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This is a list of objectives that should have been achieved after studying each chapter of the book.
Additional objectives added to ensure full coverage of the syllabus will
be covered in class. Objectives that are covered in the book but aren't required for your syllabus
are shown in this colour. You can use this list as a revision checklist.
The syllabus for this course is available from the AQA website
http://www.aqa.org.uk/qual/gcse/math_b.html
Stage 1
Perimeters
 Calculate the perimeter of simple shapes, including those with missing side lengths.
 Calculate the circumference of a circle when given the radius or diameter
 Calculate the radius or diameter of a circle when given the circumference
 Calculate the length of arcs of circles
 Calculate the perimeter of shapes involving curved sections
Fact Sheet 1: Fractions, Decimals and Percentages
 Cancel fractions, form equivalent fractions, order fractions
 Convert between improper fractions and mixed numbers
 Enter, manipulate and use fractions with a calculator
 Convert between fractions, decimals and percentages and order by size.
 Writing a number as a fraction or percentage of another
Number 1
 Solve problems using fractions, decimals and percentages
 Use noncalculator methods for calculating
 Make estimates by approximating numbers to 1 significant figure
 Add and subtract fractions without a calculator
Probability
 Use correct vocabulary
 Identify probabilities on a probability scale
 List all possible outcomes for an event using a systematic method
 List all possible outcomes for a combination of events, again using a systematic method
 Use a probability space / twoway table
 Calculate probabilities using equally likely outcomes
 Know the meaning of mutually exclusive
 Know that the sum of probabilities of mutually exclusive events is 1
 know that the prob of event not occurring is 1  prob of event occurring
 Use the "or" rule for mutually exclusive events
 Use relative frequency to estimate probabilities
 Use relative frequency to calculate the expected number of a particular outcome
 Estimate probabilities using suitable methods: equally likely outcomes, relative frequency, historical evidence
Fact Sheet 2: The language and Shorthand of Algebra
 Understand and use correct vocabulary for algebra
 Use negative numbers with the four operations, add, subtract, multiply and divide
 Input negative numbers in to a calculator
 Understand the shorthand notation used with algebra
Algebra 1
 Form algebraic expressions from a given situation
 Simplify algebraic expressions by collecting like terms
 Substitute numbers into expressions and evaluate
 Construct formulae
 Substitute numbers into formula
 Construct equations
 Solve linear equations where the unknown is on one side
Fact Sheet 3: The language of geometry
 Measure and draw angles
 Identify types of angles
 Know and work with the different labelling conventions for angles
 Perpendicular and parallel lines
 Know the names of polygons
 Label the type of angle in a polygon  interior and exterior
 Be able to label and use the properties of special triangles and special quadrilaterals
Geometry 1
 Angle facts on straight lines and at a point
 Angles on a straight line add up to 180 degrees
 Angles at a point add up to 360 degrees
 Vertically opposite angles are equal
 Angle facts on parallel lines
 Fangles  Corresponding angles
 Zangles  Alternate angels are equal
 Cangles  Interior angles on parallel lines add up to 180 degrees
 Triangles and quadrilaterals
 The interior angles of a triangle add up to 180 degrees
 An exterior angle of a triangle is equal to the sum of the interior opposite angles
 The interior angles of a quadrilateral add up to 360 degrees
 Construct accurate diagrams using a rule and compass
Fact Sheet 4: The language of graphs check with revision checklist
 Construct axes suitable for drawing a graph, ie consistent scale, large enough, etc
 Know that the independent variable is usually the horizontal axis and the dependant variable the vertical axis
 Plot coordinates in all quadrants, know where the origin is and give its coordinates
 Calculate the midpoint of two points (given as coordinates)
 Recognise the general shapes of graphs of linear, quadratic, cubic an reciprocal functions
Linear graphs 1
 Know that a graph represents the relationship between two variables
 Make a table of values
 Draw a line graph by plotting 3 suitable points
 Know the equations of graphs of horizontal and vertical lines and be able to plot them
 Use graphs in practical situations, eg. currency conversion
Area and volume 1
 Know that area is a measure of surface
 Know that area is measured in square units
 Know that measurements must be in the same units before calculating area
 Calculate the area of a rectangle and square
 Calculate the area of composite by breaking them into regular shapes
 Calculate side length of a square when area is known, and an unknown side length of a rectangle when the area and one side length is known
