 2) under
        each of following transformations.
         (i) M2,                   (ii) ML,
        (iii) LN,                  (iv) MN.            [8 marks]
    (b) On Diagram 10, draw the images of the rectangle
        ABCD under the following combined transformations.
         (i) MN,
        (ii) NM.                                       [4 marks]        15 (a) Given H = reflection at the line y =2,
                                                                                      G = translation    
                                                                                                        2 .
                                                                                                        1
                                                                                Find the coordinates of the image of point A(2, 4)
                                                                                under each of the following transformations.
                                                                                 (i) H,
                                                                                (ii) HG,
                                                                                (iii) GH.                                     [5 marks]
                                                                            (b) In Diagram 12, triangle ABC is the image of the
                             Diagram 10                                         triangle PQR under a transformtion U. Triangle DEF
                                                                                is the image of ABC under a transformation V.




                                                                                              Diagram 12 Rajah 12

© Navision (M) Sdn. Bhd. (690640-P)                                14                                                             SULIT
         (i) Describe in full the transformations U and V.
         (ii) It is given that triangle DEF represents a region of
              area 72 m2. Calculate the area, in m2, of the region
              represented by triangle PQR.
                                                          [7 marks]




                                                                                                     Diagram 14
                                                                                   Pentagon AFGHJ is the image of pentagon ABCDE
16 (a) Given P = reflection in the x-axis,
                                                                                   under a transformation V and pentagon AKLMN is the
              T = clockwise rotation of 90° about the centre
                                                                                   image of pentagon AFGHJ under a transformation W.
                  (–2, 1).
                                                                                    (i) Describe in full the transformations V and W.
       State the coordinates of image of point (1, 1) under
                                                                                    (ii) It is given that the area of shaded region is 150
       each of the following transformations.
                                                                                         cm2. Calculate the area of the pentagon ABCDE in
        (i) P2,
                                                                                         cm2.
       (ii) PT,
                                                                                                                                   [7 marks]
       (iii) TP.                                    [5 marks]
   (b) In Diagram 13, triangle DEC is image of triangle ABC
       under a transformation V. Triangle DFG is image of
       triangle DEC under a transformation W,




                                                                            18 Diagram 15 shows four quadrilaterals, P, Q, R and S
                                                                               drawn on a Cartesian plane.

                             Diagram 13
         (i) Describe in full the transformations V and W.
          (ii) It is given that the area of triangle DEC is 12 m2.
               Calculate the area, in m2, of triangle DFG.
                                                           [7 marks]




17 (a) Transformation T is a translation      
                                              2 .                                                   Diagram 15

                                                                                                                       
                                              3
                                                                               (a) Transformation T is a translation
                                                                                                                       6 . Transformation
        Transformation R is a reflection in the line y = 3.                                                            2
        Transformation S is a clockwise rotation of 90° about
                                                                                   M is an anticlockwise rotation of 90° about the point
        the centre (0, k).
                                                                                   (2, 2). Find the coordinates of the image of point (3, 1)
         (i) The point (3, 1) is the image of the point (–3, 1)
                                                                                   under each of the following transformations.
              under the transformation S. State the value of k.
                                                                                    (i) T,                     (ii) TM.              [6 marks]
         (ii) Find the coordinates of the image of point (4, 2)
                                                                               (b) Q is the image of P under a transformation V and R is
              under each of the following transformations.
                                                                                   the image of Q under a transformation W. Describe in
              (a) T2,                 (b) RT.
                                                                                   full,
                                                         [5 marks]
                                                                                    (i) the transformation V.
    (b) Diagram 14 shows three pentagons, ABCDE, AFGHJ
                                                                                    (ii) a single transformation which is equivalent to the
        and AKLMN are drawn on a Cartesian plane.
                                                                                         combined transformation WV.
                                                                                                                                     [5 marks]
                                                                               (c) It is given that quadrilateral S is the image of the
                                                                                   quadrilateral P under an enlargement.
                                                                                    (i) State the coordinates of the centre of enlargement.
                                                                                    (ii) It is given that the area of quadrilateral S is 108
                                                                                         cm2. Calculate the area of quadrilateral R, in cm2.
                                                                                                                        [3 marks]
© Navision (M) Sdn. Bhd. (690640-P)                                    15                                                            SULIT

								
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