GCSE A* FOCUS: Transformations of curves
Wilson’s School Mathematics Department
A/A* FOCUS: Transformations of curves
Technique:
For each equation given below:
• Sketch the graph on the axes provided
• Describe the transformation(s) you applied to[pic] to sketch the graph
|1) [pic] |[pic] |
|2) [pic] |[pic] |
|3) [pic] |[pic] |
|4) [pic] |[pic] |
|5) [pic] |[pic] |
Exam Style Questions:
1) A sketch of the curve y = sin x° for 0 < x < 360 is shown below.
[pic]
(a) Using the sketch above, or otherwise, find the equation of each of the following two curves.
|(i) [pic] |(ii) [pic] |
(b) Describe fully the sequence of two transformations that maps the graph of y = sin x° onto the graph of y = 3 sin 2x°
2)
[pic]
The diagram shows a sketch of part of the curve with equation
y = p + q sin(x + 90)°, where p and q are integers.
(a) Find the value of p and the value of q.
(b) The line y = 3 intersects the curve y = p + q sin (x + 90)° at the points A, B and C.
Point A has coordinates (120, 3). Find the co-ordinates of the points B and C.
3)
|[pic] |The graph of y = a – bcos(kt), for values of t between|
| |0° and 120°, is drawn on the grid. |
| |Use the graph to find an estimate for the value of |
| |(i)a, |
| |(ii)b, |
| |(iii)k. |
4)
[pic]
The diagram shows part of two graphs.
The equation of one graph is y = a sin x
The equation of the other graph is y = cos x + b
(a) Use the graphs to find the value of a and the value of b.
(b) Use the graphs to find the values of x in the range 0° < x < 720 when a sin x = cos x + b.
c) Use the graphs to find the value of a sin x – (cos x + b) when x = 450.
[pic]
-----------------------
Technique:
1) Stretch, factor 1/3, parallel to x-axis
2) Stretch, factor 2, parallel to y-axis, reflection in x-axis
3) Stretch, factor ½, parallel to y-axis; shift 2 units in the positive y direction
4) Stretch, factor 2, parallel to y-axis; shift 900 in positive x-direction
5) Stretch by factor 2 parallel to x-axis; stretch, factor 2 parallel to y-axis; shift 1 unit in positive y direction.
Exam Style Questions:
1) a) (i) [pic] (ii) [pic]
b) Stretch by factor 3 parallel to the y-axis and a stretch by factor ½ parallel to the x-axis
2) a) p=4, q=2 b) (240,3) and (480,3)
3) (i) a=50 (ii) b=50 (iii) k=4
4) a) a=2, b=-1 b) 2340 c) 3
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