## Interactive and engaging contents

### With interactive drag and drop technology, dynamic content, out-of-the-box interactions, Skoolmaths offers everything you need to teach mathematics, enthuse today’s students, and provide a strong foundation for other maths-related subjects.

## All Secondary maths topics covered on our site

YEAR 7

### All the KS3 maths topics available on our site will enable learners to develop ‘mathematical process’ skills, which include reasoning, analysis and evaluation.

### The year 7 maths topics we cover are listed below:

**Numbers**

- Place value and rounding
- Decimal place value
- Adding and subtracting whole number – a recap
- Adding and subtracting decimals
- Dealing with money
- Multiplication of whole numbers
- Long multiplications
- Multiplying with decimals
- Mental division of whole numbers
- Division of decimals
- Fractions
- Equivalent fractions
- Fractions of quantities
- Mixed numbers and improper fractions
- Negative numbers
- Adding and subtracting negative numbers
- Multiplying and dividing negative numbers

**Algebra**

- Using letters to represent numbers
- Simplifying equations
- Solving simple equations
- Number sequences
- Input, output and mapping diagrams
- Plotting graphs using co-ordinates

**Geometry and measures**

- Recognising parallel and perpendicular lines
- Calculating the sum of angles on a point, triangle and straight line
- Using the correct geometrical terms
- Geometrical problems using triangles and quadrilaterals
- Reflections, rotations and translations of 2D shapes
- Symmetry of a 2D shape
- Finding co-ordinates of points
- Using a ruler and protractor to draw accurate lines, angles and triangles, and construct 3D shapes
- Estimating and calculating problems involving measuring
- Converting metric units
- Estimating the size of acute, obtuse and reflex angles
- Learning the formula for calculating the area of a rectangle
- Surface area of cubes and cuboids

**Statistics**

- Collecting data from surveys and experiments
- Designing questionnaires to collect data
- Creating frequency tables
- Calculating statistics
- Finding the mode, median and mean
- Creating and interpreting graphs, pie charts and diagrams showing data, on paper and using ICT
- Writing a statistical report
- Understanding probability terms such as likely, unlikely, impossible, probably
- Estimating probability from a simple experiment
- Comparing probabilities

YEAR 8

### All the KS3 maths topics available on our site will enable learners to develop ‘mathematical process’ skills, which include reasoning, analysis and evaluation.

### The year 8 maths topics we cover are listed below:

#### Number

- Factors and prime numbers
- Prime factors
- Index notations
- Highest Common factor and lowest common multiples
- Squares and square roots
- Revision of the four rules – Whole numbers
- Revision of the four rules – Decimals
- Order of operations
- Problems in contexts
- Rounding
- Estimating
- Calculator logics – Bracket and memory keys
- Revision of operations with fractions
- Problems in context
- Converting fractions and percentages
- Finding percentages
- Increasing and decreasing quantities by a percentage
- Percentage increase and decrease
- Reverse percentage
- Working with money

#### Algebra

- Expanding single brackets
- Linear equations
- Common factors
- Expanding two brackets
- Substitution with simple formulae
- Substitution with complex equations
- Non-linear equations
- Changing the subject of a formula
- Coordinates
- Plotting points on straight lines
- Plotting graphs given their equations
- The equation of a straight line
- The equation of a line given two points

#### Ratio, proportion and rates of change

- Equivalent ratios
- Direct proportions
- Proportional divisions
- Linear conversions
- Inverse proportions

#### Geometry and measures

- Common 2-D shapes and 3-D shapes
- Isometric drawings
- Plans and elevations
- Nets and surface area of cubes and cuboids
- Nets of prisms and pyramids
- Pythagoras theorems
- Calculating the length of the hypotenuse
- Calculating the lengths of the other sides
- Problems in context
- Constructions and angles
- Parallel and intersecting lines
- 3-figure bearings
- Scale drawings
- Time – 24 hour clock
- Angle facts
- Angle properties of polygons
- Symmetry
- Quadrilaterals
- Introduction to circles
- Estimating the circumference of a circle
- Estimating the area of a circle
- Formulae for circumference and area
- Volume and surface area of a cylinder
- Estimating metric units of length, mass and capacity
- Conversion between metric units
- Estimating imperial units of length, mass and capacity
- Conversion between metric and imperial units
- Speed
- Calculating speed, distance and time
- Solving problems with mixed units
- Distance-time graphs
- Other compound measures
- Enlargement
- Similar shapes
- Line, area and volume ratios
- Maps and scale models

#### Probability

- Revision of basic probability of single event
- Outcome with two events
- Probability using listings
- Multiplicative law for independent event
- Conditional probability

#### Statistics

- Frequency tables – Discreet ungrouped data
- Mean, median, mode and range
- describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs

YEAR 9

### All the KS3 maths topics available on our site will enable learners to develop ‘mathematical process’ skills, which include reasoning, analysis and evaluation.

