Name: Score:
149 Multiple choice questions
Definition 1 of 149
An iterative procedure for solving f(x)=0.
Starts with a guess for a root and using the formula from the formula book, gets an answer closer
and closer to the root and converges at the root.
Other roots can be found with different guesses.
Ferrari's Method
False-position Method
Newton-Raphson Method
When Would You Substitute Atanu For An Integral
Definition 2 of 149
f(x) = I...I, so if asked to translate into another mod function you have to use f(x-a) as f(x) + a would
not be in the modulus signs.
Transforming modulus function
Integration by parts
What does iff mean
Integral of cos(kx)
,Term 3 of 149
What should you remember when making a differential equation model
Conditions e.g. weather
Y = f(x)+a: translation by 'a' units parallel to the y-axis
y = f(x-a): translation by 'a' units parallel to the x-axis
y = af(x): stretch parallel to the y-axis by a scale factor of 'a,' (1,3) goes to (1,3a)
y = f(ax): stretch parallel to the x-axis by a scale factor of '1/a,' (1,3) goes to (1/a,3)
y=-f(x): reflect f(x) in x-axis
y=f(-x): reflect f(x) in y-axis
F'(x)e^f(x)
The staircase diagram shows how the initial guess of x0 tends towards the answer which is
the intersection point of y=x and y=g(x). the diagram always starts by hitting y=g(x), then it
builds a staircase.
failure: y=g(x) could be a shape where no guess will ever tend towards the solution, e.g. a
convex curve, and instead it will either go to another root or to infinity. therefore, you have
to use another rearrangement to make x the subject.
Definition 4 of 149
y - y1 = m(x - x1)
y = mx+c
Coordinates of a point
Equation of a straight line
Gradient of parallel lines
Parametric curve
,Definition 5 of 149
Domain: x axis extremities
Range: y axis extremities
Domain vs Range
0!
Derivative of Loga(x)
How to make numerical integration more accurate
Definition 6 of 149
Use u to find dx in terms of du
Integrate the term wrt u
Sub the x term for u back in
Convex
Indefinite integration
Partial derivatives
Integration by substitution
Definition 7 of 149
1. assume what your proving is false
2. show that this is impossible (contradiction)
proof by contradiction
Geometric Sequence
Area bounded by y-axis
Transformations for trigonometric graphs
, Definition 8 of 149
-Rearrange equation so x is the subject, x=g(x)
-Make a guess and plug into g(x) then keep plugging answers back into g(x)
-Should converge to a root
Xn+1 = g(Xn) converges to a root at x=a, if g'(a)<1, and if X1 is close to a.
Simple iterative methods
Simple iterative methods, staircase + failure
How to integrate x/(x+a)
Implicit Differentiation
Definition 9 of 149
For (1+x)^n
IxI < 1, IF ASKED FOR UR VALUE MAKE SURE U KEEP THE MOD SIGNS
Condition for polynomial equations to have real roots
Rule for simplifying exponential functions
Limitations on the values of x in logarithmic functions
Restriction to make a binomial expansion convergent
149 Multiple choice questions
Definition 1 of 149
An iterative procedure for solving f(x)=0.
Starts with a guess for a root and using the formula from the formula book, gets an answer closer
and closer to the root and converges at the root.
Other roots can be found with different guesses.
Ferrari's Method
False-position Method
Newton-Raphson Method
When Would You Substitute Atanu For An Integral
Definition 2 of 149
f(x) = I...I, so if asked to translate into another mod function you have to use f(x-a) as f(x) + a would
not be in the modulus signs.
Transforming modulus function
Integration by parts
What does iff mean
Integral of cos(kx)
,Term 3 of 149
What should you remember when making a differential equation model
Conditions e.g. weather
Y = f(x)+a: translation by 'a' units parallel to the y-axis
y = f(x-a): translation by 'a' units parallel to the x-axis
y = af(x): stretch parallel to the y-axis by a scale factor of 'a,' (1,3) goes to (1,3a)
y = f(ax): stretch parallel to the x-axis by a scale factor of '1/a,' (1,3) goes to (1/a,3)
y=-f(x): reflect f(x) in x-axis
y=f(-x): reflect f(x) in y-axis
F'(x)e^f(x)
The staircase diagram shows how the initial guess of x0 tends towards the answer which is
the intersection point of y=x and y=g(x). the diagram always starts by hitting y=g(x), then it
builds a staircase.
failure: y=g(x) could be a shape where no guess will ever tend towards the solution, e.g. a
convex curve, and instead it will either go to another root or to infinity. therefore, you have
to use another rearrangement to make x the subject.
Definition 4 of 149
y - y1 = m(x - x1)
y = mx+c
Coordinates of a point
Equation of a straight line
Gradient of parallel lines
Parametric curve
,Definition 5 of 149
Domain: x axis extremities
Range: y axis extremities
Domain vs Range
0!
Derivative of Loga(x)
How to make numerical integration more accurate
Definition 6 of 149
Use u to find dx in terms of du
Integrate the term wrt u
Sub the x term for u back in
Convex
Indefinite integration
Partial derivatives
Integration by substitution
Definition 7 of 149
1. assume what your proving is false
2. show that this is impossible (contradiction)
proof by contradiction
Geometric Sequence
Area bounded by y-axis
Transformations for trigonometric graphs
, Definition 8 of 149
-Rearrange equation so x is the subject, x=g(x)
-Make a guess and plug into g(x) then keep plugging answers back into g(x)
-Should converge to a root
Xn+1 = g(Xn) converges to a root at x=a, if g'(a)<1, and if X1 is close to a.
Simple iterative methods
Simple iterative methods, staircase + failure
How to integrate x/(x+a)
Implicit Differentiation
Definition 9 of 149
For (1+x)^n
IxI < 1, IF ASKED FOR UR VALUE MAKE SURE U KEEP THE MOD SIGNS
Condition for polynomial equations to have real roots
Rule for simplifying exponential functions
Limitations on the values of x in logarithmic functions
Restriction to make a binomial expansion convergent
