# FMSQ

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- Created by: Lara Superfine
- Created on: 13-03-13 20:55

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- FMSQ
- Algebra
- Simplifying algebraic expressions
- Collecting like terms
- Removing Brackets
- Cancelling by common factors
- Factorising
- Expressing them as a single fraction

- Solving Linear Equations
- Changing the subject of an equation
- Factorising quadratic expressions
- Solving a quadratic equation
- Factorising
- Completing the square
- Using the quadratic formula

- Sketching graphs of quadratic expressions
- Solving simultaneous equations
- Drawing graphs
- Substitution
- Elimination

- Simplifying algebraic expressions
- Algebra II
- Linear inequalities are dealt with like equations BUT if you multiply or divide by a negative number you must reverse the inequality sign
- When solving a quadratic inequality SKETCH THE GRAPH
- When simplifying an algebraic fraction involving multiplying or dividing you can cancel by common factor
- When solving an equation involving fractions, MULTIPLY through by the LCM of the denominators
- Simplifying expressions involving square roots
- Make the number under the square as small as possible
- Rationalise the denominator

- Algebra III
- Polynomials have a positve integer (number before x) and can have a positive constant (+c)
- The order of a polynomial is the highest power of x
- Factor theorem states the (x-a) is a factor of a polynomial f(x), then f(a)=0 and x=a is a root of the equation f(x)=0
- if f(a)=0, then (x=a) is a factor of f(x)

- The remainder theorem states that f(a) is the remainder when f(x) is divided by (x-a)

- Algebra IV
- Binomial coefficients
- Pascal's Triangle
- The formula

- Binomial distribution can be used to model a situation in which...
- The probability of a success=p
- Probability of failure =q (1-p)
- there are n trials
- the number of successes = X

- Binomial coefficients
- Coordinate geometry
- Gradient of a straight line = y2-y1 divided by x2-x1
- Two lines are parallel if their gradient is equal
- Two lines are perpendicular if the product of their gradients is -1
- Distance AB= sqrt(difference of x^2 + difference in y^2)
- Midpoint of AB= average of (x,y)
- Equation of a straight line could be..
- parallel to y: x=a
- parallel to x: y=b
- line through origin with gradient m: y=mx
- line through (0,c) with gradient m: y=mx+c
- line through (x1,y1) with gradient m: y-y1=m(x-x1)
- line through (x1,y1) and (x2,y2)
- (y-y1)/(y2-y1)=(x-x1)/(x2-x1)
- (y-y1)/(x-x1)=(y2-y1)/(x2-x1)

- The co-ordinates of the point of intersection of 2 lines can be found by solving the equations simultaneously
- The equation for a circle with centre (h,k) and radius r is..
- (x-h)^2 + (y-k)^2 =r^2

- Coordinate Geometry II
- Drawing linear inequalities
- < or > .. draw a broken line
- "or equal to" signs are drawn with a solid line
- Region you want is NOT shaded. Shade the region you don't want

- Region where a number of inequalities are satisfied simultaneously is called the feasible region
- In linear programming, the objective function is the algebraic expression describing the quantity that you are required to maximise or minimise
- The max and min values will lie in the corners

- Drawing linear inequalities
- Trig applications
- In 3D
- A plane is a flat surface

- When solving 3D questions..
- vertical lines=vertical
- north-south lines=sloping
- east-west lines=horizontal

- In 3D
- Differentiation
- y=kx^n
- dy/dx=nkx^n-1

- y=c
- dy/dx=0

- y=f(x) + g(x)
- dy/dx= f'(x) +g'(x)

- For the tangent and normal at (x1,y1)...
- gradient of tangent, m1= dy/dx
- gradient of the normal, m2 = -1/m1

- gradient of the normal, m2 = -1/m1
- equation of tangent = y-y1=m1(x-x1)
- equation of the normal = y-1=m2(x-x1)

- gradient of tangent, m1= dy/dx
- At a stationary point, dy/dx=0
- Look at gradient either side to determine whether it is max, min or point of inflection

- y=kx^n
- Kinematics
- Time,measured from origin, seconds(s
- t

- Distance, distance travelled in given time, metres (m)
- x(or y)

- Speed= distance/time, metres per second (m/s)
- v =dy/dx

- Displacement, distance from origin (m)
- s

- Velocity, rate of change of displacement, metres per second (ms^-1)
- v= ds/dt

- Acceleration, rate of change of velocity, metres per second per second (ms^-2)
- a= dv/dt

- When acceleration is constant and the initial velocity is u;
- v=u+at
- s= (u+v)/2 x t
- s= ut+ 1/2 at^2
- v^2= u^2 +2as

- For general motion...
- v= ds/dt
- a=dv/dt
- s= {v dt
- v= {a dt

- Time,measured from origin, seconds(s

- Algebra

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