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

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download