Further Maths Flashcards
What are the exact trig values?
Draw the tan graph
Draw the sin graph
Draw the cosine graph
What is the sin Rule
What is the cosine rule?
How do you use cast diagrams?
🟢check which relm it is in to see if it is positive or negative
🟢then check which angle is nearest to the x axis, to use for calculating angle
What is the gradient of the line of a perpendicular line?
The negative reciprocal
What is symmetry of the graph?
How do you differenciate?
How do you convert an equation involving 2 variables into a ratio ?
Draw Pascal’s triangle
Expand
Domain and range
How do you multiply two different matrices?
What are singular and non singular matrices?
If singular , the determinant =0
If non - singular , the determinant !=0
What is an identity matricx?
Scalar multiplication of matrices
Adding and subtracting matrices
Figure out the determinants of the 2X2 matrices
What are the two equations of the circle?
What are the two equations of the circle?
What is an identity matrix?
Determine the equation of a circle with :
🟢 centre (0,0) , radius =3
🟢centre (4,-7) , radius =5
🟢centre (0,5) , radius = 1
determine the centre and the radius
What is the discriminant?
If less than 0 doesn’t touch the x axis and so no solutions
How do you find the midpoint of two points?
You find the average of the x and y values separately
A circle passes through the points A (0,0) and B (4,2). The centre of the circle has an x value of -1. Determine the equation of the circle:
The circle C has radius 5 and touches the y axis at (0,9). It’s centre is (-5, 9) and it’s radius is 5. A line through point P (8,-7) is a tangent to the circle at the
Point T. Find the length of PT
Differentiate :
How do you find the gradient of a tangent to a curve ?
- Differentiate the equation to give the ‘gradient function’
- Then substitute the ❎ value into the function to give m
How do you find the equation of a tangent to a curve ?
- Differentiate the equation to give the ‘gradient function’
- Then substitute the ❎ value into the function to give m
- Now that you have found m , substitute into y=mx +c
How do you find the equation of a normal to a curve ?
*a normal is a straight line that crosses the tangent at 90° (perpendicular)
- Differentiate the equation to give the ‘gradient function’
- Then substitute the ❎ value into the function to give m
- Now that you have found m , you can find m of the or all by doing negative reciprocal
- Substitute this m into y=mx + c
What is the determinant of a matrix ?
What is the inverse of a matrix
What is the inverse of a matrix ✖️matrix ?
How would you solve simultaneous equations using matrices
Convert this simultaneous equation into matrix form
And solve
How can you recognise /guess some matrix transformations?
What are some cheeky tricks to Identify some linear transformation matrices?
How do you find stationary points of a function?
Find dy/dx
Then make this gradient function =0
As at the stationary points the gradients are 0.
How do you know whether the stationary points are maximum or minimum points ?
What is the circle geometry rule of chords
The perpendicular from the centre to a chord , bisects a chord
What is the transformation matrix for the reflection in the line y=x
What is the transformation matrix for a reflection in the x axis
What is the transformation for the reflection in the y axis
What is the transformation matrix for a 90° clockwise rotation?
What is the transformation matrix for a 90° anti clockwise rotation?
What is the transformation matrix for a 180° clockwise and anti clockwise rotation?
What is the transformation matrix for a 270°clockwise rotation?
What is the transformation matrix for a 270° anti clockwise rotation?
How would you find the limiting value ?
What does it mean when it says that x is an obtuse angle for cos(x) or sin (x)?
It must mean that it is cos(x)= - …..
Eg : obtuse angle for cos (x)=-0.8
What does it mean when it says integer form?
Write out the possible numbers not an inequality
What does it mean when it says integer form?
Write out the possible numbers not an inequality
What are some general tips for myself in the exam ?
- remembering +- before square roots
- remembering that there are marks for marking and not answers. So write out each small sum made , SUBSTITUTIONS WITH BRACKETS , don’t get lazy
- be extra careful with positive and negative signs
How do you remember the reflection transformation matrices?
How do you remember the rotation matrices ?
Giving a range of values
