Secondary maths tutoring programmes

Partitioning numbers up to 10,000,000

Knowing the value of each digit in numbers with up to 3 decimal places

Comparing and ordering numbers with up to 3 decimal places

Multiplying and dividing whole numbers and decimals by 10 and 100

Rounding numbers to 2 decimal places

Using a number line to calculate across zero

Using mental methods to add and subtract whole numbers and decimals

Adding whole numbers and decimals using the column method

Subtracting whole numbers and decimals using the column method

Finding prime numbers

Finding square numbers

Using mental strategies to multiply

Using mental strategies to divide

Multiplying using short multiplication

Dividing using short division with exchange

Finding equivalent fractions

Simplifying fractions by finding common factors

Adding and subtracting fractions including mixed numbers

Finding percentages of amounts

Finding factors

Finding common multiples

Simplifying fractions

Writing simple fractions as decimals

Adding and subtracting fractions with different denominators

Using fractions to solve problems

Finding percentages of an amount

Using symbols and letters for unknown amounts

Using simple formulas

Solving one-step equations

Using ratio language and symbol

Making and describing linear sequences

Finding missing angles on a straight line

Multiplying and dividing whole numbers and decimals by 10, 100, 1,000

Using the bar model to solve multi-step problems 

Finding missing angles around a point

Find fraction of an amount (f(proper)xf(proper) or f(proper)xi)

Convert between mixed and improper fractions

Comparing and ordering fractions

Dividing fractions by whole numbers

Prime Factor Decomposition

Adding and subtracting fractions including mixed numbers

Writing percentages as fractions and decimals

Multiplying a decimal by a decimal

Finding the nth term of arithmetic sequences

Working with square numbers

Cubing and cube rooting numbers

Understanding Prime Numbers

Multiplying Fractions

Dividing fractions

Calculating the area of triangles

Rounding to significant figures

Calculating the area of parallelograms

Calculating the volume of cubes and cuboids

Adjusting numbers into standard form

Identifying the Upper and Lower bounds of a rounded value

Factorising Quadratics in the form ax^2 + bx+ c

Factorising Using the Difference of Two Squares

Finding the nth term of quadratic sequences in the Form n^2 + bn + c

Finding the nth term of quadratic sequences in the Form an^2 + bn + c

Recurring Decimals – One or More Repeating Digit

Expanding Triple Brackets

Expanding Triple Brackets involving powers

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

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

Identifying Types of Number

Understanding Fractions

Working with Powers, Squares, Cubes and Roots

Calculating with Negative Numbers

Identifying Coordinates and Midpoints

Working with Sequences

Identifying Properties of 2D and 3D shapes

Performing Transformations of Shapes

Simplifying and Collecting Like Terms

Drawing and Interpreting Charts and Tables

Converting between Measures

Calculating Averages and Range

Working with Probabilities

Calculating with Fractions

Rounding Values

Finding the HCF and LCM using listing methods

Calculating Percentages

Finding Area and Circumference of Circles

Working with Substitution

Solving Linear Equations

Calculating with Fractions in Context

Working with Fractions, Decimals and Percentages

Drawing a Linear Graph from a Table of Values

Drawing and Interpreting Scatter Graphs

Expanding and Factorising Single Brackets

Simplifying and Collecting Like Terms

Drawing and Interpreting Charts and Tables

Converting between Measures

Calculating Averages and Range

Working with Probabilities

Calculating with Fractions

Rounding Values

Finding the HCF and LCM using listing methods

Calculating Percentages

Finding Area and Circumference of Circles

Working with Substitution

Solving Linear Equations

Calculating with Fractions in Context

Working with Fractions, Decimals and Percentages

Drawing a Linear Graph from a Table of Values

Drawing and Interpreting Scatter Graphs

Expanding and Factorising Single Brackets

Using Pythagoras’ Theorem

Using Index Laws

Finding Angles in Parallel Lines

Working with Inequalities

Working with Prime Factorisation

Working with Arithmetic Sequences

Calculating Probability

Solving Area and Perimeter Problems

Calculating Volume

Calculating Surface Area

Working with Ratio

Expanding Double Brackets

Calculating Averages from Tables

Calculating with Compound Measures

Estimating

Factorising Quadratics

Drawing and Interpreting Scatter Graphs

Expanding and Factorising Single Brackets

Pythagoras’ Theorem

Index Laws

Angles in Parallel Lines

Working with Inequalities

Prime Factorisation

Arithmetic Sequences

Calculating Probability

Solving Area and Perimeter Problems

Calculating Volume

Calculating Surface Area

Working with Ratio

Expanding Double Brackets

Calculating Averages from Tables

Compound Measures

Estimating

Factorising Quadratics (coefficient equal to 1)

