Key Stage 4

Year 10

Intent

Year 10 develops the knowledge of trigonometry, more advanced algebraic skills and the use of tree diagrams to find the probability of events. It also brings the opportunity for some students to meet Matrices and Calculus for the first time with L2 further maths.

Learning Journey - Pathway 1

Powers and Standard Form

  • Powers (indices)
  • Rules for multiplying and dividing powers
  • Standard form

Counting, accuracy, powers and surds

  • Rational numbers, reciprocals, terminating and recurring decimals
  • Estimating powers and roots
  • Negative and fractional powers
  • Surds
  • Limits of accuracy
  • Problems involving limits of accuracy
  • Choices and outcomes

Quadratic equations

  • Plotting quadratic graphs 
  • Solving quadratic equations by:
    • Factorisation,
    • Using the formula,
    • Completing the square,
    • Method of intersection
  • The significant points of a quadratic curve
  • Solving one linear and one non-linear equation using graphs and algebraically
  • Quadratic inequalities

Graphs

  • Distance-time graphs
  • Velocity-time graphs
  • Estimating the area under a curve
  • Rates of change
  • Equation of a circle
  • Other graphs
  • Transformations of the graph y=fx 
  • Gradients

Algebraic Fractions and Functions

  • Algebraic fractions
  • Changing the subject of a formula
  • Functions
  • Composite functions
  • Iteration 
     

Properties of circles 

  • Circle theorems 
  • Cyclic quadrilaterals
  • Tangents and chords
  • Alternate segment theorem
  • Proof of Circle Theorems

Triangles

  • Further 2D problems
  • Further 3D problems
  • Trigonometric ratios of angles between 0° and 360°
  • Solving any triangle (Sine and Cosine rule)

Vector geometry

  • Properties of vectors
  • Vectors in geometry 
  • Proof of Vectors

Sampling and more complex diagrams

  • Collecting data
  • Frequency polygons
  • Cumulative frequency graphs
  • Box plots
  • Histograms

Variation 

  • Direct proportion
  • Inverse Proportion

Combined events 

  • Addition rules for outcomes of events
  • Combined events
  • Tree diagrams
  • Independent events
  • Conditional probability

Learning Journey - Pathway 2

Powers and standard form

  • Powers (indices)
  • Rules for multiplying and dividing powers
  • Standard form

Linear equations

  • Solving linear equations
  • Solving equations with brackets
  • Solving equations with the variable on both sides

Number and sequences

  • Patterns in number
  • Number sequences
  • Finding the nth term of a linear sequence
  • Special sequences
  • General rules from given patterns

Simultaneous equations and linear inequalities

  • Solve linear simultaneous equations 
  • Solve linear inequalities

Non linear graphs

  • Distance-time graphs
  • Plotting quadratic graphs
  • Solving quadratic equations by factorisation
  • The significant points on a quadratic curve
  • Cubic and reciprocal graphs

Volumes and surface area of prisms 

  • 3D shapes
  • Volume and surface area of a cuboid
  • Volume and surface area of a prism
  • Volume and surface area of cylinders

Constructions and Loci 

  • Constructing triangles
  • Bisectors
  • Defining a locus
  • Loci problems

Curved shapes and pyramids

  • Sectors
  • Pyramids
  • Cones
  • Spheres

Right-angled triangles

  • Pythagoras theorem
  • Calculating the length of a shorter side
  • Applying Pythagoras’ theorem in real life
  • Calculating the length of a shorter side
  • Calculating angles using trigonometry
  • Trigonometry without a calculator
  • Solving problems using trigonometry
  • Trigonometry and bearings
  • Trigonometry and isosceles triangles

Congruency and similarity

  • Congruent triangles
  • Similarity

Representation and interpretation

  • Sampling
  • Pie charts
  • Sampling
  • Pie charts
  • Scatter diagrams
  • Grouped data and averages

Percentages and compound measures

  • Equivalent percentages, fractions an decimals
  • Calculating a percentage of a quantity
  • Increasing and decreasing quantities by a percentage
  • Expressing one quantity as a percentage of another
  • Compound measures

Percentages and variation

  • Compound interest and repeated percentage change
  • Reverse percentage 
  • Direct proportion
  • Inverse proportion

 

Combined events

  • Combined events
  • Two-Way tables
  • Probability and Venn diagrams
  • Tree diagrams

Year 11

Intent

In year 11 we review and extend skills developed over the previous four years in the strands of number, algebra, geometry, statistics and ratio and proportion. Some concepts are extended to cover topics included in further maths. We focus on more complex problem solving throughout.

Learning Journey - Higher Path

  • Prime Factor Decomposition
  • Recurring Decimals
  • Fraction Operations
  • Upper and Lower Bounds
  • Surds
  • Expanding and Factorising 
  • Substitution 
  • Forming and Solving Equations  
  • Change the Subject 
  • Simultaneous Equations
  • Functions
  • Algebraic Fractions
  • Iteration 
  • Quadratics
  • Inequalities
  • Quadratic Sequences
  • Linear/Quadratic Graphs
  • Y=MX + C
  • Transformations 
  • Pythagoras 
  • Trigonometry 
  • Sine Rule 
  • Cosine Rule 
  • Area formula
  • Perimeter & Area
  • Volume & Surface Area
  • Angles with algebra and  in Polygons
  • Circles
  • Circle Theorems
  • Vectors
  •  Perimeter & Area
  • Volume & Surface Area
  • Angles with algebra and  in Polygons
  • Circles
  • Circle Theorems
  • Vectors
  • Averages  from tables 
  • Scatter Graph
  • Cumulative Frequency
  • Box Plots
  • Histograms 
  • Frequency Tree  
  • Venn Diagrams
  • Tree Diagrams
  • Conditional Probability
  • Ratio  
  • Percentages 
  • Interest
  • SDT inc graphs
  • Direct/Indirect Proportion 
  • Compound Units

Learning Journey - Foundation Path

  • Bank Statements 
  • Types of Number Problems, inc powers and standard form
  • Prime Factor Decomposition 
  • Error Intervals 
  • Fraction Operations 
  • FDP 
  • Estimation
  • Function Machines 
  • Expanding and Simplifying  
  • Factorising 
  • Substitution 
  • Forming and Solving  
  • Change the Subject 
  • Simultaneous Equations
  • Inequalities
  • Sequences
  • Nth Term
  • Drawing Linear and Quadratic Graphs
  • Transformations 
  • Pythagoras 
  • Trigonometry 
  • Bearings 
  • Plans and Elevations
  • Constructions
  • Perimeter & Area 
  • Volume & Surface Area
  • Angles
  • Circles
  • Averages  
  • Mean from table 
  • Scatter Graph 
  • Pie Chart 
  • Frequency Tree 
  • Sample Space Diagrams 
  • Venn Diagrams
  • Tree Diagrams
  • Ratio 
  • Percentages 
  • Interest  
  • Proportion  
  • (Best Buy / Recipe) 
  • Similar Shapes 
  • SDT
  • Distance Time Graphs

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