# FMSQ

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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
• Completing the square
• Sketching graphs of quadratic expressions
• Solving simultaneous equations
• Drawing graphs
• Substitution
• Elimination
• 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
• 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
• 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
• 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)
• At a stationary point, dy/dx=0
• Look at gradient either side to determine whether it is max, min or point of inflection
• 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