FSMQ Level 3 (pilot) Algebra scheme of work
This Advanced (Level 3) unit is NOT a freestanding qualification in the AQA pilot and no separate FSMQ certificate is available for it.
Also note that the AQA assessment of this unit is by examination only.
Before starting this unit learners should be able to:
 plot by hand accurate graphs of paired variable data & linear & simple quadratic functions (including the type y = ax^{2} + bx + c) in all four quadrants
 recognise and predict the general shapes of graphs of direct proportion, linear and quadratic functions (including the type y = kx^{2} + c)
 fit linear functions to model data (using gradient and intercept)
 rearrange basic algebraic expressions by collecting like terms, expanding brackets and extracting common factors
 solve basic equations by exact methods including pairs of linear simultaneous equations
 use power notation (including positive and negative integers and fractions)
 solve quadratic equations by factorising and by using at least one of: graphics calculator, the formula (must be memorised), completing the square
A suggested work scheme for this unit is given below. It includes some revision of the above as well as the other topics and methods to be covered.
The following techniques should be introduced as soon as possible and used throughout the course:
 using a calculator effectively and efficiently, including the use of memory and function facilities (recording the working as well as the result)
 doing calculations without a calculator using written methods and mental techniques
 graph plotting using computer software or a graphical calculator and using trace and zoom facilities to find significant features such as turning points and points of intersection
 checking calculations using estimation, inverse operations and different methods.
Note that the AQA assessment of this core unit is by examination only and you should disregard any references to Coursework Portfolio requirements in the assignments listed below which have not yet been updated. These have been included for possible use as classroom activities but will not form part of the AQA assessment of this core unit.
Topic area 
Content 
Nuffield resources 
Linear functions (4 hours) 
Revise the main features of graphs of direct proportional (y = mx) and linear (y = mx + c) functions. Fit such functions to real data using gradients and intercepts. Understand whether it is appropriate or not to use a particular function to model data by consideration of intercepts, long term behaviour, and so on in real world terms. Solve linear simultaneous equations using graphical and algebraic methods. 
Linear graphs 
Graphs of functions in Excel 

Interactive graphs 

Graphic calculators 

Using the CASIO fx7400G PLUS 

Graphic calculator – Equations 

Car bonnet 

Match linear functions and graphs 

Simultaneous equations on a graphic calculator 

Quadratic functions 
Draw graphs of quadratic functions of the form: · y = ax^{2} + bx + c · y = (rx – s )(x – t) · y = m(x + n)^{2} + p Relate the shape, orientation and position of the graph to the constants and zeros of the function f(x) to roots of the equation f(x) = 0. Fit quadratic functions to real data.
Revise solving quadratic equations by: Rearrange any quadratic function into the forms y = ax^{2} + bx + c and y = a(x + b)^{2} + c Find maximum and minimum points of quadratics by completing the square. 
Test run 
Model the path of a golf ball 

Broadband A, B, C Presentation shows the algebra version. 

Two on a line and three on a parabola 

Factor cards 

Water flow 

Completing the square 
Topic area 
Content 
Nuffield resources 
Gradients of curves, maxima and minima (5 hours)

Calculate and understand gradient at a point on a graph using tangents drawn by hand (and also using zoom and trace facilities on a graphic calculator or computer if possible). Use and understand the correct units for rates of change. Interpret and understand gradients in terms of their physical significance. Identify trends of changing gradients and their significance both for known functions and curves drawn to fit data. Find local maximum and minimum points and understand their significance in terms of the real situation. 
Tin can 
Maximum and minimum problems 

Power functions and inverse functions (5 hours) 
Draw graphs of functions of powers of including where is a positive integer, , , and Find the graph of an inverse function using reflection in the line y = x. Solve polynomial equations of the form ax^{n} = b . 
Interactive graphs 
Growth and decay (8 hours) 
Draw graphs of exponential functions of the form and ( positive or negative) and understand ideas of exponential growth and decay. Draw graphs of natural logarithmic functions of the form and understand the logarithmic function as the inverse of the exponential function. Understand how logarithms can be used to represent numbers. Solve exponential equations of the form Learn and use the laws of logarithms · · ·
Convert equations involving powers to logarithmic form, Use natural logarithms to solve equations such as . 
Growth and decay 
Population growth 

Calculator table 

Ozone hole 

Climate prediction A and B 

Cup of coffee 
Topic area 
Content 
Nuffield resources 
Transformations of graphs (6 hours) 
Use the following to transform graphs of basic functions: · translation of by vector to give · translation of by vector to give · stretch of scale factor , invariant line to give · stretch of scale factor , invariant line to give Describe geometric transformations fully. Use transformations to fit a function to data. 
Sea defence wall (assignment)

Trigonometric functions (10 hours) 
Draw graphs of · · Learn the general shape and position of trigonometric functions and use the terms amplitude, frequency and period correctly. Fit trigonometric functions to real data. Solve trigonometric equations of the form and . 
Coughs and sneezes 
SARS A and B (assignments) 

Sunrise and sunset times (assignment) 

Tides (assignment) 
Topic area 
Content 
Nuffield resource 
Linearising data (6 hours) 
Determine parameters of nonlinear laws by plotting appropriate linear graphs in applications of the cases below: · y = ax^{2} + b by plotting y against x^{2} · y = ax^{b} and y = a^{x} using natural logarithms 
Earthquakes  Log graphs 
Gas guzzlers 

Smoke strata 

Earthquakes (ln version only) 

Revision (8 hours) 
Revise topics. Work through revision questions and practice papers. Discuss the data sheet  make up and work through questions based on it. 

Page last updated on 25 January 2012