Maths

Use the properties of cross products
Definite Integrals
Using slope fields 8F
polynomial division by quadratics
polynomial multiplication
Calculate the length of the cross product vector
Determine the normal to a plane using a cross product from two vectors or three points
Integrate a function like f(x) = 4/(5+7x) using natural logarithms
Properties of modulus
Mode, Median, Mean, Variance and SD for Probability Density Functions
Roots of complex numbers
Determine the domain and range of an inverse function by interchanging the original domain and range
Understand how the absolute value function works
Determine the nature of a triangle ABC using distances
Derivatives of log and exponential functions
Differential Equations – solve by direct integration 8D
Restrict the domain of a function to enable the inverse to be found
Calculate the cross product
Optimisation (problem solving)
Binomial
Determine domain and range for a function using subsets of the original domain and range
Positive and negative parts of the graph (reciprocal function)
Show that f'(x) is increasing / decreasing
Integrate a function involving trig such as (sin x)^2
Find unknowns using areas and volumes
Calculate the scalar triple product
Find the inverse function through an x-y interchange
Determine the equation of a plane
Integrate using substitution
Integrate a function by dividing it into partial fractions
polynomial zeros, roots and factors.
First Principles
Determine whether two lines intersect, are skew or are parallel
Confidence Intervals (finding the interval, finding w, finding n)
Bernoulli
Solving log and exponential equations
Indefinite Integrals
Use parallel vectors
Determine the x and y intercepts of any rational function
Use program mode to find the cubic equations for a Bezier Curve if they are not given
Synthetic division
Determine the foot of the normal from a point to a plane
Determine whether a function has an inverse from its graph
Finding a logistical function 8H
Scalar multiplication of polynomials
Integrate functions using arc functions
Sample Sum Distributions
Determine the shortest distance from a point to a line (two methods here)
The Quotient Rule
Determine the angle between a line and a plane
The fundamental theorem of algebra (polynomials)
Make sure you are good at drawing parametric graphs in Graph Mode and you are able to determine points on the curve using x calc and y calc
Problem Solving with Differential Equations 8G
Second Derivatives
Determine the horizontal asymptotes of a linear/linear functions
Show that a function is an inverse using f-1(f(x)) = f(f-1(x))=x
Area under/between curves
Stationary Points
The Chain Rule
Find the area between two functions
Converting to and back from polar form.
Vertical asymptote – x intercepts (reciprocal function)
Normal Distribution (Ncd, InvNorm)
Related Rates
Equations of Tangents
Calculate the angle between two vectors
Determine domain and range for a function
Kinematics
Points of Inflection
Use the special unit vectors : I, j, k
Multiplication of complex numbers.
Nth roots of unity.
Behaviour close to the asymptotes (reciprocal function)
Testing claims of a population mean
Sketch a linear/linear function
Show that a function is self-inverse using algebra
Determine the angle between two lines
Polynomial Equations
Draw a reciprocal function from the sketch of the original function using
Probability Density Functions
Determine the direction of the cross product
Use the midpoint and distance formula for two points in 3D
Find the coordinates of the foot of the perpendicular from a point to a line
The remainder theorem
Revise finding the length of a curve
Describe the behaviour of a function close to its asymptotes using its graph
State the meaning of a 1 to 1 function
Sketch the graph of both y=|f(x)| and y = f(|x|) from the graph of y=f(x).
Trig Calculus
Testing claims about Population Proportions (p)
polynomial equality
Knowing that ABCD is a parallelogram, find an unknown point
Show that ABCD is a parallelogram using a vector approach
Determine the vertical asymptotes of any rational function
Properties of aX+b
Cubic Polynomials
Finding where two trig functions meet
Solve equations using composite functions: e.g. find x such that f(g(x))=5
Determine the angle between two planes
Find P if P divides AB in the ratio
Z-scores and Z Distributions
Quartic Polynomials
Using Rectangles to find an area
Addition and Subtraction of polynomials
Induction
polynomial division by linear equation
Local Min – Local Max (reciprocal function)
Discrete Random Variables
Show that three points A, B and C are collinear and determine the ratio in which B divides AC
De moive's theorem.
Cis properties.
Making and proving a conjecture
Confidence Intervals for Population Proportions (p)
Use the properties of the dot product
Implicit Differentiation
The factor theorem
Expected Value (mean), Variance and SD for Discrete Probability Distributions
Differential Equation – Verification 8C
Rates of Change
Sample Proportions
Revise finding highest, lowest, left most and right most
Find position vectors, like AB, given A and B
Determine the point of intersection between a plane and a line
Kinematics (horizontal and vertical)
Sketch an inverse function using a reflection in the line y=x
Find and use unit vectors
The Product Rule
Find the volume of a revolution between two curves.
Integrate using parts.
Finding an unknown mean and/or standard deviation
Rates of Change
Drawing Derivatives
Differential Equations – solve by separation 8E
polynomial division algorithm
Understand the geometric possibilities for two planes and three planes in space
Determine the distance between a point a plane (two methods here)
Sample Mean Distributions
Find function compositions
Determine the equation of a line in either vector, parametric or cartesian form
Deduce that two vectors are parallel
Calculate areas using the cross product
Show that two vectors are perpendicular
Invariant points (reciprocal function)
Draw complex numbers on the argand diagram
Curves will include Projectile Motion, Bezier Curves, Circles and Ellipse
Find the volume of a revolution using either the x axis or y axis