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Variation Theory

Sequences and behaviour to enable mathematical thinking in the classroom - by Craig Barton @mrbartonmaths

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Tag: Limiting value of sequences

October 28, 2021 Craig BartonAlgebra, Sequences

Limiting value of sequences (pattern)

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October 28, 2021 Craig BartonAlgebra, Sequences

Limiting value of a sequence

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Pythagoras – Multiple Steps
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1/2absinC 3D shapes Adding algebraic fractions Adding and subtracting vectors Adding decimals Adding fractions Adding negative numbers Adding surds Algebraic fractions Algebraic indices Algebraic notation Algebraic proof Algebraic vocabulary Alternate angles Alternate segment theorem Angle at the centre Angle bisector Angle in a semi-circle Angles Angles at a point Angles in a polygon Angles in a triangle Angles in isosceles triangles Angles in the same segment Angles on a straight line Arc length Area of a circle Area of a parallelogram Area of a quadrilateral Area of a rectangle Area of a trapezium Area of a triangle Area scale factor Arithmetic Averages and range Bar modelling Base 2 Bearings BIDMAS Binary Binomial distribution Binomial expansion Bounds of error Box and whisker diagrams Brackets Bus-stop method Capture-Recapture Chain Rule Circle theorems Circumference of a circle Class width Co-interior angles Coefficients Collecting like terms Combined percentage change Combining ratio Completing the square Complex numbers Composite functions Compound interest Compound ratio Conjugates Constructions Conversion graphs Converting between 12 hours and 24 hours Converting decimals to percentages Converting fractions to decimals Converting fractions to percentages Converting percentages to decimals Converting percentages to fractions Converting ratio to fractions Converting to different bases Coordinates Correlation Corresponding angles Cosine rule Cube numbers Cube root Cumulative probabilities Cyclic quadrilaterals Definite integration de Moivre’s Theorem Denary Density Depreciation Difference of two squares Differential equations Differentiation Direct proportion Distributive law Dividing algebraic fractions Dividing decimals Dividing fractions Dividing negative numbers Dividing terms Drawing axes Enlargement Equation of a circle Equation of a straight line graph Equation of a tangent Equations from ratio Equivalent fractions Equivalent ratio Error intervals Estimating angles Estimation Exact trigonometric values Exchange rates Expand double brackets Expand single brackets Expand triple brackets Experimental probability Exponential function Exterior angles Factorise into a single bracket Factorise into double brackets Factorise into triple brackets Factors Factors multiples primes Factor theorem Finding one part of a ratio Forming expressions Fractional decrease Fractional increase Fractional indices Fraction decimal percentage equivalence Fractions Fractions of an amount Fractions on a number line Frequency Frequency density Frequency tree Function machines Function notation GCSE Revision Geometric sequences Gradient Group width Highest common factor Histograms Horizontal lines Hyperbolic functions Hypotenuse Imperial units Improper fractions Indices Inequalities on a number line Inequality notation Integration Interior angles Inverse functions Inverse operations Inverse proportion Isometric drawings Law of indices - division Law of indices - multiplication Law of indices - negatives Law of indices - powers Length of a line segment Length scale factor Limiting value of sequences Linear inequalities Linear sequences Line of best fit Loci Logarithms Lowest common multiple Mean Mean from a frequency table Mean from grouped data Measuring angles Median Mental addition Mental multiplication Mental subtraction Midpoint Minutes and hours Mixed number fractions Mode Mode from a frequency table Multiples Multiplication law of indices Multiplying Multiplying algebraic expressions Multiplying algebraic fractions Multiplying decimals Multiplying fractions Multiplying negative numbers Multiplying surds Multiplying terms Multiplying vectors Mutually exclusive events Naming coordinates Negative numbers - adding Negative numbers - subtracting Normal distribution nth term rule Operations with surds Ordering decimals Ordering fractions Ordering negative numbers Order of operations Parallel lines Parallel vectors Parts of a circle Percentage change Percentage decrease Percentage increase Percentage of an amount Percentages Perimeter of a rectangle Perpendicular lines Pictograms Pie chart angles Pie charts Plans and elevations Polygons Polynomial division Positive integer powers Power of zero Powers Pressure Prime factors Prime numbers Prisms Probability Probability of a single event Probability of combined events Probability on a number line Product of factors Product of prime factors Product rule Properties of a triangle Properties of quadrilaterals Properties of shapes Pythagoras Quadratic inequalities Quadratic sequences Quotient rule Range Ratio as equations Ratio as fractions Rationalising the denominator Reading scales Rearranging equations Rearranging formula Reciprocals Recurrence relations Recurring decimals Reflection Related calculations Representing on a number line Reverse percentages Roots Roots of an equation Rotation Rounding to 1 decimal place Rounding to 2 decimal places Rounding to 3 decimal places Rounding to nearest 10 Rounding to nearest 100 Rounding to nearest multiple Rounding to nearest whole Rounding to significant figures Sample space diagram Scatter diagrams Sector area Sector of a circle Set notation Sharing in a ratio Significant figures Similar shapes Simplifying algebraic fractions Simplifying expressions Simplifying fractions Simplifying ratio Simplifying surds Simultaneous equations Sine rule Sketching quadratic graphs Sketching straight line graphs SOH CAH TOA Solving equations with powers Solving equations with roots Solving inequalities Solving linear equations Solving quadratic equations Solving simultaneous equations Speed distance time Square numbers Square root Standard deviation Standard form Stem and leaf diagrams Stratified sampling Sub sets Substitution Subtracting algebraic fractions Subtracting decimals Subtracting fractions Subtracting negative numbers Surface area of a cuboid Surface area of a cylinder Surface area of a prism Surface area of a sphere Table of values Tangent and radius Tangents Telling the time Temperature Term to term sequences Time Transformation of functions Translation Tree diagrams Trigonometry Turning points Two-way tables Unitary ratio Unit fractions Units of area Units of length Units of volume Using place value Using the quadratic formula Value of a decimal Value of a digit Vector notation Venn diagrams Vertical lines Vertically opposite angles Volume of a cone Volume of a cuboid Volume of a cylinder Volume of a frustrum Volume of a prism Volume of a pyramid Volume of a sphere Volume scale factor Writing expressions Writing formula Writing ratio Written addition Written division Written subtraction x-intercept y-intercept

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