Working with Standard Form

Working with y = mx + c

Applying Pythagoras’ Theorem

Trigonometry: Using SOHCAHTOA

Forming and Solving Linear Equations

Solving Linear Simultaneous Equations

Calculating Compound Interest and Depreciation

Finding Angles in Polygons

Calculating with Reverse Percentages

Finding Probabilities using Tree Diagrams

Venn Diagrams

Drawing a Non-Linear Graph from a Table of Values

Calculating Average Speed and Density.

Angles in Parallel Lines

Calculating Averages from Tables

Compound Measures

Estimating

Factorising Quadratics (Coefficient Equal to 1)

Working with y = mx + c

Applying Pythagoras’ Theorem

Trigonometry: Using SOHCAHTOA

Forming and Solving Linear Equations

Solving Linear Simultaneous Equations

Calculating Compound Interest and Depreciation

Finding Angles in Polygons

Calculating with Reverse Percentages

Finding Probabilities Using Tree Diagrams

Venn Diagrams

Drawing a Non-Linear Graph from a Table of Values

Calculating Average Speed and Density

Combining and Subdividing Ratios

Factorising Quadratics (coefficient not equal to 1)

Identifying Parallel and Perpendicular Lines

Finding Arc Lengths and Area of Sectors

Finding the Nth Term of a Quadratic Sequence

Converting Recurring Decimals to Fractions

Using the Product Rule for Counting

Expanding Triple Brackets

Working with Similar Shapes

Using Cumulative Frequency and Box Plots

Using Negative and Fractional Indices

Rearranging Formulae

Using Direct and Inverse Proportion

Applying the Capture-Recapture Method

Calculating Average Speed and Density

Combining and Subdividing Ratios

Factorising Quadratics (Coefficient Not Equal to 1)

Identifying Parallel and Perpendicular Lines

Finding Arc Lengths and Area of Sectors

Finding the nth term of a Quadratic Sequence

Converting Recurring Decimals to Fractions

Using the Product Rule for Counting

Expanding Triple Brackets

Working with Similar Shapes

Using Cumulative Frequency and Box Plots

Using Negative and Fractional Indices

Rearranging Formulae

Using Direct and Inverse Proportion

Applying the Capture-Recapture Method

Simplifying Algebraic Fractions

Completing the Square

Using Circle Theorems

Simplifying Surds

Working with Spheres and Cones

Drawing and Reading from Histograms

Working with Vector Geometry

Using Function Notation

Working with Upper and Lower Bounds

Applying Transformations of Functions

Comparing numbers up to 10,000

Rounding numbers to the nearest 10

Finding factors

Finding common multiples

Multiplying 2-digit numbers using the area model

Dividing using short division with exchange

Adding decimals using the column method

Subtracting decimals using the column method

Simplifying fractions

Writing simple fractions as decimals

Adding and subtracting fractions with different denominators

Using fractions to solve problems

Finding percentages of an amount

Using symbols and letters for unknown amounts

Using simple formulas

Solving one-step equations

Using ratio language and symbol

Making and describing linear sequences

Finding missing angles on a straight line

Knowing the value of each digit in numbers up to 10,000,000

Using the number line with decimal values

Rounding numbers to 2 decimal places

Multiplying and dividing whole numbers and decimals by 10, 100, 1,000

Finding the lowest common multiple using listing

Finding the highest common factor using listing

Finding equivalent fractions.

Solving problems using the order of operations.

Probability Scales

Change the subject of a formula – Simple One-step equations

Express one quantity as a fraction of another

Constructing angles with a protractor

Form algebraic expressions given information in words

Form algebraic expressions

Use 4 operations with algebra

Using the bar model to solve multi-step problems

One and two step function machines

Work out inputs and outputs of a functions machine.

Work out missing operations given a function machine.

Work with algebraic expressions as input or output of a function machine.

Derive rules for patterns and be able to work out consecutive patterns.

Find missing terms in the middle or start of a sequence.

