Calculus

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Differentiation from 1st Principles. ( 6 Questions)

Differentiation by Rule (Product, Quotient, Chain) (10 Questions)

Differentiation of Trigonometric Functions. (27 Questions ).

Implicit Differentiation. (11 Questions ).

Parametric Differentiation. (15 Questions ).

Differentiation of Inverse Trigonometric Functions. (21 Questions)

Differentiation of Exponential Trigonometric Functions. (24 Questions)

Differentiation of Logarithmic Functions. (30 Questions )

Differentiation Using Logarithmic Differentiation. (8 Questions )

Applications of Calculus

Find Equation of Tangent to Curve. (11 Questions).

Increasing/Decreasing Functions. (22 Questions).

General Points on Max/Min/Pts of Inflection

Max Point, Min Point, Point of Inflection. (28 Questions).

Asymptotes ( 9 Questions).

Rates of Change ( 9 Questions).

Related Rates of Change. (5 Questions)

Using Newton-Raphson to solve Cubic Equations. ( 3 Questions)

Induction

Proof By Induction. (Series) (9 Questions)

Proof By Induction. (Divisibility) (10 Questions)

Proof By Induction. (InEqualities) (6 Questions)

The Line Leaving Cert

General Notes on Line

Distance,Mid-Pt,Slope, Equation Line Formulae
Slopes of Parallel/Perpendicular Lines Formulae
Verify Pt. Belongs to Line.
Pt. Intersection and Graphing of Lines.
Transformations of Plane (Translation,Central Symmetry, Axial Symmetry. ( 7 Questions )

Division of Line in a given Ratio.. ( 7 Questions )

Centroid, Circumcentre, Orthocentre of a Traingle.. ( 8 Questions )

Perpendiculat Distance from Pt. To Line.. ( 12 Questions )

Angle Between Two Lines.. ( 9 Questions )

Concurrent Lines. ( 6 Questions )

Parametric Equation of a Line.. ( 6 Questions )

Linear Transformations and their Properties.( 4 Questions )

Statistics and Difference Equations

Mean. (Set of Numbers, Frequency Dist., Grouped Frequency Dist.) ( 9 Questions)

Weighted Mean. ( 4 Questions)

Standard Deviation. (Set of Numbers, Frequency Dist., Grouped Frequency Dist.) ( 5 Questions)

Algebraic Questions on the Mean and Standard Deviation. ( 10 Questions)

Difference Equations. ( 8 Questions)

Permutations. Combinations and Probability

Permutations. ( 20 Questions )

Combinations.( 16 Questions )

Probability. ( 8 Questions )

Probability (Addition Rule). ( 6 Questions )

Probability (Multiplication Rule). ( 23 Questions )

Sequences and Series

Sequence and Series Notes

Sequences (General Term) ( 6 Questions)

Series and Sigma Notation. ( 5 Questions)

Arithmetic Sequences and Series. ( 9 Questions)

Geometric Sequences and Series. ( 9 Questions)

Infinite Geometric Series. ( 20 Questions)

Series of Form 1. ( 6 Questions)

Limits of Sequences. ( 11 Questions)

Series of Form 2. ( 6 Questions )

Series of Powers of Natural Numbers. ( 13 Questions)

Vectors

Equality, Negative, Multiplication, Addition of Vectors. ( 3 Questions)

Representing Vectors with Single Letters.( 4 Questions)

Parallel and Non-Parallel Vectors. ( 3 Questions)

Perpendicular Unit Vectors. ( 7 Questions)

Modulus of Vectors. ( 10 Questions)

Dot Product of Vectors and their Properties. ( 11 Questions)

Related Perpendicular Vector and it's Property. ( 13

Integration

The Indefinite Integral. (12 Questions).

The Definite Integral. (10 Questions).

Integration by Substitution. (8 Questions).

Integrating Trigonometric Functions. (13 Questions).

Integrating Exponential Functions. (20 Questions).

Integrals leading to a Logarithmic Function. (15 Questions).

Integrals of Standard Formats.(3 Types) (47 Questions).

Area Under Curve by Integration. (25 Questions).

Volume of Revolution by Integration. (12 Questions).

Matrices

Addition, Subtraction of Matrices ( 2 Questions)

Multiplication of Matrices ( 2 Questions)

Inverse Matrices ( 19 Questions)

Diagonal Matrices( 6 Questions)

Binomial Theorem

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Factorials. ( 5 Questions)

Combinatorial Numbers. ( 5 Questions)

Binomial Theorem. ( 4 Questions)

Evaluating Sum/Diff. ( 3 Questions)

Unknown CoEfficient Index. ( 5 Questions)

Selecting Particular Terms. ( 11 Questions)

Complex Numbers

Addition, Subtraction, Multiplication of Complex Numbers ( 3 Questions)

Conjugate/Division of Complex Numbers ( 4 Questions)

Equality of Complex Numbers ( 5 Questions)

Argand Diagram and Modulus. ( 6 Questions)

Quadratic Equations with Complex Roots. ( 4 Questions)

Square Roots and Quadratic Equations with Complex Roots. ( 3 Questions)

Cubic Equations with Complex Roots. ( 4 Questions)

Polar CoOrdinates and Polar Form of a Complex Number. ( 13 Questions)

De Moivre's Theorem and Finding Powers of Complex Numbers. ( 11 Questions)

De Moivre's Theorem and Proving Trigonometric Identities. ( 3 Questions)

De Moivre's Theorem and Finding Roots of Complex Numbers. ( 6 Questions)

Algebra revision

Simplify Algebraic Expressions. ( 9 Questions)

Change Subject of Formula. ( 3 Questions )

Undetermined Coefficients. ( 3 Questions )

Simplification of Surds. ( 7 Questions )

Simultaneous Linear Equations. ( 5 Questions )

Solving Quadratic Equations. ( 7 Questions )

Modulus and Irrational Equations. ( 11 Questions )

Simultaneous Equations ( One Linear, One Quadratic). ( 4 Questions )

Sum/Product of Roots of Quadratic Equation. ( 8 Questions )

Factor Theorem. ( 6 Questions )

Solving Cubic Equations. ( 5 Questions )

Solving InEqualities. ( 10 Questions )

Roots of Quadratic Equations. ( 5 Questions)

InEquality Proofs. ( 9 Questions)

Indices. ( 7 Questions)

Exponential Equations. (6 Questions)

Recurrence Equations. (5 Questions)

Logarithms. ( 15 Questions )

The Circle

General Notes on Circle.

General Eqn. of Circle. ( 6 Questions)

Prove that a Locus is a Circle. ( 3 Questions)

Parametric Eqns. of Circle. ( 8 Questions)

Intersection of Line/Circle. ( 3 Questions)

Find Eqn. of Circle given 3 Pts. ( 3 Questions)

Find Eqn. of Circle given 2 Pts. ( 3 Questions)

Find Eqn. of Circle given Radius Length. ( 4 Questions)

Find Eqn. of Tangent to Circle at a given Pt. ( 8 Questions)

Find Eqn. of Tangent Parallel/Perp to a given Line. ( 9 Questions)

Find Eqn. of Circle with Axes as Tangents. ( 7 Questions)

Prove that Circles touch Internally/Externally. ( 4 Questions)

Find Eqn. of Circle given Chord Length. ( 10 Questions)

Leaving Cert Option Integration by parts

Integration By Parts Questions

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