Personalised Key Stage 4 maths tutoring to secure the essentials for GCSE

Adjusting numbers into standard form

Identifying the Upper and Lower bounds of a rounded value

Reverse Percentages – Calculating from a Difference

Reverse Percentages – from repeated percentage change

Average Speed and Density – Complex Problems

Ratio Problems – Subdividing Part of a Ratio

Ratio Problems – Subdividing a Whole Ratio

Factorising Quadratics (coefficient not equal to 1)

Factorising Quadratics (coefficient not equal to 1) – Difference of Two Squares

Parallel and Perpendicular Lines – Identifying Using y = mx + c

Finding Perpendicular Lines Through Points

Sectors – Finding a Missing Angle or Radius

Quadratic Sequences – Finding nth Terms in the Form n^2 + (bn) + c

Quadratic Sequences – Finding nth Terms in the Form an^2 + bn + c

Recurring Decimals – 1/2/3 repeated digits

Recurring Decimals – Calculating

Product Rule for Counting – One Item Per Set

Product Rule for Counting – More Than One Item Per Set

Product Rule for Counting – Selecting in Any Order

Triple Brackets – Expanding in the form (ax+b)(cx+d)(ex+f)

Triple Brackets – Expanding Raised to Powers

Triple Brackets – Expanding in Context

Using Negative Indices

Unit Fractional Indices

Indices – Non-unit Fractional Indices

Indices – Using Negative Fractional Indices with Integer Bases

Proportionality – Using Direct Proportion

Proportionality – Using Inverse Proportion

Algebraic Fractions – Simplifying by Factorising

Completing the Square – (x+b)^2+c

Completing the Square – solving simple quadratics

Surds – Simplifying Surds

Surds – Expanding Brackets with Surds

Surds – Rationalising Single term Denominators

Finding the Surface Area of Spheres

Finding the Volume of Spheres

Finding the Volume of Cones

Finding the Surface Area of Cones

Calculating with Column Vectors

Finding Routes using Vectors

Using Exact trig values

Solving Quadratics using the Formula

Using the Sine Rule to find Missing Sides

Using the Sine Rule to find Missing Angles

Pythagoras in 3D

Rearranging formulae involving factorising

Completing the Square – a(x+b)^2+c

Functions – Using Function Notation

Using the Cosine Rule to find Missing Sides

Using the Cosine Rule to find Missing Angles

Using 1/2abSinC to find the area of a triangle

Venn diagram set notation

Change the subject of a formula – formulae involving fractions

Adjusting numbers into standard form

Adding and subtracting numbers written in standard form

Multiplying and Dividing numbers written in standard form – Multiplying numbers written in standard form

Multiplying and Dividing numbers written in standard form – Dividing numbers written in standard form

Working on Mixed Index Law Problems (including zero index)

Factorising a quadratic expression into two brackets

Drawing graphs in the form y=mx+c

Finding gradients

Finding equations of straight lines in the form y=mx+c

Identifying the Upper and Lower bounds of a rounded value

Solving simple simultaneous equations by elimination

Calculating the volume of prisms

Finding the volume of cylinders

Generating a non-linear sequence from an nth term

Expanding Brackets (application e.g. perimeter and area)

Converting between metric units of area

Converting between metric units of volume

Compound interest

Compound depreciation

Reverse percentages – from original amounts

Finding the original given the fraction.

Solving inequalities with the unknown on both sides

Find missing terms in a sequence (algebraic)

Problems involving ratio and fraction of amount.

Area and Perimeter of semi circles and other sectors

Find arc lengths of sectors

Find area of sectors

Work fluently to find the area/arc, radius/diameter.

Finding the area of compound shapes – Cut outs and shaded regions (including circles and sectors)

Finding the equation of a line through 2 points (not y-intercept)

Calculating the distance between two points

Expand a double bracket – (ax+-b)(cx+-d) or (b+-ax)(d+-cx)

Factorise quadratic (x^2 coef =1) into two brackets and solve for when = 0.

Understand and be able to identify the roots of a quadratic graph

Understand and be able to identify the turning point of a quadratic graph

Use the graph to determine values for specific solutions. EXAMPLE: Find solutions for when x2 + 3x + 1 = 3

Draw a line at y = n and see where it intersect the curve; state the x coordinate.

Draw quadratic/cubic graphs given a table of values both non-calculator and calculator.

Sketching Graphs and recognising characteristics – quadratic

Sketching Graphs and recognising characteristics – cubic

Sketching Graphs and recognising characteristics – reciprocal

Sketching Graphs and recognising characteristics ALL

Solving Simultaneous Equations by elimination (no matching coefficients)

Forming and solving simultaneous equations from worded problems

Work with surface area in more complex scenarios.

Working with volume in more complex scenarios e.g. given a net

Flow rate

Reverse Volume of Cubes and Cuboids

Reverse Volume of Prisms

Enlarge shapes given a fractional scale factor.

Use parallel line rules to find missing bearings.

SOHCAHTOA – missing sides (harder)

Estimate using 1 significant figure Work with area, perimeter, volume to estimate calculations in context.

Estimating powers and roots

Problems involving fractional increase/decrease Interleave with best buy, area etc.

Choose and explain which statistic gives you the best information given a set of data.

Find missing frequencies given the mean/ estimated mean.

Understand how changes affect the MMMR.

Work out new mean dependent on new data or changing data.

Understand that the more trials the more accurate the probability.

Use experimental probability to scale to find estimates.

Work out the relative frequency based off number of times the outcome has arisen over total trials.

