# Ages 11-16

###### Author and programmer: Ron Barrow

### 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 `x`² + b`x` + 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 - `n`th term in the form a`n` + 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 a`x`² + b`x` + 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

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

Vector Addition - adding and substracting multiples of 2D column vectors

#### 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 - `n`th term, sequences of the form a`n`² + b

Harder Quadratic Sequences - `n`th term in the form a`n`² + b`n` + c

Cubic Sequences - `n`th term in the form a`n`³ + b`n`² + c`n` + d