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 non-calculator 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 / two-way 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
• F-angles - Corresponding angles
• Z-angles - Alternate angels are equal
• C-angles - 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

• 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 co-ordinates in all quadrants, know where the origin is and give its co-ordinates
• Calculate the mid-point of two points (given as co-ordinates)
• 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 mid-interval 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 right-angled 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 right-angled triangles in diagrams, in particular half of isosceles triangles, angle in a semi circle, rhombus)
• Calculate the distance between two points (given as co-ordinates)

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 gradient-intercept 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 cover-up 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 x-axis
• given the co-ordinates 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 right-angled 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 n-sided regular polygon
• Identify lines of symmetry of regular polygons and know the an n-sided regular polygon has n lines of symmetry
• Identify rotational symmetries and know that an n-sided 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 x²+bx+c
• Solve quadratic equations of the type x²+bx+c=0 by factorising, including where rearrangement is required first
• Factorise difference of two squares and recognise the pattern x²-a²
• 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: