##### Edexcel 9MA0/02 Jun 2024 A2 Exam Q. 3 : 4 marks in 4:48 min.

##### Edexcel 9MA0/01 Jun 2022 A2 Exam Q. 1 : 4 marks in 4:48 min.

##### Edexcel 8MA0/01 Oct 2020 AS Exam Q. 9 ab : 3 marks in 3:36 min.

##### Edexcel 9MA0/01 Oct 2020 A2 Exam Q. 9 bc : 6 marks in 7:12 min.

##### Edexcel 9MA0/01 Mar 2020 A2 Mock Q. 8 a : 2 marks in 2:24 min.

##### Edexcel 9MA0/01 Jun 2019 A2 Shadow Exam Q. 5 c : 4 marks in 4:48 min.

##### Edexcel 9MA0/01 Jun 2019 A2 Exam Q. 5 c : 4 marks in 4:48 min.

##### Edexcel 9MA0/02 Jan 2019 A2 Mock Q. 11 b : 4 marks in 4:48 min.

##### Edexcel 9MA0/01 May 2017 A2 Sample Exam Q. 15 b : 4 marks in 4:48 min.

##### Explore translations of a graph

##### Explore stretches of a cubic graph

##### Explore transformations of exponential function

##### Explore combined tranformations of logarithms

##### Transformation: y = a f(x)

A transformation may look like a rotation, but the draggable green point, shows they are all, in fact, stretches away from the x-axis by a factor of a.

What is the effect of making a = -1, so y = -f(x) ?

##### Transformation: y = f(x + a)

The green sample points show how graphs are translated horizontally in the opposite direction to what you might expect.

##### Transformation: y = f(x - a)

The green sample points show how graphs are translated horizontally.

##### Transformation: y = f(x) + a

You can drag the green point, and then use the slider to see the effect of the transformation on that particular point.

##### Transformation: y = f(a x)

The green sample points show how graphs expand or contract horizontally in the opposite directions to what you might expect.

What is the effect of making a = -1, so y = f(-x) ?

##### Exponential and Log Combined Transformations

This display shows the transformation \(y = \ln \left( {ax} \right)\) What is the effect of increasing \(a\)? It should be a stretch factor \({1 \over a}\), but it looks like a translation. Noting that \(\ln \left( {ax} \right) = \ln \left( x \right) + \ln \left( a \right)\), you can see that the transformation is the same as a translation vertically by \(y = \ln \left( {a} \right)\). When \(a = - 1\), the transformation is a reflection in the \(y\) axis.

This display shows the transformation \(y = \ln \left( {x - b} \right)\) Increasing the value of \(a\) will move the curve to the right.

This display shows the transformations \(y = \ln \left( {{ax} - b} \right)\)

##### a sin (b x + c) + d Transformations

The original sin function is showed as a green dashed line, and the transformed sin function is shown as a solid blue line. Initially the lines coincide. You can drag green and blue gliders to read coordinates at corresponding points on the original and transformed curves.

##### a cos (b x + c) + d Transformations

The original cos function is showed as a green dashed line, and the transformed cos function is shown as a solid blue line. Initially the lines coincide. You can drag green and blue gliders to read coordinates at corresponding points on the original and transformed curves.

##### a tan (b x + c) + d Transformations

The original tan function is showed as a green dashed line, and the transformed tan function is shown as a solid blue line. Initially the lines coincide. You can drag green and blue gliders to read coordinates at corresponding points on the original and transformed curves.

##### Investigate Order of Transformations 1

For $\color{blue}{f(x) = ( a \, \sin ( x ) ) + d }$ the vertical stretch (factor $\color{purple}{ a }$) is applied before the vertical translation (of $\color{purple}{ d }$).

For $\color{red}{g(x) = a \, ( \sin ( x ) + d ) }$ the vertical translation (of $\color{purple}{ d }$) is applied before the vertical stretch (factor $\color{purple}{ a }$).

You can drag a glider on the x-axis to help read cooordinates at corresponding sample points.

##### Investigate Order of Transformations 2

For $\color{blue}{f(x) = \sin ( ( b \, x ) + c ) }$ the horizontal translation (of $\color{purple}{ - c }$) is applied before the horizontal stretch (factor $\color{purple}{ { 1 \over b } }$).

For $\color{red}{g(x) = \sin ( b ( x + c ) ) }$ the the horizontal stretch (factor $\color{purple}{ { 1 \over b } }$) is applied before the horizontal translation (of $\color{purple}{ - c }$).

These orders may seem counter-intuitive if considering 'BIDMAS' precedence.

You can drag a glider on the x-axis to help read cooordinates at corresponding sample points.