 Calculate the area of a triangle
 Calculate the area of a circle
 Calculate the area of a sector
 Know that the volume of a solid shape is the amount of space it occupies
 Calculate the volume of a cube and cuboid
 Calculate the surface area of a cuboid
 Draw the net of a solid shape
 Represent a solid object on isometric paper when given a net or orthographic views
Transformations 1
 Know and use accurately the terminology object, image, map, displacement, congruent
 Translation
 Know the properties of a translation. (position changes, what properties stay the same (are invariant), object and image are congruent)
 Describe a translation using a column vector
 Perform a translation
 Reflection
 Describe the preserved properties of a reflection
 Know the properties of a reflection
 Perform a reflection
 Describe fully a reflection
 Rotation
 Describe the preserved properties of a rotation
 Know the properties of a rotation
 Perform a rotation
 Describe fully a rotation
 Enlargement
 Describe the preserved properties of an enlargement
 Know the properties of an enlargement
 Perform an enlargement
 Describe fully an enlargement
Fact Sheet 5: The language of data handling
 Know that data can be classified into descriptive and numerical and numerical data are either discrete of continuous
 Identify methods for collecting data
 Construct and evaluate questionnaires for collecting data
 Use a variety of methods for displaying data including frequency tables, bar charts, comparative bar charts, histograms, line graphs, pie charts, histograms
Data handling
 Draw statistical diagrams including bar charts, histograms, pie charts and line graphs
 Interpret statistical diagrams
 Calculate the three averages: mean, median, mode
 Know properties of each average
 Range
 Use statistical measures (mean, median, mode, range) to compare data sets
 Know that a scatter diagram can be used to compare bivariate data
 Plot a scatter diagram
 Draw a line of best fit
 Use terminology positive / negative correlation
Stage 2
Fact Sheet 6: The language of Number
 Define integer, multiple, common multiple, lowest common multiple, factor, common factor, highest common factor, prime number, prime factor.
 Use square and square root keys on a calculator, cube and cube root
 Understand the meaning of square / cube root as the reverse of squaring / cubing and as the number multiplied by itself 2/4 times to obtain the number started with
 Use index numbers for repeated multiplication
 Decompose a number into a product of its primes
 Use the reciprocal function
Number 2
 use square and cube numbers in problems
 Round to significant figures
 Form equivalent ratios and cancel ratios to their lowest form
 Write ratios in the form 1:x, x:1
 Share out a quantity in a given ratio (Proportional division)
 Find a missing amount in a ratio: Multiple, Unitary, Algebraic methods
 Direct proportion and relate it to a graph with no intercept
 Calculate the scale factor of enlargement
 Use ratios in enlargements and map scales
Algebra 2
 Expand brackets
 Evaluate formula containing brackets
 Solve linear equations with unknowns on both sides
 Solve linear equations requiring prior removal of brackets
 Represent inequalities on a number line
 Solve linear inequalities (inc. multiplying or dividing by a negative number)
Geometry 2
 Use three figure bearings to describe location, find the bearing of A from B, plot a point B on a given distance and bearing from a point A
 Constructions using a ruler (unmarked) and compass
 Perpendicular bisector of a straight line
 Bisector of an angle
 Parallel line
 the perpendicular from a point to a line
 Loci  mark out the locus of
 a point that is a constant distance from a fixed point
 a point that is equidistant from two fixed points
 a point that is equidistant from two intersecting straight lines
 combinations of the above rules
Data Handling 2
 Know and use the formula for the mean of raw data
 Calculate the mean for data given in a frequency table
 Estimate the mean of grouped data
 Find midinterval values for discrete and continuous data (pg 244, Crawshaw)
 Construct a frequency polygon for data with equal class intervals
 Identify a modal class
Algebra 3
 Find the HCF of an algebraic expression
 Factorise an expression by taking the HCF outside of a bracket. Check by multiplying out the bracket.
 Substitute into a formula (involving powers and square roots) and evaluate
 Rearrange formulae, including formulae involving squares and square roots including cases where the subject occurs twice or where a power of the subject occurs
 Linear sequences
Area and Volume 2
 Calculate the area of a parallelogram
 Calculate the area of a trapezium
 Know that prisms have a constant cross section
 Calculate the volume of a prism
 Calculate the volume of a cylinder
 Calculate the surface area of solids
Transformations 2
 Find the centre and angle of rotation by construction methods when necessary.
