CIE Further Pure Mathematics 1
Do matrices in this form
(a b)
(Ka Kb)
have an inverse - answer- No
How can we use b^2 - 4ac to find the turning point - answer- Find the values we're b^2-4ac < 0 , to find
the values of your that are invalid.
how do u find an inverse matrix - answer- A --> minor matrix --> cofactor matrix --> adjoint matrix --> A^-
1= 1/det(A) x adjoint matrix
how do u find the angle between a line and a plane - answer- cos x = b ⋅ n / |b| |n|
then use
a = 90 - x or a = x - 90
How do you find the acute angle between 2 planes
and
What do the acute and obtuse angle between the planes add up to - answer- cos theta = n1 ⋅ n2 / |n1|
|n2|
the 2 angles equal 180
How do you find the common perpendicular of 2 lines - answer- use matrix determinates using the
coordinates of 2 line
How do you find the equation of the line intersecting 2 planes - answer- b = n1 x n2
the position vector:
- set x=0 and obtain 2 equations and solve using simultaneous equations to get the y and z coordinates
, CIE Further Pure Mathematics 1
How do you find the maximum distance from the origin for polar curves - answer- dr/d theta = 0
How do you find the maximum distance from the x-axis for polar curves - answer- dx/ d theta = 0
How do you find the maximum distance from the y-axis for polar curves - answer- dy/d theta = 0
How do you find the point where a line and plane intersect - answer- solve for t by putting both
equations together
how do you find the shortest distance from a point P to a line r= a + bt - answer- 1. PQ is the shortest
distance
2. Use PQ ⋅ b to find the value of t to get the coordinate of OQ
3. PQ = OQ - OP
4. |PQ|
or
A- any point on the line
u = unit vector of b
|AP x u|
How do you transform the curve y= f(x) into y= |f(x)| - answer- All the values under y=0 will be reflected
in the x-axis
How do you transform the curve y= f(x) into y= f( |x| ) - answer- Ignore all the negative x values and all
the positive x values are reflected in the y-axis
How does the graph of r= theta look - answer- Spiral
Do matrices in this form
(a b)
(Ka Kb)
have an inverse - answer- No
How can we use b^2 - 4ac to find the turning point - answer- Find the values we're b^2-4ac < 0 , to find
the values of your that are invalid.
how do u find an inverse matrix - answer- A --> minor matrix --> cofactor matrix --> adjoint matrix --> A^-
1= 1/det(A) x adjoint matrix
how do u find the angle between a line and a plane - answer- cos x = b ⋅ n / |b| |n|
then use
a = 90 - x or a = x - 90
How do you find the acute angle between 2 planes
and
What do the acute and obtuse angle between the planes add up to - answer- cos theta = n1 ⋅ n2 / |n1|
|n2|
the 2 angles equal 180
How do you find the common perpendicular of 2 lines - answer- use matrix determinates using the
coordinates of 2 line
How do you find the equation of the line intersecting 2 planes - answer- b = n1 x n2
the position vector:
- set x=0 and obtain 2 equations and solve using simultaneous equations to get the y and z coordinates
, CIE Further Pure Mathematics 1
How do you find the maximum distance from the origin for polar curves - answer- dr/d theta = 0
How do you find the maximum distance from the x-axis for polar curves - answer- dx/ d theta = 0
How do you find the maximum distance from the y-axis for polar curves - answer- dy/d theta = 0
How do you find the point where a line and plane intersect - answer- solve for t by putting both
equations together
how do you find the shortest distance from a point P to a line r= a + bt - answer- 1. PQ is the shortest
distance
2. Use PQ ⋅ b to find the value of t to get the coordinate of OQ
3. PQ = OQ - OP
4. |PQ|
or
A- any point on the line
u = unit vector of b
|AP x u|
How do you transform the curve y= f(x) into y= |f(x)| - answer- All the values under y=0 will be reflected
in the x-axis
How do you transform the curve y= f(x) into y= f( |x| ) - answer- Ignore all the negative x values and all
the positive x values are reflected in the y-axis
How does the graph of r= theta look - answer- Spiral
