FSMQ Level 2 Algebra and graphs scheme of work
Before starting this Higher (Level 2) FSMQ students should be able to:
 calculate with numbers (including large and very small numbers) by carrying out operations in the correct order, working both by hand and with a calculator
 calculate with fractions and decimals (including expressing one quantity as a fraction of another and converting between decimals and fractions)
 calculate with percentages
 round values to the nearest whole number, 10, 100, 1000, (0.1), (0.01) or to an appropriate number of decimal places or significant figures.
 substitute into formulae expressed in words and symbols
A suggested work scheme showing topic areas and methods to be covered is given below. This recommends a total of 60 guided learning hours that could be used in a variety of ways such as 2 hours per week for 30 weeks, 4 hours per week for 15 weeks, or 5 hours per week for 12 weeks. There is plenty of scope for varying the order and time allocation as many of the mathematical techniques can be introduced/revised in several different contexts. Although the topics are listed separately, it would often be beneficial to use a variety of skills within the same piece of work.
Some techniques should be introduced as soon as possible and used throughout the course. These include:
 using a (scientific or graphic) calculator effectively and efficiently, including the use of memory facilities, functions and standard form for large and small values
 doing calculations without a calculator using written methods and mental techniques
 recording and presenting data in tables using an appropriate degree of accuracy and correct units (grouping data where appropriate)
 graph plotting by hand and using either computer software or a graphic calculator
 checking calculations using estimation, inverse operations and alternative methods.
Note that the assessment of this AQA FSMQ is by examination only and you should disregard any references to Coursework Portfolio requirements in the assignments which have not been updated. These are included for possible use as classroom activities but will not form part of the assessment of this FSMQ.
Topic area 
Content 
Nuffield resource 
Plot graphs of real data 
Plot accurate graphs of data pairs by hand and using either a graphic calculator or function plotting software, ensuring that the graphs are correctly scaled and labelled. Average data if necessary (mean, mode, median for discrete data). Use coordinates in all four quadrants where appropriate. Fit lines by eye (both straight and curved, as appropriate). Find the intercepts of linear and nonlinear graphs with axes and where appropriate understand their physical significance. Use trace facilities with graphic calculators or function plotting software where possible. Identify errors in data by inspection of the data set and by graphical means. Recognise that measurements expressed to a given unit can have a maximum error of half a unit; using notation such as 300±50 to express errors. 
Road test 
Errors (Use the first part only) 

Matching graphs and scenarios 

Linear graphs 
Calculate in appropriate units and understand the physical significance of the gradients of linear graphs. Consider the intercepts of linear graphs with axes and where appropriate understand their physical significance. 
Hire a coach 
Standard Form 
Convert between standard form and ordinary numbers. Use a calculator to perform calculations with numbers expressed in standard form. 
Large and small 
Topic area 
Content 
Nuffield resource 
Graphs of functions 
Use functions to find data pairs:
Use tables to display results and where appropriate stages of calculations. Use function notation such as
Look for patterns which datafitting proportional Plot graphs of functions, using coordinates in all four quadrants. Consider the main features of direct and indirect proportional, linear and quadratic models and their differences. Predict the shapes of graphs of direct and inverse proportion, linear and quadratic functions from an algebraic statement. 
Linear graphs 
Graphs of functions in Excel 

Spreadsheet graphs 

Linear relationships 

Quadratic graphs 

Substitution into formulae including conversion of units 
Convert within and between metric and imperial systems, including inches, feet, yards, miles using conversion factors and the use of formulae such as = 3.28 for converting metres to feet. Substitute data into other formulae, using BIDMAS to find secondary data including formulae with multiples and fractions of linear terms, powers (positive and negative integers and fractions) and brackets. 
Hot water tank: Formulae 
Nonlinear graphs 

Rearrange algebraic expressions 
Rearrange algebraic expressions by: i collecting like terms, for example , , ii expanding brackets, for example , , iii extracting common factors from expressions like and

Algebraic expressions 
Topic area 
Content 
Nuffield resource 
Areas under graphs (4 hours) 
Calculate estimates of areas under graphs and understand their physical significance (if any) using the formula for the area of a trapezium (and triangle if necessary). 
Speed and distance 
Rearrange formulae 
Include examples such as: · to give if · to give if or · to give if

Goldfish bowl: rearrange formulae 
Line and curve fitting 
Recognise the main features of the data and graphs of:
· direct proportional ( ) and linear · quadratic models of the form Recognise the graphs of inverse proportional models Use the gradient and intercept of a straight line fitted to data to find an algebraic statement for it. Understand when it is appropriate or not to use a particular function to model data by consideration of intercepts, long term behaviour etc. in real world terms. Find a function to fit data using substitution of values into a given expression for the model

Match linear functions and graphs 
Modelling a test drive 

Boyle’s Law (assignment) 

Shoot (assignment) 

Experiments 
Topic area 
Content 
Nuffield resource 
Solve equations 
Using graphs · to determine a value of when you know
· to solve equations involving functions of the form , , , ,
Using algebra
· to form and solve exactly equations where the unknown appears in two terms, each of the same power such as

Quadratic factors and graphs 
Solve simultaneous equations 
Find the approximate solution of linear simultaneous equations by finding the point of intersection of two straight lines. Form and solve pairs of linear simultaneous equations by an algebraic method and interpret solutions geometrically when appropriate.

Plumbers’ prices 
Circuit boards (assignment) 

Solve quadratic equations 
Form and solve quadratic equations of the form
by · factorising with · using the formula

Factor cards 
Quadratic formula 

Road tunnel 

Revision 
Revise topics and try past papers. Discuss data sheet – make up and try questions based on it. 

Page last updated on 20 February 2012