### The year 9 maths topics we cover are listed below:

#### Number

- Factors and prime numbers
- Prime factors
- Index notations
- Highest Common factor and lowest common multiples
- Squares and square roots
- Revision of the four rules – Whole numbers
- Revision of the four rules – Decimals
- Order of operations
- Problems in contexts
- Rounding
- Estimating
- Calculator logics – Bracket and memory keys
- Revision of operations with fractions
- Problems in context
- Converting fractions and percentages
- Finding percentages
- Increasing and decreasing quantities by a percentage
- Percentage increase and decrease
- Reverse percentage

#### Algebra

Pupils should be taught to:

- Expanding single brackets
- Linear equations
- Common factors
- Expanding two brackets

#### Ratio, proportion and rates of change

Pupils should be taught to:

- Equivalent ratios
- Direct proportions
- Proportional divisions
- Linear conversions
- Inverse proportions

#### Geometry and measures

- Common 2-D shapes and 3-D shapes
- Isometric drawings
- Plans and elevations
- Nets and surface area of cubes and cuboids
- Nets of prisms and pyramids
- Pythagoras theorems
- Calculating the length of the hypotenuse
- Calculating the lengths of the other sides
- Problems in context
- Constructions and angles

#### Probability

- Revision of basic probability of single event
- Outcome with two events
- Probability using listings

#### Statistics

- Frequency tables – Discreet ungrouped data
- Mean, median, mode and range
- describe simple mathematical relationships between 2 variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs

GCSE (1-9)

### The GCSE maths topics we cover are listed below:

#### Grade 1/2

- Addition and subtraction
- Multiplication and division
- Rounding
- Estimating
- Powers and roots
- Factors and multiples
- Fractions of a quantity
- Fraction, decimal and percentage
- Negative numbers
- Order of operation
- Area and perimeter
- Bar charts
- Pie charts
- Stem and leaf diagrams
- Frequency polygons
- Algebra – collecting like terms
- Averages

#### Grade 3

- Error intervals
- Addition and subtraction of fractions
- Multiplication of fractions
- Division of fractions
- Sharing between a ratio
- Proportions
- Percentage of an amount
- Percentage increase and decrease
- Percentage change
- Substitution
- Solving equations
- Solving equations with unknown on both sides
- Linear graphs
- Area and circumference of circles
- Transformations
- Area of compound shapes
- Probability
- Two-way tables

#### Grade 4

- Compound interest and depreciation
- Indices
- HCF and LCM
- Functional maths
- Inequalities
- Forming and solving equations
- Types of sequences
- Generating sequences
- Sequences – Nth term
- Expanding and factorising
- Pythagoras theorem
- Angle problems
- Angles in polygons
- Angles in parallel lines
- Surface area
- Volume of prisms
- Volume and surface area of a cylinder
- Construction and loci
- Bearings
- Calculating averages from frequency tables
- Probability
- Scatter diagrams

#### Grade 5

- Writing a Ratio as a Fraction or Linear Function
- Direct and Inverse Proportion
- Speed and density
- Reverse Percentages
- Standard form
- Changing the Subject of a Formula
- Expanding and Factorising Quadratics
- Solving equations
- Drawing quadratic graphs
- Drawing Other Graphs: Cubic/Reciprocal
- Simultaneous equations
- Solving Simultaneous Equations Graphically
- Midpoint of a Line Segment
- Gradient of a line
- Equation of a Line
- Arc lengths and sector area
- Volume and surface area of pyramids, spheres and cones
- Similar Shapes (Lengths)
- Trigonometry
- Exact trigonometric values
- Probability trees
- Venn diagrams
- Vectors

