# Ages 11-16

### UK KS3, KS4, GCSE - US Grades 6 - 10

#### Number, Algebra and Graphs

Positive and Negative Numbers - getting familiar with basic arithmetic
Standard Index Form (Scientific Notation) - adding, subtracting, multiplying, dividing, simplifying
Fraction arithmetic - adding, subtracting, multiplying, dividing, simplifying
Equations 1 - simple linear equations, 5 levels of difficulty
Equations 2 - harder linear equations with more levels of difficulty
Prime Numbers 1 - Eratosthenes' Sieve for primes less than 100
Prime Numbers 2 - Eratosthenes' Sieve for primes less than 400
Factors of numbers - factors of numbers up to 9000 updated!
Prime Factors, HCF, LCM - numbers as products of prime factors, HCF, LCM
Factorising Quadratics - expressions of the type x² + bx + c
Graph recognition - quadratic, cubic and reciprocal (rational) graphs
Inequalities and inequations - linear inequalities and inequations
Inequalities - regions - regions defined by linear inequalities
Simple linear sequences - nth term in the form an + b
Simultaneous (systems of) equations - graphs - intersecting graphs
Simultaneous (systems of) equations - algebra - elimination
Straight line graphs 1 - gradients, y-intercepts and equations
Straight line graphs 2 - two forms of the equation

#### Higher Number, Algebra and Graphs

Converting recurring decimals to fractions - calculator
Circles and Lines - points of intersection of circles and straight lines
Completing the square - quadratic graphs, vertex coordinates
Factorising Harder Quadratics - expressions of the type ax² + bx + c
Function Transformations - basic transformations, shifts and stretches
Trigonometric Transformations - transformations of sin, cos, tan

#### Shape, Space and Measure

The Pythagoras Rule (Pythagorean Theorem) - side-lengths in right-angled triangles
Simple Trigonometry - side-lengths and angles in right-angled triangles
Angle Rule 1 - vertically opposite angles
Angles and Parallel Lines - alternate, corresponding and adjacent angles
Angles and Triangles - angle sum, straight lines and exterior angles
Areas of Parallelograms - using base and height lengths
Areas of Triangles - using base and height lengths
Parts of Circles - naming the different parts of a circle
Circle Theorems 1 - cyclic quadrilaterals, angles in the same segment
Circle Theorems 2 - angle at the centre, angle in a semicircle
Circle Theorems 3 - the Alternate Segment Theorem
Circle Theorems 4 - tangent and radius, tangents from a point
Circles and Triangles - isosceles triangles in circles
Circles Theorems 5 - Intersecting Chords and Secants NEW!
Circles Theorems 7 - Intersecting Radii and Chords NEW!
Angles in Polygons - unfinished applet
Translations - translations, shifts and column vector notation
Rotations - varying the object, the angle and the centre
Reflections - varying the object and the reflection line
Enlargements (dilations) - varying the object, the scale factor, centre
Symmetry 1 - combining simple rotations and reflections
Symmetry 2 - squares - investigating symmetries of square shapes
Symmetry 3 - hexagons - symmetries of hexagonal shapes
Sectors, Arcs and Segments - arc lengths, areas of sectors and segments

#### Higher Shape, Space and Measure

Sine Rule (Law of Sines) - angles and lengths in triangles
Cosine Rule (Law of Cosines) and Triangle Areas - angles, lengths and areas

#### Probability and Data Handling

Probability tree diagrams 1 - choice of 2 colours with 2 selections
Probability tree diagrams 2 - choice of 2 colours with 3 selections
Probability tree diagrams 3 - choice of 3 colours with 2 selections
Combining Probabilities - 'and', 'or' etc using a pack of cards
Cumulative Frequency - diagrams, medians, quartiles and boxplots
Moving Averages - trends and time series, varying moving averages
Scatter Diagrams - drawing lines-of-best-fit and correlation

#### Higher Data Handling

Histograms - unequal interval widths and frequency density

#### Investigative Tools

Simple Quadratic Sequences - nth term, sequences of the form an² + b
Harder Quadratic Sequences - nth term in the form an² + bn + c
Cubic Sequences - nth term in the form an³ + bn² + cn + d