Project Maths | Leaving Certificate

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Statistics & Probability

Geometry & Trigonometry

Number

Algebra

Functions

Calculating the mean of a set of numbers

Investigating the effect on the mean of adding a constant

Investigating the effect on the mean of multiplying by a constant

Investigating the effect on the mean of adding a new data item

Understanding stem and leaf plots

Investigating the effect on a histogram of changing one data value

Investigating the effect on a histogram of changing the class interval

Investigating the mean and standard deviation of a dataset

Investigating correlation and a line of best fit

Investigating the effect of an outlier on a scatter plot

Understanding the language of probability and statistics

Probability Applet

Axioms, theorems and corollaries

Theorem 7 - The angle opposite the greater of two sides...

Theorem 8 - Two sides of a triangle together...

Theorem 11 - If three parallel lines cut off equal segments...

Theorem 12 - In a triangle if a line parallel to one side cuts...

Theorem 13 - If two triangles are similar, their sides...

Theorem 16 - For a triangle, base times height...

Theorem 17 - A diagonal of a parallelogram bisects...

Theorem 18 - The area of a parallelogram is...

Theorem 20 - Each tangent is perpendicular to the radius...

Theorem 21 - The perpendicular bisector of a chor...

Proofs (HL only)

Proof of Theorem 11 - If three parallel lines cut...

Proof of Theorem 12 - In a triangle if a line parallel to one side...

Proof of Theorem 13 - If two triangles are similar then...

Constructions

Construction 16 - Circumcentre and circumcircle of a given triangle...

Construction 17 - Incentre and incircle of a given triangle...

Construction 18 - Angle of 60° without...

Construction 19 - Tangent to a given circle...

Construction 20 - Parallelogram, given the length of the sides...

Construction 21 - Centroid of a triangle

Construction 22 - Orthocentre of a triangle

Reviewing constructions

Transformations

Reflection in a point

Reflection in axes

Translation

Enlargements

Coordinate geometry

Circle with centre (0,0)

Circle with centre (h,k)

Circle with centre (-g,-f)

Dartboard

Intersection of a line and a circle

Tangents to a circle

Circle with centre (-g,-f)

Trigonometry

f(x)=asin(bx)

f(x)=acos(bx)

f(x)=tan(x)

Comparing the functions sin(x) and cos(x)

Investigating the function f(x)=acos(bx)+csin(dx)

Investigating sin(x) and cos(x) along the unit circle

Is the function a sine or a cosine function?

Area of a triangle quiz

Circle quizes

Arithmetic sequences and series

Geometric sequences and series

The sum to infinity of a geometric sequence

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

The sum of the first n natural numbers

The sum to a geometric sequence

(1+x)ⁿ > 1 + nx

2ⁿ > n²

n! > 2n

3 as a factor of 4n - 1

The Argand Diagram and modulus of a complex number

Addition of complex numbers

Subtraction of complex numbers

The conjugate of a complex number

Multiplying a number by i

Multiplication of complex numbers

Division of complex numbers

The area of a trapezium

Estimating the area of a semi-circle using the trapezoidal rule

Finding the area of a circular pond and its surrounding path

Finding the area of a rectangular picture frame

Race-track problem

Investigating the rate of change of height as volume changes

Investigating √2 and √3

Relations without formulae

Changing the base of a logarithm

Logarithms

Understanding an ESB bill

Understanding exchange rates

Understanding value added tax (VAT)

Amortisation of a loan

Understanding the rules of indices

Net of a cube

Net of a cylinder

Net of a cone

Net of a pyramid

Net of an octahedron

Solving a linear and quadratic equation simultaneously

Understanding absolute-value functions

Absolute value - less than

Absolute value - greater than

Writing complex numbers in polar form

Proof of De Moivre's Theorem

De Moivre's Theorem

Proof of Sin(3x) and Cos(3x) formulae

Solving quadratic inequalities

Inequalities in context

Understanding polynomial functions

Finding the equation of a linear function

Finding the equation of a quadratic function

Scaling a quadratic function f (x) = ax² where a is a positive number

Scaling a quadratic function f (x) = ax² where a is positive or negative

Vertically shifting a quadratic function f (x) = x² + c

Scaling and vertically-shifting a quadratic function f (x) = a x² + c

Horizontally shifting a quadratic function f (x) = (x+h)²

Shifting and scaling a quadratic function f (x) = a (x+h)² + k

Different forms of the quadratic function

Different representations of quadratic functions

Scaling a cubic function f (x) = a x³

Vertically shifting a cubic function f (x) = x³ + c

Horizontally shifting a cubic function f (x) = (x + h)³

Introducing the factor theorem

Roots of a cubic function

Relating the graph of a cubic function to its algebra

Understanding exponential functions

Understanding logarithmic functions

Understanding the relationship between e^x and ln(x)

Derivative of a constant

Derivative of a linear function

Derivative of a quadratic function

Derivative of a cubic function

Integration and area 1

Integration and area 2

Integration and area 3

Integration and area 4

Average value 1

Average value 2

Average value 3