Welcome to the Year 12 Topic Test Closing the Gap microsite.
Below are resources to help you close gaps you have identified when completing Topic Tests throughout the year. Answers will not be provided here, ask your teacher to share them via Google Classroom.
You will need to be logged in with your school email account to access some of the resources below.
The following content will be assessed in this topic test.
Use direct proof, proof by exhaustion and counter examples to prove results
Use and manipulate the index laws for all powers
Manipulate surds and rationalise a denominator
Solve quadratic equations using a variety of methods
Understand and use the coordinate geometry of the straight line and of the circle
Understand and solve simultaneous equations involving only linear or a mix of linear and non-linear equations
Solve linear and quadratic inequalities algebraically and graphically
The following content will be assessed in this topic test.
Manipulate, simplify and factorise polynomials
Understand, expand and use the binomial theorem
Divide polynomials by algebraic expressions
Understand and use the factor theorem
Use a variety of techniques to analyse a function and sketch its graph
The following content will be assessed in this topic test.
Calculate the values of sine, cosine and tangent for angles of any size
Use trigonometric identities
Recognise the equation of a circle
Sketch graphs of trigonometric functions and describe their main features
Solve various types of trigonometric equations
Use the sine and cosine rules and the area formula for a triangle
The following content will be assessed in this topic test.
Differentiate from first principles
Differentiate polynomial functions
Use differentiation to calculate rates of change
Work out equations, tangents and normals
Work out turning points and determine their nature
Work out and interpret the second derivative
Work out the integral of a function
Understand and calculate definite integrals
Use definite integrals to calculate the area under a curve
The following content will be assessed in this topic test.
Convert between powers and logarithms
Manipulate expressions and solve equations involving powers and logarithms
Use the exponential functions and their graphs
Verify and use mathematical models, including those of the form y=ax^n and y=kb^x
Consider limitations of exponential models