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

Wednesday the 26th of November

Advanced Higher
Differential Equations
L.I. To solve differential equations that are separable.
S.C. I can seperate the variables and get the equation ready to be integrated
       I can integrate both sides and solve the equation.

 

Tuesday the 25th of November

Advanced Higher
Further integration
L.I. To look at integrals that return to the original integral once you have integrated by parts
S.C. I can integrate by parts
       I can recognise the original integral appearing in the second integration by parts
       I can deal with this by substitution and finding the value of the integral.

Monday the 24th of November

2(1)
Circles
L.I. To use the correct formula for calculating the circumference or the area as asked for in the question
S.C. I can pick the correct formula and use it correctly when asked to find the circumference or a fraction of a circles circumference
       I can pick the correct formula and use it correctly when asked to find the area or a fraction of a circles area
       I can use circles as part of a composite shape and calculate its area and circumference as needed.

Advanced Higher
Further integration
L.I. To continue to look at integration by parts
S.C. I can integrate by parts twice in order to integrate an expression
       I can use integration by parts to find a definite integral.

Friday the 21st of November

2(1)
Circles
L.I. To calculate the radius given the area of a circle
S.C. I understand how the formula for area of a circle can be re-arranged to find the radius
       I can plug the numbers in correctly to calculate the radius of the circle given the area
       I always make sure to put the correct units in my answer
       I can use the radius to calculate other things in the circle (diameter, circumference)

National 5
Simultaneous Equations
L.I. To solve simultaneous equations in context
S.C. I can create the two formula from the example given
       I can multiply up the equations as needed to get one variable ready to be eliminated
       I can solve the equations to find the two variables.

Thursday the 20th of November

2(1)
Area of a circle
L.I. To use the formula given to calculate the area of a circle
S.C. I can substitute into the formula for area of a circle, using the radius
       I can calculate the radius if I am given the diameter
       I can remember the formula for calculating the area and differentiate it from the formula for calculating the circumference.

National 5
Simultaneous Equations
L.I. To use simultaneous equations to solve problems in context
S.C. I can set up the two equations from the information given
       I can solve the equations simultaneously
       I can put the answers back into the appropriate context.

Wednesday the 19th of November

Advanced Higher
Integration by parts
L.I. To use integration by parts to find the integral of expressions that can be written as two functions muliplied together
S.C. I can identify the part of the function to be called u and the part of the function to be called dv/dx
       I can find du/dx and v from these functions
       I can plug the appropriate functions into the integration by parts formula
       I can state my final answer to the integration after using integration by parts

2(1)
Circles
L.I. To calculate the diameter or radius given the circumference.
S.C. I can use the circumference to calculate the diameter of a circle by dividing the circumference by pi.
       I can use this to find the radius.
       I can round to a given accuracy.

Tuesday the 18th of November

National 5
Simultaneous Equations
L.I. To solve a set of equations with two variables
S.C. I can multiply up one or both of the equations to get the variables coefficients to be the same
       I can decide whether to add or subtract the two equations to eliminate one of the variables
       I can find the value of the variable I don't eliminate
       I can find the other variables value by substituting into one of my original equations

 

 

 

 

Advanced Higher
Further integration
L.I. Using algebraic long division and partial fractions to simplify an expression to then integrate it
S.C. I can use algebraic long division to simplify an expression
       I can use partial fractions to simplify an expression
       I can integrate this new basic expression

Monday the 17th of November

2(1)
Circle
L.I. To introduce the formula for calculating the circumference of a circle from the investigation they carried out last time
S.C. I know the relationship between the circumference and the diameter
       I can calculate the circumference of a circle given the diameter
       I can calculate the circumference of a circle given the radius

Advanced Higher
Further integration
L.I. To use partial fractions to make integration of rational functions easier
S.C. I can put a rational function into partial fractions
       I can integrate the terms from the partial fraction

Algebraic Long Division
L.I. To use algebraic long division before integrating to make it easier
S.C. I can write an improper algebraic rational function as a sum of a polynomial and a proper rational function.
       I can integrate the expression found

 

Friday the 14th of November

2(1)
Circles
L.I. To use the formula C = pi d to calculate the circumference of a circle
S.C. I know what pi is to 2 decimal places
       I know what the diameter is and it's connection to the radius
       I know the connection between the circumference and diameter of a circle
       I can calculate the circumference of a circle given it's diameter or radius

National 5
Simultaneous equations
L.I. To find the point of intersection graphically and using elimination
S.C. I can sketch the graph of a linear equation
       I can find, by looking, the point of intersection of two lines
       I can set up two equations to be solved simultaneously
       I can eliminate one of the variables in the two equations
       I can solve for the first variable
       I can substitute into one of the original equations to find the other variable

Wednesday the 12th of November

Advanced Higher
Further integration
L.I. to learn how to integrate to get inverse trigonometric functions as answers
S.C. I can integrate to get the inverse sine function as an answer
       I can integrate to get the inverse cosine function as an answer