RI C8B Curve Transformation Add Prac (Qn)

RAFFLES INSTITUTION H2 Mathematics (9758) 2025 Year 5 ________________________________________________________ Additional Practice Questions for Chapter 8B: Curve Transformation Page 1 of 8 Additional Practice Questions for Chapter 8B: Curve Transformations Transformations 1 The diagram shows the graph of f( )yx . The curve passes through the points (1 , 1 )A  and (1, 0)B , and has a maximum point at (2,1)C . The curve has asymptotes 0x and 0y . Sketch, on separate diagrams, the graphs of (i) f( 2 1 )yx , (ii) f( 1 )yx  , (iii) 2f (2 ) 1yx . In each case, state the coordinates of the points corresponding to A, B, and C, and the equations of the asymptotes, whenever applicable. [9] 2 State precisely how each of the following curves may be obtained by applying a sequence of geometrical transformations from the given starting curve. (a) 23exy  (starting curve : exy  ), (b) 12 1yx  (starting curve : yx ). [7] 3 The transformations , a n d AB C are as follows: :A A translation of 1 unit in the negative y -direction; :B A stretching parallel to the y -axis (with x-axis invariant) by a factor of 2; :C A reflection about the x-axis. A curve undergoes in succession, the transformations , and AB C , and the equation of the resulting curve is 226yx  . (i) Determine the equation of the curve before the transformations were effected. [3] Suppose the curve undergoes in succession, th e above transformations in the reverse order (i.e. , a n d CB A ). (ii) Determine the equation of the resulting curve. [3] (iii) Suggest one amendment to the above transformations for the reverse order such that the resulting equation is still 226yx  . [1] x O y

Raffles Institution H2 Mathematics 2025 Year 5 __________________________________________________________________________________________ _______________________________________________________ Additional Practice Questions for Chapter 8B: Curve Transformation Page 2 of 8 4 9758/2021/01/Q6 A curve C has equation 2 1 , 4 y ax x   where a > 0. (a) Sketch C and give the equations of any asymptotes, in terms of a where appropriate. [4] (b) Find the smallest possible value of y in terms of a. [1] (c) Describe the transformatio n that maps the graph of C onto the graph of 22 1 . 4 y ax   [3] Transformations involving Modulus Functions 5 The graph of f2 1yx is shown. Sketch on separate diagrams, the graphs of (i) 2f 2yx , (ii) fyx , (iii) fyx . Your sketch should show clearly the coordinates corresponding to A , B and C , and the equations of asymptotes (if any). [8] 6 The diagram shows the graph of f( )yx . Sketch, on separate diagrams, the graphs of (i) f( )yx , (ii) f( )yx , (iii) f1yx , (iv) f1 2yx . [12] x A (2, 2) y B (4, 0) y = –1 y C x y 1 3 2

Raffles Institution H2 Mathematics 2025 Year 5 __________________________________________________________________________________________ _______________________________________________________ Additional Practice Questions for Chapter 8B: Curve Transformation Page 3 of 8 7 MI Promo 9758/2018/PU2/02/Q4a The graphs of  fyx and  fyx are shown below. Sketch the graph of  fyx , stating the equations of any asymptotes, the coordinates of any turning points and intersections with the axes. [2] 8 VJC Mid-yr 9740/2006/Q11 Modified The following shows the graph of 1axy bx  . Sketch, on separate diagrams, the graphs of (a) 1axy bx  , (b) 1axy bx  , (c) 1axy bx  . Given that 12cd , write down the values of and ab . [8] x y y = c O x = d 1x  1x  yx yx O 0, 1 O yx     2,3 2,3  fyx x y  yx 0, 1  fyx x y

Raffles Institution H2 Mathematics 2025 Year 5 __________________________________________________________________________________________ _______________________________________________________ Additional Practice Questions for Chapter 8B: Curve Transformation Page 4 of 8 Transformations involving Conic Sections 9 VJC Prelim 9740/2009/ 01/Q6 A curve C1 has equation 22 2 2x ay a where 1a . Sketch C1, indicating the axial intercepts, asymptotes and stationary points, if any. [2] C1 undergoes a single transformation to become C2. Given that C2 has a line of symmetry 4y  and the point (4, 3) lies on C2, find the value of a . [3] 10 MI Promo 9758/2018/PU1/Q8 The curve C1 has equation 2291 8 48 2 3xx y y  . (i) By completing the square, show that the equation of C1 can be expressed as   22 22 11 123xy  . [2] (ii) Sketch C1, stating the coordinates of any points of intersection with the axes. [3] (iii) By adding a suitable graph to part (ii), solve the equation  2 2 22 1 123x x  . [2] (iv) State a sequence of transformations which transform the graph of C1 to the graph of C2 with equation 22 1.xy [3] 11 ACJC Prelim 9740/2011/02/Q5 The curves 1C and 2C have equations 229() 9yx k  and 2 2 2 1x yk  respectively, where k is a real constant such that 3k  . (a) Describe a sequence of transformati ons which transforms the graph of 22 1xy to the graph of 1C . [2] (b) (i) On the same diagram, sketch the graphs of 1C and 2C , stating clearly the coordinates of any points of in tersection with the axes and the equations of any asymptotes. [5] (ii) Find the range of values of the positive constant a such that the equation  22 2 9 19xkxa  has four real roots. [2]

Raffles Institution H2 Mathematics 2025 Year 5 __________________________________________________________________________________________ _______________________________________________________ Additional Practice Questions for Chapter 8B: Curve Transformation Page 5 of 8 12 HCI Prelim 9740/2010/01/Q12 modified The curves 1C and 2C have equations 22 2(2 ) ( 1 )xa y  and 2 4 1 xy x   respectively, where 12 a . State a sequence of transformations which transforms the graph of 22 1xy to the graph of 1C and describe the geometrical shape of 1.C [4] (i) Sketch 1C and 2C on the same diagram, stating the coordinates of any points of intersection with the axes and the equations of any asymptotes. [6] (ii) Show algebraically that the x-coordinates of the points of intersection of 1C and 2C satisfy the equation 22 2 2 2 2 2(1 ) (2 ) (1 ) ( 4 )x x ax ax    . [2] (iii) Deduce the number of real ro ots of the equation in part (ii). [1] Graphs of Derivative Functions & Reciprocal Functions 13 DHS Prelim 9758/2018/02/Q4 modified The diagram below shows the curve f' ( ) .yx It has turning points at (0, 6), (5, 0) and (7, 7) and intersects the x-axis at (3, 0) and (8, 0). (i) State the x-coordinates of the stationary points for the curve f( ) .yx Hence determine the nature of these stationary points. [3] (ii) State the range of values of x such that the curve f( )yx is concave downwards. [2] (iii) A student makes a claim on the following statement: If the curve y = f(x) passes through the point (3, 7), then f( ) 7x  for 35 .x  Explain briefly whether the student is right to make such a claim. [1] (7, 7) y x (5, 0) (0, 6) (3, 0) O (8, 0)

Raffles Institution H2 Mathematics 2025 Year 5 __________________________________________________________________________________________ _______________________________________________________ Additional Practice Questions for Chapter 8B: Curve Transformation Page 6 of 8 14 DHS Prelim 9740/2009/02/Q1 modif