Angles around a point add to 360

Know the different types of angles and descriptors

Label and identify parts of a circle

Perimeter of squares and rectangles

Area of squares and rectangles

Solving measure problems involving reading scales

Writing decimals as fractions and percentages

Ordering FDPs

Working out quantities using FDP

Use estimation to check answers to calculations

Find fraction of an amount (f(proper)xf(proper) or f(proper)xi)

Addition and subtraction of fractions with common denominator

Convert between mixed and improper fractions

Comparing and ordering fractions

Dividing fractions by whole numbers

Fractions of Time (1/2 hour = 30 mins)

Develop full understanding of the order of operations

Comparing and ordering numbers with up to 3 decimal places

Finding and estimating the position of decimals on a number line

Ordering numbers up to 10,000,000

List numbers that could be rounded to a given accuracy.

Represent percentages in diagrams

Increasing and decreasing by percentages by finding the amount and adding on/subtracting

Understanding Tally Charts

Understanding Pictograms

Prime Factorisation

Adding and subtracting fractions including mixed numbers.

Writing percentages as fractions and decimals.

Finding percentages of amounts without using a calculator.

Sharing in Ratio.

Multiplying using long multiplication.

Dividing a number and writing the remainder as a fraction or decimal (incl. recurrance)

Multiplying a decimal by a decimal.

Simplifying an expression by collecting like terms.

Substituting into expressions.

Finding the nth term of arithmetic sequences.

Solving two-step equations involving fractions.

Finding missing angles

Adding or subtracting a negative number

Multiplying and dividing directed numbers

Working with square numbers

Defining and finding square roots

Cubing and cube rooting numbers

Reading, writing and evaluating powers

Understanding Prime Numbers

Finding prime factors

Multiplying Fractions

Dividing fractions

Writing the equation of a line parallel to the x-axis or y-axis

Area of triangles

Change the subject of a formula – Simple Two-step equations

Solve two step equations with negative x e.g. 3 – x = 10 or 3 – x = 1

Write integer solutions to bounded inequalities

Inequalities on a number line

Angles on a straight line at a point add to 180

Vertically opposite angles are equal

Work in real life context with area and perimeter

Converting between miles and kilometres

Solving area and perimeter problems

Solving problems involving time tables

Be able to find the surface area of basic 3D shapes

Be able to work with surface area in real life context

Work with volume in real life context

Plans and elevations of cube structures

Plans and elevations of standard 3D shapes

Dividing using short division giving remainders as decimals

Multiplying decimals using powers of 10

Solving mixed multiplication and division problems

Fraction of amounts where the fraction is improper or mixed

Mixed number of an amount

Problems involving fractional increase/decrease.

Finding common factors

Be able to recognize multiples, factors, square and cube numbers, prime numbers, powers and roots.

Using a calculator

Simplify ratio

Write ratios in the form 1:n

Find limiting factors to a given recipe

Use proportion to find any given amount needed to make a quantity.

Understanding Bar Charts (single, dual and composite)

Understanding Line graphs

Use a set of instructions to complete a sample space diagram

Interpret sample space diagrams given some parameters

Applying the order of operations to multi-step calculations

Simplify a more complex expression by collecting like terms

Expanding a single bracket

Factorise an algebraic expression by taking out common factors

Rounding to significant figures

Working with metric units of length

Area of parallelograms

Working with metric units of mass and capacity

Calculating the volume of cubes and cuboids

Averages and range – Finding the Mode

Averages and range – Finding the Median

Averages and range – Finding the Mean

Averages and range – Finding the Range

Substitute positive and negative numbers into formulae

Calculating with ratios and fractions

Using multipliers to solve direct proportion problems

Solving equations with negative solutions

Solving equations with the unknown on both sides

Constructing Triangles SSS

Constructing Triangles ASA

Constructing Triangles SAS

Understand and use a frequency tree

Use frequency trees to state probabilities

Using a frequency tree to work with a wider problem

Solve fractional equations involving one variable on one side

Solve simultaneous equations graphically

Find missing lengths given the area of quadrilaterals

Find missing lengths given the perimeter of quadrilaterals

Find lengths given the surface area or volume

Fractions to Recurring Decimals

Comparing fractions of amounts (best buy, area etc)

Finding percentages of amounts

Convert ratio to fraction and percentage.

Work with ratio given a difference

Work with ratio given a part

Best Buy

Use listing strategies to find total number of combinations for a given problem

Write a probability given the listed outcomes

Using prime factorisation to find the Highest Common Factor

Using prime factorisation to find the Lowest Common Multiple

Hard Function machines including roots

Form expressions and equations from both worded and geometric problems including angle problems, perimeter, area etc.