#### Grade 6

- Recurring Decimals to Fractions
- Fractional and Negative Indices
- The Product Rule for Counting
- Repeated Percentage Change
- Expanding Triple Brackets
- Parallel and Perpendicular Lines
- Length of a line segment
- Inequalities on Graphs
- Similar Shapes (Area and Volume)
- Enlarging with Negative Scale Factors
- Cumulative Frequency
- Circle theorem
- Box and whisker plot

#### Grade 7

- Direct and Inverse Proportion
- Surds
- Upper and lower bounds
- Quadratic formula
- Factorising Harder Quadratics
- Algebraic Fractions
- Rearranging Harder Formulae
- Harder Graphs: Trig/Exponential
- Inverse and Composite Functions
- Finding the area of any triangle
- Iteration
- Congruent Triangles
- The sine rule
- The cosine rule
- Venn Diagrams (“Given that” questions)
- 3D Pythagoras
- Histograms

#### Grade 8/9

- Quadratic Simultaneous Equations
- Transforming Graphs y=f(x)
- Proof
- Completing the Square
- The Nth Term of a Quadratic Sequence
- Quadratic Inequalities
- Velocity Time Graphs
- Proof of the Circle Theorems
- Perpendicular Lines and the equation of a tangent
- Vectors Proof Questions
- Probability Equation Questions

AS-LEVEL

## A-level mathematics is currently modular giving students a choice in the maths they study for their AS (1 year course) or A level (extending the AS). Modules are Core pure maths (C1-4), Statistics (S1, S2), Mechanics (M1, M2) and Decision (D1, D2).

### All AS maths students will do C1 and C2 and one of S1, M1 and D1

### For potential biology students, the strong recommendation is to choose the S1 option.

### For potential physics or engineering students, the strong recommendation is to choose M1.

### The topics we cover are listed below:

#### Core 1

- Indices and Surds
- Algebra and Functions 1
- Algebra and Functions 2
- Coordinate Geometry
- Sequences and series
- Differentiation and Integration 1
- Differentiation and Integration 2

#### Core 2

- Factor Theorem and Remainder Theorem
- The Binomial Expansion
- Sequences and Series
- Coordinate Geometry – Circles
- Logs
- Geometry – Sine Rule, Cosine Rule, Sectors, Arcs
- The Trapezium Rule
- Differentiation and Integration
- Trigonometry
- Trig Identities

#### Statistics 1

- Representing Data
- Correlation and Regression
- Probability
- Discrete Random Variables
- The normal distribution

#### Mechanics 1

- SUVAT
- Velocity Time Graphs
- Resolving Forces
- Dynamics – F=ma
- Dynamics – Plane
- Momentum
- Moments
- Vectors

A-LEVEL

## A-level mathematics is currently modular giving students a choice in the maths they study for their AS (1 year course) or A level (extending the AS). Modules are Core pure maths (C1-4), Statistics (S1, S2), Mechanics (M1, M2) and Decision (D1, D2).

### For a full A-level in maths students will have done C1-C4 and two of S1, D1, M1, S2, D2, M2

### Where there is a choice, potential biologists would be strongly recommended to choose S1 and S2. Physicists and engineers should choose M1 and M2.

### A-level maths candidates will know the graphs of e, ln, trig identities, trig differentiation, product, quotient and chain rule.

### If they have taken S2 then they will also know some other distributions, know what a random variable is and know about hypothesis testing in simple contexts.

### The topics we cover are listed below:

#### Core 1

- Indices and Surds
- Algebra and Functions 1
- Algebra and Functions 2
- Coordinate Geometry
- Sequences and series
- Differentiation and Integration 1
- Differentiation and Integration 2

#### Core 2

- Factor Theorem and Remainder Theorem
- The Binomial Expansion
- Sequences and Series
- Coordinate Geometry – Circles
- Logs
- Geometry – Sine Rule, Cosine Rule, Sectors, Arcs
- The Trapezium Rule
- Differentiation and Integration
- Trigonometry
- Trig Identities

#### Core 3

- Functions
- Logs
- Numerical methods
- Trigonometry
- Differentiation

#### Core 4

- Partial Fractions and The Binomial Expansion
- Differentiation
- Integration
- Parametric Equations
- Differential equations
- Vectors

#### Statistics 1

- Representing Data
- Correlation and Regression
- Probability
- Discrete Random Variables
- The normal distribution

#### Mechanics 1

- SUVAT
- Velocity Time Graphs
- Resolving Forces
- Dynamics – F=ma
- Dynamics – Plane
- Momentum
- Moments
- Vectors

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