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 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
    • 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

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