Expand a single bracket – a(bx+-c) where a>0 and a<0

Expand a single bracket – ax^d(bx+-c) where a>0 and a<0

Expand a single bracket – a(bx+-c)+-d(ex+f)

Expanding double brackets

Substituting into tables

Substituting into geometric representations and tables

Substitution to find an expression given another expression. EG: x + y = 6 find 3x + 3y

solving basic linear inequalities

Describing inequality solutions sets using a number line – bounded

Describing inequality solutions sets using a number line – unbounded

Solving Simultaneous Equations by elimination (positive and negative coefficients)

Types of Sequence: Arithmetic, Geometric and Fibonacci sequences

Using the nth term to identify if a number is in a sequence

Solving problems in pattern sequences

Finding the nth term of arithmetic sequences – Increasing

Finding the nth term of arithmetic sequences – decreasing (including a-bn)

Finding the nth term of arithmetic sequences – fractional and decimal

Geometric sequences

Use Fibonacci rule with numbers and algebra

Understanding and applying the Index Laws for multiplication

Understanding and applying the Index Laws for division

Understanding and applying the Index Laws for Powers

Changing the subject of a formula – Area, Perimeter, Surface Area and Volume

Changing the subject of a formula – SUVAT

Change the subject of a formula – multi-step formulae involving powers and roots

Changing the subject of a formula – Other formulae: Pythagoras’ Theorem, y=mx+c

Using coordinates to solve problems

Combining properties of quadrilaterals with coordinates and symmetry with y=a or x=b

Finding the midpoint between two coordinates

Evaluating if a given point is on a line

Given an equation not in the form y = mx+c, be able to rearrange and find the gradient and y-intercept

Sketching Graphs and recognising characteristics – linear

Working with y=x+a and y=-x+a

Parallel lines

Conversion graphs – plot identify values, extrapolate, comparisons

Write error intervals given an accuracy of rounding including lengths and area

Estimating the answer to a calculation by rounding to 1 significant figure

Estimation with money

Using Standard Form to write Large Numbers

Using Standard Form to write Small Numbers

Calculating with Mixed Numbers

Dividing an integer by a decimal

Writing a value as a percentage of another

Increasing and decreasing by percentages using multipliers

Calculating a percentage change

Work with ratio given a part or a difference

Calculate speed from a distance time graph

Calculating the area of a trapezium

Calculating the Circumference

Finding the area of circles

Finding the area of compound shapes – L-shapes

Finding the area of compound shapes – Including Pythagoras

Finding the area of compound shapes – Regular Polygons and Nets

Finding the area of compound shapes – Cut outs and shaded regions

Solving Area and Perimeter Problems – Reverse Area and Perimeter

Solving Area and Perimeter Problems – Patterns and compound

Finding a longest side of a right-angled triangle using Pythagoras’ theorem

Finding a short side of a right-angled triangle using Pythagoras’ theorem

Reflecting on a coordinate grid

Describing reflections on a coordinate grid

Rotating on a coordinate grid

Describing rotations on a coordinate grid

Translating on a coordinate grid

Describing translations on a coordinate grid

Enlarging on a coordinate grid – Enlarge shapes given a positive scale factor

Describing enlargements on a coordinate grid

Invariant points

Use ratio, fraction of amount and algebra to find missing angle values.

Interior angles of polygons – Irregular

Interior angles of polygons – Regular

Exterior angles of polygons

Calculating the number of sides of a regular polygon from an angle

Angle sum of polygons

Know the correct terminology and types of angles in parallel lines

Finding angles in parallel lines

Identify bearings from a given point

Use bearings to draw on maps and find missing locations.

Finding missing lengths of similar shapes (basic)

Finding missing lengths of similar triangles

SOHCAHTOA – missing angles

SOHCAHTOA – missing sides

Draw simple vector resultants

Writing a resultant to two or more vector movements e.g. Given A and B, Find 2A + 3B

Probability of mutually exclusive events, P(not A)

Completing two-way tables

Interpreting two-way tables

Mode from a frequency table

Median from a frequency table

Mean from a frequency table

Range from a frequency table

Find missing numbers based on information given

Find missing values given the MMMR

Estimating the mean from a frequency table

Modal class from a grouped frequency table

Estimating the range from a grouped frequency table

Median class from a grouped frequency table

Given information find missing areas of a Venn diagram.

Scatter Graphs – Accurately draw and use a line of best fit for interpolation

Scatter Graphs – Know the three correlations and how to determine the strength of the correlation

Scatter Graphs – Plot values and identify outliers

Expand a single bracket – a(bx+-c) where a<0

Write answers for area and perimeter of circles and sectors in terms of π

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