 Compound transformations  perform a compound transformation, define a compound transformation and determine whether the effect of a compound transformation can be obtained from a single transformation. (use the yr9 end of year exam question i wrote for this)
Pythagoras' Rule
 Recall Pythagoras' theorem and know that it only applies to rightangled triangles
 Identify right angled triangles using Pythagoras' theorem
 Find the length of the hypotenuse
 Find the length of one of the shorter sides
 Use Pythagoras' theorem to 'problem type' questions
 Be able to spot rightangled triangles in diagrams, in particular half of isosceles triangles, angle in a semi circle, rhombus)
 Calculate the distance between two points (given as coordinates)
Linear Graphs 2
 Calculate the gradient of straight line segments
 Know that parallel lines have the same gradient
 Know the the gradient is the rate of change of one variable with respect to another. (Go up m units for every 1 unit across)
 Speed, distance and time.  Compound measures
 Use the gradientintercept form of the equation of a line
 Know that line graphs represent a linear relationship between two numbers
 Know the effect of scale changes on the overall look of a linear graph
 Draw graphs of straight lines without plotting three values (use y=mx+c or coverup method)
 Sketch graphs given in y=mx+c form (and rearrange to y=mx+c if necessary)
 Recognise a linear relationship from a table
 determine the solution of a linear equation from a graph  ie where it cross the xaxis
 given the coordinates of two points, determine the euqation of the line passing through them
Simultaneous Linear equations
 Solve simultaneous linear equations graphically
 Solve using substitution
 Solve using elimination, including where both equations need to be multiplied
Trigonometry
 Know that the trigonometric functions give the ratios of side length of triangles
 Label hypotenuse, opposite and adjacent
 Recall the trig formulae / definitions
 Use a calculator to find the values of the trig ratios
 Use trig ratios to find missing lengths (in right angled triangles)
 Use trig ratios to find missing angles
 Be able to spot rightangled triangles in diagrams, in particular half of isosceles triangles, angle in a semi circle, rhombus)
 use trig to solve 'problem' questions
Quadratics 1
 Multiply out two brackets, and recognise (a+b)^{2} as a question of this type
 Draw graphs of quadratic equations
 Solve quadratic (and other)equations using graphs
 Solve quadratic equations using trial and improvement to a given
number of (n) decimal places and know how to terminate correctly
(either halve interval differing by 1 in the n^{th} decimal place or by determine closest)
Geometry 3
 Calculate the sum of the interior angles of a polygon by splitting into triangles
 Calculate the interior angle of a regular polygon
 Know that the exterior angles of a polygon sum to 360 degrees (the book has a justification, maybe give proof too)
 Hence calculate the exterior angle of an nsided regular polygon
 Identify lines of symmetry of regular polygons and know the an nsided regular polygon has n lines of symmetry
 Identify rotational symmetries and know that an nsided regular polygon has rotational symmetry of order n
 Tessellations determine whether shapes can tessellate by considering the interior angles at a vertex
Stage 3
Number 3
 Simplify and evaluate indices for numbers and algebra. Use a calculator to calculate powers of numbers. Including negative powers
 Standard form: write large and small numbers in standard form
 Standard form on a calculator
 Calculate Percentages  profit / loss
 Percentage error
 Increase / decrease by a percentage
 Compound percentages
 Reverse percentages
 Multiplying and dividing fractions (change mixed numbers to improper fractions)
Data handling 3
 Calculate the probability of combined events using or and and rules
 Draw and use tree diagrams to calculate the probabilities of combined events
 Calculate the median for and odd or even number of pieces of data.