Finding scale factor and drawing pie charts when quantity is below and above 360.

Interpreting pie charts given a part or difference using angle proportion.

Using a tree diagram to represent outcomes of events.

Combine two or more ratios

Compare best buy problems involving fractions and percentage discounts.

Identify movement and speed from a Distance time graph.

DMV problems when more than one material is compared and worked with.

Work with DMV when the volume might need to be found from a shape.

PFA problems

Work with PFA when the area might need to be found from a shape.

Algebraic Fractions – 4 operations with simple denominators and numerators

Finding Parallel Lines Through Points

Writing an error interval for truncated values

Reverse Percentages – Calculating from a Difference

Indicating regions on a coordinate axes from inequalities

Reverse Percentages – from repeated percentage change

Tree Diagrams – Selection Without Replacement

Tree Diagrams – Conditional Probability Problems

Venn Diagrams – Finding Probabilites

Venn Diagrams – Completing Two Sets

Venn Diagrams – Completing Three Sets

Average Speed and Density – Complex Problems

Ratio Problems – Subdividing Part of a Ratio

Ratio Problems – Subdividing a Whole Ratio

Factorising Quadratics (coefficient not equal to 1)

Factorising Quadratics (coefficient not equal to 1) – Difference of Two Squares

Parallel and Perpendicular Lines – Identifying Using y = mx + c

Parallel and Perpendicular Lines – Identifying Using Graphs

Finding Perpendicular Lines Through Points

Sectors – Finding a Missing Angle or Radius

Quadratic Sequences – Finding nth Terms in the Form n^2 + (bn) + c

Quadratic Sequences – Finding nth Terms in the Form an^2 + bn + c

Recurring Decimals – 1/2/3 repeated digits

Recurring Decimals – Calculating

Product Rule for Counting – One Item Per Set

Product Rule for Counting – More Than One Item Per Set

Product Rule for Counting – Selecting in Any Order

Triple Brackets – Expanding in the form (ax+b)(cx+d)(ex+f)

Triple Brackets – Expanding Raised to Powers

Triple Brackets – Expanding in Context

Similar Shapes – Areas and Volumes

Similar Shapes – Solving Problems in Context

Completing Cumulative Frequency Tables

Drawing Cumulative Frequency Graphs

Finding Quartiles and Median from Cumulative Frequency

Finding Quartiles from listed data

Drawing Box Plots from listed data

Comparing Box Plots of Two Data Sets

Using Negative Indices

Unit Fractional Indices

Indices – Non-unit Fractional Indices

Indices – Using Negative Fractional Indices with Integer Bases

Proportionality – Using Direct Proportion

Proportionality – Using Inverse Proportion

Capture-Recapture – Estimating the Total Population

Capture-Recapture – Finding Other Amounts

Algebraic Fractions – Simplifying by Factorising

Completing the Square – (x+b)^2+c

Completing the Square – solving simple quadratics

Circle Theorems – Angles In Segments and At The Centre

Circle Theorems – Semicircles and Cyclic Quadrilaterals

Surds – Simplifying Surds

Surds – Expanding Brackets with Surds

Surds – Rationalising Single term Denominators

Finding the Surface Area of Spheres

Finding the Volume of Spheres

Finding the Volume of Cones

Finding the Surface Area of Cones

Calculating with Column Vectors

Finding Routes using Vectors

Using Exact trig values

Solving Quadratics using the Formula

Using the Sine Rule to find Missing Sides

Using the Sine Rule to find Missing Angles

Pythagoras in 3D

Rearranging formulae involving factorising

Indices – Using Negative Fractional Indices with Fractional Bases

Indices – solving equations by changing the base

Proportionality – Combining Proportional Relationships

Algebraic Fractions – Simplifying a Multiplication or Division

Algebraic Fractions – Simplifying an Addition or Subtraction

Completing the Square – a(x+b)^2+c

Completing the Square – Turning Points

Circle Theorems – Tangents and Alternate Segments

Surds – Rationalising Multi-term Denominators

Spheres and Cones – Compound Solids

Volume of a Pyramid

Histograms – Frequency Density

Histograms – Finding Proportions

Vectors – Using Ratios

Functions – Using Function Notation

Functions – Evaluating Composite Functions

Functions – Expressions for Composite Functions

Functions – Expressions for Inverse Functions

Functions – Solving Problems with Inverse Functions

Lower and Upper Bounds – Addition and Multiplication

Lower and Upper Bounds – Subtraction and Division

Lower and Upper Bounds – using bounds to find a suitable approximation

Transformations of Functions – Vertical Translations

Transformations of Functions – Horizontal Translations

Transformations of Functions – Reflections

Using the Cosine Rule to find Missing Sides

Using the Cosine Rule to find Missing Angles

Using Sine and Cosine rules to solve Bearings Problems

Using 1/2abSinC to find the area of a triangle

Using an iterative formula to generate a sequence

Locating a root in an interval

Solving an equation using iteration

Trigonometry in 3D

Understanding the Sine Graph

Understanding the Cosine Graph

Understanding the Tan Graph

Transformations of the Sine and Cosine graphs

Algebraic Proof – Odd and Even

Algebraic Proof – Multiples

Proof of congruence

Quadratic Inequalities

Average rates of change

Instantaneous rates of change

Distance from a Speed-Time graph – uniform acceleration

Distance from a Speed-Time graph – variable acceleration

Understanding the equation of a circle centre (0,0)

Finding a tangent to a circle centre (0,0)

Finding a tangent to a circle centre (a,b) at a point (c,d)

Solving linear and non-linear simultaneous equations algebraically