Name: Teacher Assessment Section A Grade A*. The diagram shows the graph of = for. 5 5 5 Each of the graphs below is a transformation of this graph. Write down the equation of each graph. 5 (a) 5 (b) 5 5 5 5 5 5 5 (c) 5 Answer (a) =... 5 5 5 Answer (b) =... Answer (c) =... (Total 3 marks) St Paul s Catholic School
. The diagrams, which are not drawn to scale, show the graph of = and four other graphs A, B, C and D. A, B, C and D represent four different transformations of =. Find the equation of each of the graphs A, B, C and D. = Graph A Graph B = 3 Answer Graph Ais =... Answer Graph Bis =... = 3 = Graph D Graph C Answer Graph Dis =... Answer Graph Cis =... (Total 4 marks) St Paul s Catholic School
3. The sketch below is of the graph of = n the aes provided, sketch the following graphs. The graph of = is shown dotted on each set of aes to act as a guide. (a) = + St Paul s Catholic School 3
(b) = ( ) (c) (Total 3 marks) St Paul s Catholic School 4
4. A(, ) and B(, 4) are two points on the graph of = = 4 8 6 B(, 4) 4 A(, ) Here are three transformations of the graph =. n each diagram the graph of = is shown dotted. The images A and B of A and B are shown. Write down the equation of the transformed graph in each case. (a) 4 B'(, 8) 8 6 4 A'(, 5) =... St Paul s Catholic School 5
(b) 4 B'(, 8) 8 6 4 A'(, ) =... (c) 4 8 6 B'(, 4) 4 A'(, ) =... (Total 3 marks) St Paul s Catholic School 6
5. The diagram shows the graph of a function f ( ). 5 4 3 3 4 5 6 4 5 n the aes below sketch the graphs of each of these functions. In each case, the graph of f ( ). is shown to help ou. (a) f ( ) 5 4 3 3 4 5 6 4 5 St Paul s Catholic School 7
(b) f ( ) 5 4 3 3 4 5 6 4 5 (c) f () 5 4 3 3 4 5 6 4 5 (Total 3 marks) St Paul s Catholic School 8
6. (a) The graph = is transformed as shown. = Not drawn accuratel (,) Write down the equation of the transformed graph. Answer =... (b) The graph of = 3 is sketched below. n the same aes, sketch the graph of = 3 () (Total 3 marks) Success: Target: St Paul s Catholic School 9
Teacher Assessment Section B Transformations of Trigonometric Graphs Grade A*. This is the graph of = cos for 36 9 8 7 36 Write the equation of each of the transformed graphs. In each case the graph of = cos is shown dotted to help ou. (a) 9 8 7 36 Equation =... (b) 9 8 7 36 Equation =... (c) St Paul s Catholic School
9 8 7 36 Equation =... (d) 9 8 7 36 Equation =... (Total 4 marks). This is the graph of = sin for 36 St Paul s Catholic School
3 9 8 7 36 Draw the graphs indicated for 36 In each case the graph of = sin is shown to help ou. 3 (a) = sin (b) = sin (c) = sin 3 9 8 7 36 9 8 7 36 3 9 8 7 36 (Total 3 marks) St Paul s Catholic School
3. This is the graph of = cos for 36 9 8 7 36 (a) n the aes below draw the graph of = cos( 9) for 36 9 8 7 36 () (b) Write down a possible equation of the following graph. 9 8 7 36 Answer (Total 3 marks) St Paul s Catholic School 3
4. This is the graph of = sin. 9 8 7 36 n the grid below, sketch the graph of = sin ( - 9 ) 9 8 7 36 (Total marks) 5. The graph of = sin for 36 is shown on the grid below. The point P(9, ) lies on the curve. P 9 8 7 36 n both of the grids that follow, sketch the graph of the transformed function. In both cases write down the coordinates of the transformed point P. St Paul s Catholic School 4
(a) = sin ( 45) 9 8 7 36 P (...,...) () (b) = sin 9 8 7 36 P (...,...) () (Total 4 marks) St Paul s Catholic School 5
6. You are given that sin 7 =.9397 (a) n the aes below sketch the graph of = sin for 36 9 8 7 36 () (b) Hence write down the four solutions of the equation sin =.9397.................................... Answer...degrees... degrees... degrees... degrees (3) (Total 5 marks) Success: Target: St Paul s Catholic School 6
Teacher Assessment Section C Shapes of Graphs Grade A. Match three of these equations with the graphs shown below. = + 3 = 3 = 3 = + 3 = 3 3 3 Answer =.. Answer =.. Answer =.. (Total 3 marks) St Paul s Catholic School 7
. Each of the graphs represents one of the following equations. A = 3 + 4 B + 3 = C = D = 3 Write down the letter of the equation represented b each graph Equation... Equation... 4 4 4 6 4 Equation... (Total 3 marks) St Paul s Catholic School 8
3. (a) Four graphs are sketched. Graph A Graph B Graph C Graph D Complete the following statements. = + 4 = + 4 + = 4 matches graph. matches graph. matches graph. (3) (b) Sketch the graph of = 3 on the aes below. () (Total 5 marks) St Paul s Catholic School 9
4. Below are three graphs. Match each graph with one of the following equations. Equation A: = 3 p Equation B: = + p Equation C: 3 + 4 = p Equation D: = p 3 In each case p is a positive number. (i) (ii) (iii) Answer Graph (i) Equation... Graph (ii) Equation... Graph (iii) Equation... (Total 3 marks) St Paul s Catholic School
5. Match each of the sketch graphs to one of these equations. A = B = + C = 3 D = 3 + 4 E = 3 4 Graph represents equation... Graph represents equation... Graph 3 represents equation... Graph 4 represents equation... (Total 4 marks) 6. The graph shows four curves A, B, C and D. St Paul s Catholic School
A B C D Match each curve to its equation. (a) = is curve... (b) = is curve... (c) = 3 is curve... (d) = 4 is curve... (Total 4 marks) Success: Target: St Paul s Catholic School