Wednesday the 10th of December

Advanced Higher
Complex Numbers
L.I. To find the nth roots of a complex number
S.C. I can find the polar coordinates of the complex number in Cartesian form
       I know that the modulus will stay the same for all roots
       I know that there will be n roots if it is the nth roots we are trying to find
       I know that the next root will occur 2pi/n radians on
       I can calculate the roots and make sure they are in the correct range

2(1)
Equations of a straight line
L.I. To calculate the equation of a line joining two points, one of which is on the y-axis
S.C. I can calculate the gradient of the straight line connected the two coordinates
       I can calculate the y-intercept of the line
       I can form the equation of the straight line connecting the two points in the form y = mx + c

Tuesday the 9th of December

Advanced Higher
Complex numbers
L.I. To multiply and divide complex numbers in polar form
S.C. I can multiply two complex numbers in polar form
       I can divide two complex numbers in polar form
       I can use De Moivre's Theorem to calculate a complex number to a given power if it is in polar form.

Monday the 8th of December

2(1)
Equation of a straight line
L.I. To find the equation of a straight line given two points, one of which is the y-intercept.
S.C. I know that y = mx + c where m is the gradient and c is the y-intercept
       I can calculate the gradient using m = (y1 - y2)/(x1 - x2)
       I can substitute into the formula y = mx + c to get the equation of the straight line

Advanced Higher
Complex Numbers
L.I. To calculate the modulus and argument of a complex number and to write it in polar form.
S.C. I can find the modulus of a complex number |z|
       I can find the principal argument of a complex number arg(z)
       I can use these to find the complex number in polar form
       I can work backwards from polar form into cartesian form.

Thursday the 4th of December

2(1)
Gradient and linear equations
L.I. To use the gradient formula to calculate the gradient of a straight line joining two points
S.C. I understand what the gradient formula is when using coordinates
       I can use the gradient formula to calculate the gradient of a straight line
       I can put the coordinates into the gradient formula in the correct way

National 5

Sketching quadratics

L.I. To figure out the equation of the graph given the turning point

S.C. I can identify the turning point of the graph

       I can identify whether it is a maximum or minimum turning point

       I can write the equation of the graph in the form y = (x - b)^2 + c 

Wednesday the 3rd of December

Advanced Higher
Complex Numbers
L.I. To introduce the idea of imaginary numbers and how to use them to solve quadratics.
      To show pupils the basic arithmetic operations of complex numbers
S.C. I know that the sqaure root of -1 can be denoted i
       I can use this fact to solve quadratic equations with a discriminant less than 0 (has no real roots)
       I can plot a complex number on an Argand diagram
       I can use the basic arithmetic operations on complex numbers

2(1)

Gradient y = mx + c

L.I. To introduce the idea of a straight line equation (linear equation) being connected to the gradient and y-intercept

S.C. I can sketch a graph of an equation in the form y = mx + c

       I understand that the gradient = m

       I understand that the y-intercept = c

       Given the equation I can state the gradient and y-intercept

       Given the gradient and y-intercept I can state the equation



Tuesday the 2nd of December

National 5
Quadratics
L.I. To sketch graphs from the form f(x) = a(x-b)^2 + c
S.C. I know that the equation of the line of symmetry is x = b
       I know that the turning point (vertex) is the point (b,c)
       I know that if a > 0 then it is a minimum turning point and if a < 0 it is a maximum turning point
       I can calculate the y-intercept by substituting x = 0 into the function
       I can use all of this information to sketch an annotated quadratic function

Advanced Higher
Integration and differential equations.
L.I. To use Newton's Law of Cooling and other differential equations in context that are slightly harder than the simple examples looked at previously
S.C. I can set up the equation from the information given
        I can solve the equation using integration and logs as necessary

Monday the 1st of December

2(1)
Straight line
L.I. To draw graphs of the type y = mx + c
S.C. I can calculate the y value of a function given the x value
       I can plot the points from my table of values
       I can join up the points to make a straight line

Advanced Higher
Differential Equations
L.I. To use differential equations to solve problems in context
S.C. I can set up the equation for decay or growth
       I can find the constant of proportionality
       I can find the answer to the question being asked of me