 Estimate quartiles from a cf diagram
 Find the upper and lower quartile values
 Construct a box plot and compare box plots
 Interquartile range. Know that it gives the range of the middle 50% of the values
 Cumulative frequency
 Compare two cumulative frequency distributions
Quadratics 2
 Factorise quadratics of the type x^{2}+bx+c
 Solve quadratic equations of the type x^{2}+bx+c=0 by factorising, including where rearrangement is required first
 Factorise difference of two squares and recognise the pattern x^{2}a^{2}
 Quadratic sequences  generate terms of, find n^{th} term of, construct formula for n^{th} term of one
Further shape and space
 Dimension analysis  determine whether a given expression could represent a length, area, volume, none,
 Similar shapes  identify by using properties of, find missing length and angles
 Similar triangles  know the properties of, use properties in questions, find missing lengths in,
 Solve mixed problems requiring the use of Pythagoras' theorem, trigonometry and similar shapes
Algebra 4
 Solve quadratic inequalities
 Represent inequalities in two variables as regions on a graph. Linear programming.
 Solve cubic equations by trial and improvement
 Draw cubic and reciprocal graphs
 Sketch standard graphs
 Use graphs to model real life graphs
You must also be able to:
stem and leaf
(extracted from syllabus but not covered in the book or at least not listed in the above objectives)
noncalculator methods
understand how errors are compounded in certain calculations
present and interpret solutions in the context of the original problem
understand the difference between a practical demonstration and a proof
know the meaning of and use the words ‘equation’, ‘formula’, ‘identity’ and ‘expression’
change the subject of a formula, including cases where the subject occurs twice
distinguish between practical demonstrations and proofs
distinguish between lines and line segments; use
parallel lines, alternate angles and corresponding
angles, understand the consequent properties of
parallelograms and a proof that the angle sum of a
triangle is 180 degrees; understand a proof that the
exterior angle of a triangle is equal to the sum of the
interior angles at the other two vertices
recall the definition of a circle and the meaning of
related terms, including centre, radius, chord,
diameter, circumference, tangent, arc, sector and
segment; understand that the tangent at any
point on a circle is perpendicular to the radius at
that point; understand and use the fact that
tangents from an external point are equal in
length; explain why the perpendicular from the
centre to a chord bisects the chord; understand
that inscribed regular polygons can be constructed
by equal division of a circle; use the facts that the
angle subtended by an arc at the centre of a
circle is twice the angle subtended at any point
on the circumference, the angle subtended at
the circumference by a semicircle is a right
angle, that angles in the same segment are
equal, and that opposite angles of a cyclic
quadrilateral sum to 180 degrees
understand and use vector notation
recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction
distinguish between
fractions with denominators that have only
prime factors of 2 and 5 (which are represented
by terminating decimals), and other fractions
(which are represented by recurring decimals)
understand and use unit fractions as multiplicative
inverses [for example, by thinking of multiplication
by 1/5 as division by 5; or multiplication by 6/7 as
multiplication by 6 followed by division by 7 (or vice
versa)], multiply and divide a given fraction by an
integer, by a unit fraction and by a general fraction
understand the
multiplicative nature of percentages as operators
[for example, a 15% increase in value Y, followed by
a 15% decrease is calculated as 1.15 × 0.85 × Y]
recall integer squares from 2 × 2 to 15 × 15 and the
corresponding square roots, the cubes of 2, 3, 4, 5
and 10
develop a range of strategies for mental calculation
recognisning that, in many cases, only a fraction can express the exact answer (add this to the fractions objs)
use surds and pi in exact calculations, without a calculator
use calculators effectively and efficiently; know how
to enter complex calculations; use an extended
range of function keys, including
trigonometrical and statistical functions relevant
across this programme of study
know not to round during the intermediate steps of a calculation
check and estimate answers to problems; select and
justify appropriate degrees of accuracy for answers to
problems; recognise limitations on the accuracy of
data and measurements
box plots
moving averages
use statistical functions on a calculator
know that zero correlation does not necessarily imply "no relationship" but merely "no linear relationship"
understand the increasing sample size will generally lead to better estimate s of probabilities and population parameters
interpret a wide range of graphs and diagrams and draw conclusions; identify seasonality and trends in time series
look at data to find patterns and exceptions

The Lessons
Perimeters
Number 1
Probability
Algebra 1
Geometry 1
Linear Graphs 1
Area and Volume 1
Transformations 1
Data Handling
Number 2
Algebra 2
Geometry 2
Data Handling 2
Algebra 3
Area and Volume 2
Transformations 2
Pythagoras' Theorem
Linear Graphs 2
Simultaneous Equations
Trigonometry
Quadratics 1
Geometry 3
Number 3
Data Handling 3
Quadratics 2
Furhter Shape and Space
Algebra 4
