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
Mathematics News
- Reading in Maths
Do you want to learn about mathematical mistakes? (22/02/2021) - UKMT Senior Challenges
UK Mathematical Trust Girl’s Mathematical Olympiad and Senior Mathematics Challenges (18/11/2019) - NFS and UKMT
Planning for further success in 2019-20 (24/09/2019)